Polygon 2021 by MDC-Polygon

Editorial Note:

1780 West 49th Street, Hialeah, Florida 33012, USA

Polygon is MDC Hialeah's Academic Journal. It is a multi-disciplinary online publication whose purpose is to display the academic work produced by faculty and staff. We, the editorial committee of Polygon, are pleased to publish the 2021 Spring Issue Polygon which is the fourteenth consecutive issue of Polygon. It includes six regular research articles. We are pleased to present work from a diverse array of fields written by faculty from across the college. The editorial committee of Polygon is thankful to the Miami Dade College President Madeline Pumariega, Miami Dade College District Board of Trustees, Hialeah Campus President, Dr. Anthony Cruz, Dean ofFaculty Dr. Michelle Ploetz, Chairperson of Hialeah Campus Liberal Arts and Sciences, Dr. Caridad Castro, Chairperson of Hialeah Campus World Languages and Communication, Professor Liliana Cobas, Director of Hialeah Campus Administrative Services, Ms. Andrea M. Forero, Director of Hialeah Campus Network & Media Services, Mr. Juan Villegas, all staff and faculty of Hialeah Campus and Miami Dade College, in general, for their continued support and cooperation for the publication of Polygon. Sincerely, Editorial Board Members of Polygon: Dr. M. Shakil (Editor-in-Chief), Dr. Jaime Bestard (Editor) and Professor Victor Calderin (Editor). Advisory & Reviewer Committee of Polygon: Dr. Kelly Kennedy, Dr. Alex Gancedo, Prof. Loretta Blanchette, Prof. Rene Barientos, Dr. Melissa Lammey, Dr. Carlos Ruiz, Prof. Rodolfo Cruz, Dr. Victoria Castells, Dr. Mariana Vaillant Molina, Dr. Allison Thomas Johnson Patrons: Dr. Anthony Cruz, President, Hialeah Campus; Dr. Michelle Ploetz, Dean of Faculty; Dr. Caridad Castro, Chairperson of Liberal Arts and Sciences; Professor Liliana Cobas, Chairperson of World Languages and Communication; Professor Charles Williams, III, Chairperson of Business, Engineering & Technology; Dr. Nelson Magaña, Dean of Student Services; Mr. Alexander Hernandez, Director of Learning Resources; Ms. Youdaris Mira, Chairperson of Continuing Education; Ms. Andrea M. Forero, Director of Hialeah Campus Administrative Services; Mr. Juan Villegas, Director of Hialeah Campus Network & Media Services; Ms. Andrea Nicholson, Director of Admissions, Registration & Financial Aid; Ms. Tiffany Nicholson, Assistant Dean of Faculty and Student Services; Mr. Jacob Shilts, Director of Student Services. Miami Dade College District Board of Trustees: Chair (Trustee) Michael Bileca; Vice Chair (Trustee) Nicole Washington; Trustee Dr. Anay Abraham; Trustee Marcell Felipe; Trustee Roberto Alonso; Trustee Ismare Monreal; Miami Dade College President Madeline Pumariega; Miami Dade College Executive Vice President and Provost Dr. Malou C. Harrison.

ii CONTENTS

ARTICLES / AUTHOR(S)

PAGES

Most Evident Ionospheric Characteristics Related with the On-Going Solar Minimum - Dr. Eduardo Araujo-Pradere, Ernesto Suarez, Denisse de Armas, Leisy Alvarez-Tuero, Alexandra Gonzalez,and Jose Lopez

1 – 11

The Impacts of a Chemistry Mobile Web Application on Student Learning in an Introductory Chemistry Course - Dr. Davia T. Hudson-Holness

12 – 23

Introducing Nonlinear Dynamical Systems and Chaos Studies in MDC Undergraduate Programs. First Results. - Dr. Adolfo Mendez, Felipe Mairhofer, and Marcos Rivas

24 – 31

An Exploratory Statistical Data Analysis of Some Covid-19 Death Data - Dr. M. Shakil

32 – 41

A Statistical Analysis of Students’ Opinions Towards the Best Practices for Online Teaching and LearningApproaches of Instructions - Dr. M. Shakil, and Dr. Subhojit Majumdar

42 – 62

Narrative Memory: The Poetic Response to the Aporia Between Personal and Collective Memory in Ricoeur’sHermeneutics - Professor Kristofer C Arca

63 – 87

Previous Editions Link: https://issuu.com/mdc-polygon Disclaimer: The views and perspectives of the authors presented in their respective articles published in Polygon do not represent those of Miami Dade College. Mission of Miami Dade College As democracy’s college, Miami Dade College changes lives through accessible, high-quality teaching andlearning experiences. The College embraces its responsibility to serve as an economic, cultural and civic leader for the advancement of our diverse global community.

iii Solicitation of Articles for the 2022 Issue (15th Issue) of Polygon: The editorial committee would also like tocordially invite the MDC community to submit their articles for consideration for the 2022 Issue (15th Issue) ofPolygon. Guidelines for Submission POLYGON “Many Corners, Many Faces (POMM)” A premier professional refereed multi-disciplinary electronic journal of scholarly works, feature articles and paperson descriptions of Innovations at Work, higher education, and discipline related knowledge for the campus, collegeand service community to improve and increase information dissemination, published by MDC Hialeah Campus Liberal Arts and Sciences Department (LAS). Editorial Board: Dr. Mohammad Shakil (Mathematics) (Editor-in-Chief) Dr. Jaime Bestard (Mathematics) Prof. Victor Calderin (English) Manuscript Submission Guidelines: Welcome from the POLYGON Editorial Team: The Department of Liberal Arts and Sciences at the Miami Dade College–Hialeah Campus and the members of editorial Committee - Dr. Mohammad Shakil, Dr. Jaime Bestard, and Professor Victor Calderin – would like to welcome you and encourage your rigorous, engaging, and thoughtful submissions of scholarly works, feature articles and papers on descriptions of Innovations at Work, higher education, and discipline related knowledge for the campus, college and service community to improve and increaseinformation dissemination. We are pleased to have the opportunity to continue the publication of the POLYGON, which will be biannually during the Fall & Spring terms of each academic year. We look forward to hearing from you. General articles and research manuscripts: Potential authors are invited to submit papers for the next issues of the POLYGON. All manuscripts must be submitted electronically (via e-mail) to one of the editors at mshakil@mdc.edu, or jbestard@mdc.edu, or vcalderi@mdc.edu. This system will permit the new editors to keep thesubmission and review process as efficient as possible. Typing: Acceptable formats for electronic submission are MSWord, and PDF. All text, including title, headings, references, quotations, figure captions, and tables, must be typed, with 1 1/2 line spacing, and one-inch margins all around. Please employ a minimum font size of 11. Please see the attached template for the preparation of the manuscripts. Length: A manuscript, including all references, tables, and figures, should not exceed 7,800 words (or at most 20 pages). Submissions grossly exceeding this limit may not be accepted for review. Authors should keep tables and figures to a minimum and include them at the end of the text. Style: For writing and editorial style, authors must follow guidelines in the Publication Manual of the American Psychological Association (5th edition, 2001). The editors request that all text pages be numbered. You may also please refer to the attached template for the preparation of the manuscripts.

iv Abstract and keywords: All general and research manuscripts must include an abstract and a few keywords. Abstracts describing the essence of the manuscript must be 150 words or less. The keywords will be used by readersto search for your article after it is published. Book reviews: POLYGON accepts unsolicited reviews of current scholarly books on topics related to research, policy, or practice in higher education, Innovations at Work, and discipline related knowledge for the campus, college and service community to improve and increase information dissemination. Book reviews may be submittedto either themed or open-topic issues of the journal. Book review essays should not exceed 1,900 words. Please include, at the beginning of the text, city, state, publisher, and the year of the book’s publication. An abstract of 150words or less and keywords are required for book review essays. Notice to Authors of Joint Works (articles with more than one author). This journal uses a transfer of copyright agreement that requires just one author (the Corresponding Author) to sign on behalf of all authors. Please identify the Corresponding Author for your work when submitting your manuscript for review. The Corresponding Author will be responsible for the following: -

ensuring that all authors are identified on the copyright agreement, and notifying theeditorial office of any changes to the authorship. securing written permission (via email) from each co-author to sign the copyrightagreement on the coauthor’s behalf. warranting and indemnifying the journal owner and publisher on behalf of all coauthors.

Although such instances are very rare, you should be aware that in the event a co-author has included content in their portion of the article that infringes the copyright of another or is otherwise in violation of any other warrantylisted in the agreement, you will be the sole author indemnifying the publisher and the editor of the journal againstsuch violation. Please contact the editorial office if you have any questions or if you prefer to use a copyright agreement for all coauthors to sign.

Instructions for the Preparation of Manuscripts for the Polygon: (THE TITLE IS HERE) (12 pt, bold, 32 pt above) NAME IS HERE (11 pt 16 pt above, 32 pt below) ABSTRACT is here, not exceeding 160 words. It must contain main facts of the work. (11 pt) Key words and phrases (11 pt) Introduction (11 pt, 24 pt above, 12 pt below) Main Body of the Article Discussion Conclusion Acknowledgements REFERENCES (11 pt, 30 pt above, 12 pt below) [1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables. Dover, New York, 1970. [2] J. Galambos and I. Simonelli, Products of Random Variables – Applications to Problems of Physics and to Arithmetical Functions, CRC Press, Boca Raton / Atlanta, 2005.

[3] S. Momani, Non-perturbative analytical solutions of the space- and time-fractional Burgers equations. Chaos, Solitons & Fractals, 28(4) (2006), 930-937. [4] Z. Odibat, S. Momani, Application of variational iteration method to nonlinear differential equations of fractional order, Int. J. Nonlin. Sci. Numer. Simulat. 1(7) (2006), 15-27. (11 pt) Author’s Biographical Sketch (Optional): Dr. Y. Abu received his Master’s and Ph. D. Degrees in Mathematics from the University of Small Town, USA, in 1987, under the direction of Dr. M. Opor. Since 1989, he has been teaching at the Community College of Small Town, USA. His research interests lie in the Fractals, Solitons, Undergraduate Teaching of Mathematics, and Curriculum Development. (11 pt) Address: Department of Liberal Arts & Sciences (Mathematics Program), Community College of Small Town, P. O. Box 7777, Small Town, USA. E-mail: yabu@ccst. (11 pt)

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Most Evident Ionospheric Characteristics Related with theOn-going Solar Minimum *Eduardo Araujo-Pradere, Ph.D., Ernesto Suarez, Denisse de Armas, Leisy Alvarez-Tuero, Alexandra Gonzalez, and Jose Lopez Department of Math and Sciences Miami Dade College, Homestead Campus, Miami, FL *E-mail: earaujop@mdc.eduAbstract

In order to understand the full range of solar influence on earth system, it is necessary first to clarify the connecting mechanisms between solar wind (which is, essentially, the extension of thesolar corona into the solar system) and the atmosphere, which happens through the only charged layer therein: the ionosphere. As it is well known, the ionosphere behavior follows a diurnalcycle as well as a seasonal one, and the physical processes supporting these cycles are well understood. However, it is less comprehended the mechanisms behind the ionospheric cycle following the 11-year solar cycle. Our project is focused on an initial description of the ionospheric behavior under solar minimum conditions, and it is part of a broader project targeting a detailed comparison of the last two solar minima. For this project, we have identified,downloaded and analyzed data from five ionospheric stations distributed globally. In order to describe the average ionospheric behavior, we calculated a “mean day” by averaging the ionospheric parameters for each hour for the whole month. We then ran basic statistics to have an idea of the data variability around each mean and proceed to graph the mean days using the standard deviation as the error bar at each point. Our results show that although there is a clear descending solar activity, the ionospheric parameters remain fairly leveled, with only average trends in the South Hemisphere of -0.35% for foF2 and -0.745% for hmF2, and respectively - 0.130% and -3.49% for the North Hemisphere. These results could be explained by a consistent amount of ionospheric plasma being produced, but at lower heights during the descendant phasedof the solar cycle, a clear indication of a contracted atmosphere. Keywords: solar minimum, ionospheric response, ionospheric trends

7 Introduction Since the ionosphere is the direct product of the absorption of the solar energy in the upper atmosphere, it is expected to follow the solar behavior in some way. The solar cycle, shown in Figure 1, has been tracked for a long time, and today it is widely accepted that it follows an 11- year cycle. This figure presents the progression of the sunspot number (the original measure of thesolar cycle) since very early observations, including the well-known maunder Minimum, when there was almost no sunspot for a long period of time.

Figure 1: Solar Cycle Sunspot Number. Of special interest is the lowering trend of the solar activity, and how the earth system responds. Many studies have focused their attention on the ionospheric response to solar activity with emphasis on the most recent solar minima (see, for example, Araujo-Pradere et al., 2005,Emmert, et al., 2010, AraujoPradere et al., 2011). In this study, we target the most recent solar minimum, between solar cycles 24 and 25, which continues the trend to diminishing values. Notice in Figure 2, obtained from the National Oceanic and Atmospheric Administration’s Space Weather Prediction Center (NOAA’s SWPC), that not just the maxima values show a decreasing trend, the same is observed for the last three solar minima, con values that are not just lower, but flatter (less variability) and extending for longer periods of time. The specific period of study is enclosed by the black frame in Figure 2.

Figure 2: Solar Cycle Sunspot Number, last three solar minima. Period of study appears enclosed by the black frame. In our effort to understand the ionospheric response to the decreasing phase of cycle 24, the most recent trend conducing to the latest minimum, we have selected ionospheric data running from January 2014 (solar cycle 24 maximum) to late 2020 (solar minimum between cycles 24 and 25), encompassing the period of interest. Although a recent announcement from NOAA’s SWPC located the solar minimum between Solar Cycle 24 and 25 - the period when the sun is least active - in December 2019, we used data for all 2020.

Ionospheric Parameters This breve description of the ionospheric parameters of interest has been adapted from AraujoPradere et al., 2011. There are many parameters that describe the ionospheric structure, dynamics, and composition. We have focused our analysis on the critical frequency of the F region (foF2), directly obtained from the maximum concentration of the F region (NmF2), normally expressed as number of particles per cubic centimeter, and the height of this peak of concentration (in Km). Figure 3 shows

9 sketches of both parameters. NmF2, the maximum concentration of theF region, is a direct measure from an ionosonde. The ionosonde transmittersweeps the high frequency range,transmitting short pulses. These pulses are reflected at various layers of the ionosphere, at heights of 100–400 km. The maximum frequency reflected is known as the F region critical frequency (foF2). The relation between the plasma frequency foF2 and the electron density NmF2 at the F peak

hmF2

can be expressed as NmF2 = foF2/80.3 (for details see Budden, 1985), where NmF2 is expressed in electron/m3 and foF2 in Hertz. In order to cover different seasonal, longitudinal and latitudinal dependences, several stations were selected across the planet, including three stations in the north hemisphere and two in

NmF2 Figure 3: Graphical description of the parameters used in the study.

the south hemisphere, all localized in mid-to-midhigh geomagnetic latitudes so to avoid thecomplex dynamics of high- and low- geomagnetic latitudes. they are shown in Figure 4.

Figure 4: Ionospheric stations selected.

10 These stations are well- established, with a long history of high-qualitydata, and efficient methods to verified and preserve the measurements. This was an important factor considered in the identification of the stations for the study.

Method A massive amount of data corresponding to the descendant phase of the solar cycle 24 was identified, downloaded and quality checked. Ionospheric data was mainly obtained from the Global Ionosphere Radio Observatory (GIRO, http://giro.uml.edu). The quality assurance process was quite stringent, with all missing values flagged, substituted by interpolated values when possible (and flagged accordingly), with time stamp verified and corrected when needed, and with missing batch of data identified and downloaded from other sources (specifically from NOAA’s National Geophysical Data Center, NGDC, https://www.ngdc.noaa.gov/stp/iono/ ionohome.html). Once confident in the quality of the data, the method of “mean day” (first proposed by AraujoPradere, et al., 2005) was applied to the data. This method consists in the calculation of the monthly average for each hour, and the construction of an average day for the month. As a result,we were working with only twelve “mean days” per year, which makes the data handling a lot lighter. Next, a basic statistical analysis was applied to the data to obtain the average values, and the root mean square error (RMSE) to describe the dispersion around the mean. Data was plotted, and trends calculated. There were two main grouping of the data, first data was plotted for the whole period of interest and the rends determined, and second, the same month for all years considered were plotted together to observe the ionospheric trend from max to min solar activity. Finally, months with higher and lower dispersion were identified.

Results Given the significant output of our analysis, just a sample will be shown in this section. With this in mind, we selected two stations, Pt. Arguello, a north-hemisphere, mid-latitude station in the east coast of USA, and Hermanus, a south-hemisphere, mid-latitude station in the southern coast of the Western Cape province of South Africa. We will focus our discussion on the periods with the higher and lowest foF2 dispersion for each of the stations and the full foF2 data in order to remark our findings. The main results for the critical frequency foF2 measured in Pt. Arguello, a north-hemisphere, mid-latitude station in the east coast of USA, are shown in Figure 5. The same results are presented for

11 Hermanus in Figure 6. These figures are divided in three panels: panel (a) at the topright shows the “mean days” for the month with the higher dispersion, while panel (b), top left, presents the period with lower dispersion. The bottom panel (c) displays the whole set of dataand the trend calculated for the full descendant phase of solar activity. It is interesting to notice that the months of higher and lower dispersion occurs at the same time in both hemispheres, which indicates that there is no seasonal dependence underlying in these results. Although there is a significant difference between these two plots for both stations, it is observed that the lowest values consistently correspond to 2019/2020, the deepest part of the latest solar minimum. As expected, the highest dispersion of the data happens during daytime values (the higher values in each of the top plots), when there is a more direct solar control of the ionosphere, in contrast, nocturnal values are less dispersed because they are controlled mostly by transport and recombination processes). The bottom panels for both figures are slightly different. While the foF2 data for Hermanus shows no significant change in the variability and an almost non-existent trend (- 0.02%), the same plot for Pt. Arguello shows a significant attenuation of the variability of the data and a trend of negative 0.13%, an order of magnitude higher.

(a) Period with higher dispersion.

(b) Period with lower dispersion.

(a) Period with higher dispersion.

(b) Period with lower dispersion.

14 Table 1 presents the results from our trend analysis. It is quite clear that the ionospheric trend, although consistently negative, is much less significant that the solar trend during this descendantphase of the solar activity. Of interest is the difference between the trends for foF2 and for hmF2,and the differences between the hemispheres. While the ionosphere concentration remained roughly constant, with just a marginal decreasing trend, the trend of the altitude of the peak of concentration of the ionosphere (hmF2) to lowering values is consistently higher, with valuesone and even two orders of magnitude higher. In contrast, trend values for both parameters are more pronounced for foF2 for the South Hemisphere while trends for hmF2 are deeper for the North Hemisphere.

Station Canberra Hermanus

Data time frame from

foF2

hmF2

2016/05 2015/01

2020/08 2020/08

-0.050% -0.020%

-1.190% -0.300%

-0.35%

-0.745%

-0.130% -0.130% -0.130%

-3.660% -3.300% -3.500%

-0.130%

-3.49%

Average South Hemisphere Pt. Arguello Boulder Athens

Slope

2015/01 2015/01 2015/01

2020/08 2020/08 2020/08

Average North Hemisphere Conclusions

All stations selected for this study show a consistent decreasing of the ionosphere concentration and height. This trend corresponds with the solar activity descending phase, as expected. However, the concentration (foF2) trends are significantly smaller that height (hmF2) trends, which could be explained by a consistent amount of ionospheric plasma being produced, but at lower heights during the descendant phased of the solar cycle, a clear indication of a contracted atmosphere. There is also a hemispheric dependence yet to be explained.

Acknowledgements First, the authors are thankful to the reviewer for his valuable and constructive suggestions which considerably improved the presentation of the paper. This original research was supported, in part, by U.S. Department of Education grant award P031C160161 (STEM SPACE).

REFERENCES [1] Araujo-Pradere, E.A., T.J. Fuller-Rowell, M.V. Codrescu (2005), Characteristics of the ionospheric variability as a function of season, latitude, local time, and geomagnetic activity, Radio Sci., 40, RS5009, doi:10.1029/2004RS003179. [2] Araujo-Pradere, E.A., R. Redmon, M. Fedrizzi, R. Viereck, and T. J. Fuller-Rowell (2011), Some characteristics of the ionospheric behavior during solar cycle 23/24 minimum, Solar Phys., The Sun– Earth Connection near Solar Minimum, edited by M. M. Bisi, B. Emery, and B. J. Thompson, doi:10.1007/s11207-011-9728-3, Springer. [3] Budden, K. G. (19850 The Propagation of Radio Waves, Cambridge University Press, New York, 669 pp. [4] Emmert, J. T., J. L. Lean, and J. M. Picone (2010), Record-low thermospheric density during the 2008 solar minimum, Geophys. Res. Lett., 37, L12102, doi:10.1029/2010GL043671

The Impacts of a Chemistry Mobile Web Application on Student Learning in an Introductory Chemistry Course Davia T. Hudson-Holness, Ph.D. Department of Natural Sciences, Health and Wellness Miami Dade College, Wolfson Campus 300 N.E. 2nd Ave, Miami, FL 33132 Email: dholnes@mdc.edu and David Freer, M.S. School of Engineering and Technology Miami Dade College, Kendall Campus 11011 SW104 Street, Miami, FL 33176 Email: dfreer@mdc.edu

ABSTRACT The goal of this project was to gamify a portion of an Introductory Chemistry Course (CHM 1025) curriculum through the creation of a mobile web application. This application was used to determine the impacts on students’ learning; impacts such as engagement and ultimately long- term success in chemistry. Creation of the application was interdisciplinary, requiring collaboration between the Natural Sciences Department, the School of Engineering and Technology (ENTEC) and the Miami Gaming and Animation International Complex (MAGIC)at Miami Dade College (MDC). Creation of the mobile application was also aligned with the College’s Strategic Plan to increase innovation in teaching and learning. Comparisons of the mean scores for the assessments that the game targeted, showed no significant differencesbetween the control and the test group. However, comparisons of pass rates and retention rates showed that the test group was four percentage points higher than the control group. Key words and phrases: Gamification, Mobile Web Application, Introductory Chemistry

17 Introduction Gamification (game-based learning) is the use of game mechanics to make learning and instruction more fun (Kapp, 2012). Gamification can provide an additional resource for facultyto improve students’ performance in courses such as Introductory Chemistry by utilizing instructional technology to enhance the curriculum. Gamifying the curriculum has been reported as a means of engaging students’ competitive drive and applying it to improved learning. This can also create a space for students to motivate themselves with the long-term goal of building intrinsic motivation. Games if well-developed can provide rapid feedback, recognize achievement early and often, and even offer encouragement through failure all with the long- term goal of building intrinsic motivation. By developing this intrinsic motivation, it could allow for improved success in courses such as Introductory Chemistry and ultimately long-term success as students move through the additional sequences of chemistry courses. There are several factors present in students’ environment that influence the way this current generation of students learn. One such factor is technological changes; the phenomenal growth of the internet and mobile devices has caused students to spend significant amounts of time online either playing online games or on social media (Cheong et. al., 2013). Since these technological changes can alter the way students learn, it can also alter the way in which the subject matter is delivered. Researchers believe that gamification has the potential to improve instruction which can lead to improved engagement, intrinsic motivation, and potentially long- term academic success. Despite this belief however, there is still a lack of high-quality empirical evidence to support this claim. A study conducted by Cheong et. al. (2013) which investigated the use of gamification to motivate and enhance learning, showed improved learning and beneficial effects but concluded that further research was needed in this area. Literature also shows that games are most beneficial when specific content was targeted and the objectives precisely defined (Kapp, 2012). Introductory Chemistry provides the requisite foundation chemistry knowledge for students who intend to pursue degrees in Science, Technology and Engineering (STEM). A solid foundation in this course allows for success in subsequent chemistry and other STEM courses. Despite the implementation of various initiatives to obtain improved pass rates and increased student motivation and engagement in this course, the college wide pass rates for Introductory Chemistry have been stagnant and range from 55.5 % to 60.5% indicating that there is still room for improvement. Over the course of one year, observation of students’ performance on tests and exams led to the identification of “threshold concepts” which can act as barriers to student success if these concepts are not fully understood. The goal of this project was to gamify this portion of the curriculum to help students become more proficient with these

18 concepts byteaching it in a new and innovative way. In addition to helping students, this project was also aimed at providing faculty an opportunity to explore innovative ways to teach, to expand their capabilities and skills and allow them to match students’ needs with appropriate instructional strategies.

Methodology Approval for this study was granted by the Institutional Review Board at Miami Dade College.

Phase 1 – Development of the Application Creation of the gamified mobile application required a development team that had to blend art, software, and content (learning objectives and outcomes) into the finished product. The development team for this project was comprised of four groups; the pedagogy team, the organization team, the programming team, and the design team.

•

Pedagogy o A chemistry faculty member from the Natural Sciences Department was the sole member of the pedagogy team and was responsible for developing the content to be embedded into the game, implementation of the developed application in the classroom and evaluating the effectiveness of the application by analyzing student success in the Introductory Chemistry courses.

•

Organization o

A Title V Grant Team in the Natural Science Department - Accelerate, Retain, Complete with Opportunities and Support (ARCOS) assisted with the organizational aspects of the project. They were responsible for arranging the initial introductory meetings between the pedagogy, programming, and design teams. The ARCOS team also provided funding to ensure the success of the project.

•

Programming o Two students under the guidance of a faculty member from the Technology department at Miami Dade College’s Kendall Campus comprised the programming team. They were responsible for the coding that implemented the user interfacefeatures, communication requirements, scoring systems and

anything that required coding. The game was developed using Unity Studio (2018.3.0f2) for dual platforms; iOS and Android. The game was developed to promote competence by allowing the students to keep improving through multiple attempts following the self- determination theory of Deci and Ryan (2012). The game was comprised of ten levelsand it was also built with a leaderboard; this allowed for connection and relatednessas well as autonomy since students could select the level they wished to play. •

Design o Two students from the Miami Animation and Gaming International Complex (MAGIC) at Miami Dade College’s Wolfson Campus made up the design team. Theywere responsible for developing the appearance and the entertainment component of the application. The created Chemistry Mobile Application was named MDChem andcan be found on the Google Play Store or on the App Store. The key words “Learn Chemistry MDC” can be used to search for the game on the Google Play Store while “Chemistry Miami Dade” can be used to search on the App Store. Figures one and two show screenshots of the game.

Phase II – Testing the Usability of the Application The purpose of this phase was to test the application to identify any improvements that were needed prior to implementation in the classroom. Current STEM students at the Wolfson Campus of MDC were invited to participate in the study through announcements made in the classroom and during STEM events. Eighteen students were recruited for the study and an orientation was held for these students. All eighteen students agreed to participate in the study and signed informed consent forms. The students were given one week to play the game to completion and then provide feedback via focus groups. Two sets of focus groups were conducted, and the results were used to improve the game. Students who participated in the study were compensated for their effort with a $20 stipend.

Phase III – Testing the effectiveness of the application Two sections of Introductory Chemistry taught by the same professor were used to determine the

20 impact of gaming on student learning. Both classes were taught on Mondays, Wednesdays, and Fridays for fifty minutes. No efforts were made to control the students enrolling in each section. Through random selection, one section was chosen as the control group and the other section as the test group. Both groups were treated in the same manner (Table 1) except for a homework assignment that was presented via different mediums. The control group was given a traditional homework assignment while the test group used the game as their homework assignment. The traditional homework assignment had the same content as the game but was completed using paper and pencil. The homework assignment was a low stakes assessment which targeted the “threshold concepts” that were being barriers to student success. The mean scores for the assessments (threshold concepts) related to the contents of the game and the paper and pencil assignments were compared to determine the impacts of the game on learning. Qualitative analyses were also conducted via paper surveys.

Statistical Evaluation Comparisons of the mean scores were performed using JMP Statistical Analysis Software, version 13. A One-way Analysis of Variance (ANOVA) at 95% confidence was usedto perform a hypothesis test for the difference between the means. The null hypothesis, (H0: p = 0.05) stated that the means are equal. A comparison of the means for the “names and ions” assessments showed that the control group had a mean of 3.83 and the test group had a mean of 3.77 while the means obtained for the “formulas” assessments were 3.27 and 2.76 for the control and the test group respectively. The cumulative assessment showed means of 75.9 for the controlgroup and 74.9 for the test group. The Prob > F generated by the software is the p-value for the model; If the P-value was ≤ α, H0 was rejected and if the P-value > α, H0 would not be rejected. For all three assessments, the Prob > F was greater than 0.05 so the null hypothesis was not rejected.

Discussion At the time that these data points were collected and analyzed, 42 students were enrolledin each section of the control and the test groups. Since no efforts were made to correct for the students who were enrolled in each section, a comparison of the mean grade point average (GPA) was performed using a pooled t-test at 95% confidence. The control group had a mean GPA of 3.08 while the test group had a mean GPA of 3.23. The pooled t-test produced a p-value > α, resulting in a failure to reject the null hypothesis meaning there was no significantdifference in the mean GPAs of the two groups. Even though the aim of the game was to help students overcome the “threshold concept”of

21 writing chemical formulas, it also addressed other concepts that had to be known prior to writing chemical formulas. Some of the other concepts which were a part of the game included the names and symbols of elements, names and formulas of ions and their charges. Via a paper survey, the students who played the game were asked about the impacts of the various concepts on their learning. More than 80% of the students responded positively regarding their learning for each of these concepts. The portion of the game that targeted polyatomic ions received the lowest rating as students thought it could have been more challenging (Figure 3). In addition to the qualitative analysis conducted via the paper surveys, quantitative analysis was also done based on content area assessments administered in the classroom. Two low stakes content assessments were administered; one that targeted the names and symbols ofelements and ions and their charges and a second content assessment that targeted writing chemical formulas. A low stakes cumulative assessment was also administered that covered alltargeted topics. The mean scores showed that the control group had higher scores than the test group on all assessments. Pooled t-tests were conducted at 95% confidence which produced p- values > α, resulting in a failure to reject the null hypotheses meaning there was no significant difference in the mean scores of the groups (Figure 4). A comparison of the pass rates and retention rates for both groups was performed and it showed that the test group had rates whichwere four percentage points higher than the control group (Figure 5).

Conclusion Comparison of the mean scores between the control and the test group showed no significant difference between them. However, comparisons of pass rates and retention rates showed that the test group was four percentage points higher than the control group; 56% vs 52%and 95% vs 91% respectively. The distribution of final grades within the test group reflected an overall improvement in student performance within the class, with fewer students receiving failing grades compared to the control group. Since both groups were provided with a homework assignment that targeted the thresholdconcept and its underlying “scaffolding concepts”, this could have resulted in there being no differences in the mean scores for the groups. It can be inferred that having additional reinforcement outside of the classroom regardless of the medium will be beneficial to students’ learning. Overall, the gamification of this chemistry course improved both pass and retention rates and revealed that this approach may easily be combined with other interventions to further enhance student success. It should be noted that the sample size of the study was small so additional studies need to be conducted before a definitive conclusion can be made.

Acknowledgements First, the authors are thankful to the reviewer for his valuable and constructive suggestions which considerably improved the presentation of the paper. The authors wish to thank Miami Dade College’s President’s Innovation Fund and a U.S. Department of Education the Title V Grant (P031S150046) Accelerate, Retain, Complete with Opportunities and Support(ARCOS) for the financial support that they provided. The author would also like to thank the students who worked on developing the application; Jason Balladares, Earl Cameron, Jorge Sanchez, and Kevin Quinones. Jason Balladares and Earl Cameron were able to use the experiential knowledge from the creation of this application to secure lucrative jobs in the technology industry.

REFERENCES [1] Christopher Cheong, F. C. (2013). Quick Quiz: A Gamified Approach for Enhancing Learning.Pacific Asia Conference on Information Systems. [2] Daly, J. (2012, November). Where Does Gamification Fit in Higher Education? https://edtechmagazine.com [3] Deci, E. L., & Ryan, R. M. (2012). Self-determination theory. Handbook of theories of social psychology (p. 416–436) [4] Hand, B. (2016, December 28). Gamification Successes and Failures in Higher Education. www.gettingsmart.com [5] Kapp, K. M. (2012). The gamification of learning and instruction: game-based methods andstrategies for training and education. Wiley. [6] TED Talk. (n.d.). [video] https://www.ted.com/talks/jane_mcgonigal_gaming_can_make_a_better_world?utm_campaign= tedspread--b&utm_medium=referral&utm_source=tedcomshare [7] Toyama, K. (2015). The Looming Gamification of Higher Ed. The Chronicle of HigherEducation. [8] Valerie Emin-Martinez, M. N. (2013). Supporting Teachers in the Process of Adoption of Game Based Learning Pedagogy. European Conference on Game Based Learning, (pp. 156 - 162).

23 Author’s Biographical Sketch: Dr. Davia Hudson-Holness is currently a Professor in the Department of Natural Sciences, Health and Wellness at Miami Dade College’s Wolfson Campus. She received her Ph.D. in Chemistry from Florida International University and her B.Sc. in Pure and Applied Science from the University of the West Indies, Jamaica. Dr. Holness’primary areas of teaching since she joined Miami Dade College in 2010 are Introductory Chemistry and General Chemistry I. She was a 2018 recipient of the inaugural President’s Innovation Fund from Miami Dade College and the 2019 Peter Masiko Jr. Endowed Teaching Chair recipient. Dr. Holness has publications in the Journal of Forensic Sciences and the Journal of Forensic Research. Address: Department of Natural Sciences, Health and Wellness, Miami Dade College, WolfsonCampus, 300 N.E. 2nd Ave, Miami, FL 33132. Email: dholnes@mdc.edu Author’s Biographical Sketch: David Freer received his master’s degree in Decision and Information Science and bachelor’s degree in Economics from the University of Florida. Currently he is in his second year of the Doctor of Business Administration at Florida International University. He has been teaching full-time at Miami Dade College since 2017 and was an adjunct since 2008 teaching courses for the School of Engineering and Technology. From2003 through 2016, he taught in the Miami Dade County Public Schools. Address: School of Engineering and Technology, Miami Dade College, Kendall Campus, 11011SW104 Street, Miami, FL 33176. Email: dfreer@mdc.edu

Appendix Tables and Figures

Table 1: Comparison of Control and Test Group Description

Control Group

Test Group

Class length

50 minutes/3 times/week

Number of students

Number of Tests

Number of Quizzes

Number of Homework Assignments

Paper and Pencil

Game via the application

Type of Homework Assignment Final Cumulative Exam

Figure 1: Screenshot of Login Screen for the Application

Figure 2: Screenshot of Level 1 of the Application

Figure 3: Percentage of Students Responding Positively to the Topics Assessed by the Game

Figure 4: Comparison of Mean Scores of the Test and Control Groups for the Assessments which Content was targeted by the Game

Figure 5: Comparison of Pass Rates and Retention Rates

Introducing Nonlinear Dynamical Systems and Chaos Studies in MDC Undergraduate Programs. First Results. Adolfo Mendez, PhD(*); Felipe Mairhofer; Marcos Rivas Math and Natural Sciences Department, Miami Dade College-Padron Campus amendez4@mdc.edu, felipe.mairhofer001@mymdc.net, marcos.rivas001@mymdc.net (*) Corresponding author

Abstract The coexistence of order and disorder in Nature constitute an unparallel enigma for the world of science. Physics’ laws imply order, but Nature is complex and often shows chaotic behavior. In this sense, a few decades ago, the paradigm of chaos was introduced, and the interest in this fieldof research has risen quickly with applications not only in Physics but also in Engineering, Biology, Social, and Environmental sciences. Therefore, several attempts have been made to integrate the nonlinear dynamical systems and chaos theory into the undergraduate curriculum asan elective subject. We present the first results and our short-term proposals to encourage students of natural sciences and engineering to get familiar with Nonlinear Dynamical Systems applications. This paper summarizes the work presented in Florida Undergraduate Research Conference FURC2021, hosted virtually by Florida State University. Keywords: nonlinear dynamical systems, determinism, chaos.

28 Introduction In the past 20th century, there were three great revolutions in science that marked a turnin the vision of how Nature works. These three revolutions are comparable to the Copernican revolution between 16th and 17th centuries, and Maxwell and Darwin revolutions both in the 18th century. Two of the three great revolutions in the 20th century were the General Theory ofRelativity and Quantum Mechanics. General Theory of Relativity and Quantum Mechanics removed two pillar statements of Newtonian physics: the illusion of absolute space and time, as well as the dream of controllable measurement processes. The third revolution in the 20th century removed the Newton and Laplace idea of a deterministic world totally predictable: Chaos Theory. One of the most impressive facts about Chaos Theory is that it applies to practically all processes and phenomena in Nature: from the large-scale Universe to the atomicworld; from Physics to Biology; from Sociology to Stock Market. In this paper, we present the short-term proposals and activities carried out during two semesters to encourage students of natural sciences and engineering from Miami Dade College-Padron Campus to get familiar with Nonlinear Dynamical Systems applications. Also, the first applied research work carried out on the study of the ionosphere deterministic respond to the solar activity depending on solar cycle phase is showed. This paper summarizes the work presented in Florida Undergraduate Research Conference FURC2021, hosted by Florida State University.

Nonlinear Dynamical Systems and Chaos studies in undergraduate programs Since the paradigm of chaos was introduced (Lorenz, 1963), the interest in this field of research has risen rapidly due to its wide spectrum of application. The term chaos was introducedin math as a technical term to denote a particular property of deterministic processes: sensitive dependence on initial conditions. In 1975 the term chaos was coined to refer the surprising fact that disorder appears in deterministic systems which are highly ordered (Tien-Yien and Yorke, 1975). Although there are reports regarding on the introduction of chaos theory into the undergraduate curriculum (Rodgers 1992; Borcherds, 1995; Perc, 2006) it is not common to findany program including this subject. In this sense, a group of undergraduate students from Miami Dade College-Padron Campus, under the direction and supervision of one of the authors of this paper (Dr. Mendez), meet periodically to learn and discuss about this subject. For that, the so- called “Poincare Group for the Studies on Nonlinear Dynamical Systems” was created during theFall 2020 Term. Jules Henri Poincaré (1854-1912) was one of the most influential mathematicians and philosopher of science. His work on the stability of the Solar System was the starting point for the

29 development of Chaos Theory. In his research on the three gravitationally linked bodies problem, Poincaré became the first to describe a chaotic deterministic system. What Poincaré discovered was that a general solution to that problem is essentially impossible due to the properdynamics of such system, which is highly sensitivity to initial conditions. Poincaré became the first scientist to discover that we call today as chaotic system which laid the foundations of modern Chaos Theory. For that reason, although Chaos Theory is a relatively new discipline, Henri Poincare is considered the father of the discipline. Poincare’s research proved that the problem of determinism and the problem of predictability are distinct problems.

Results Let us to divide the main results in two sections: academic where a resume of the learning and familiarization activities is presented, and the research work properly with the first work applying in this subject.

Academic Activities Due to the novelty of the subject, as well as the scarcity of available bibliography, the non-credit course “Introductory Lectures to Nonlinear Dynamical Systems” was designed and taught during the Fall 2020 term at MDC-Padron Campus. With a duration of 200 hours, the course includes both theoretical and conceptual topics as well as the necessary training in the useof Math tools for detecting chaotic or deterministic behavior in time series representing temporalevolution of dynamical systems. A total of nine students were enrolled in this course. As part of the course, the booklet “Glossary of terms on Nonlinear Dynamics and Chaos Theory” (Mendez, 2020; in process of editing to be sent to publish) was written and used as one of the principal reference texts. This booklet includes a minimum not exhaustive but indispensable number of concepts and terms used in Chaos Theory as well as a general algorithmenclosing the main steps in the characterization of a chaotic dynamical system. The aim is to help undergraduate students to be familiar with the use of these very useful and powerful tools inthe study of processes that can be described as a dynamical system. Another important goal is the proposal to implement some lab practices. The main objective of these simple lab practices is to introduce the collecting and processing data of dynamical systems with a chaotic behavior. These lab practices are very easy to set up using thetools and devices in our Physics lab. These lab practices for detecting chaos are related to three of the main subjects covered in the Physics

30 courses (PHY2048 and PHY2049): mechanics, electricity, and magnetism. The labs under discussion and preparation are Chaotic Motion of a Double Pendulum, Magnetism Strange Attractor, and chaotic behavior of a very simple periodically driven RLC circuit.

Research Work The first applied research work carried out on the study of the ionosphere deterministic respond to the solar activity depending on solar cycle phase. The ionosphere is a region of the Earth’s upper atmosphere where the population of free electrons is enough to cause a sufficient strong ionization. It is located between about 50 km and 1000 km above the Earth’s surface. Thishigh ionization is caused by solar radiation. Depending on the ascending and descending phase of the solar cycle, we analyzed the dynamic response of the ionospheric critical frequency f0F2, the most important parameter characterizing the ionospheric free electron density profile, which is critical for to communicateat very large distances in navigations, positioning and surveillance systems, etc. The aim is to determine if the underlying responding process of the ionosphere to the solar cycle can be described as a deterministic chaotic process. The 2-dimensional state-space is reconstructed for the response of the f0F2 ionospheric parameter in different phases of the solar cycle, to determine the presence or not of strange attractors. Sunspot number was used as index of solar activity. The ionospheric data (f0F2 profiles, hourly data) is from the Ionosonde Station Juliusruh (Germany, 54.6 N 13.4 E) and was obtained from Space Weather Service/Australian Government/Bureau of Meteorology (https://www.sws.bom.gov.au/Space_Weather). The data for the solar cycles was obtained from the Space Weather Prediction Center, National Oceanic and Atmospheric Administration, NOAA (https://www.swpc.noaa.gov). The attractors were characterized for two different phases of the solar cycle: ascendingphase of cycle 22 and descending phase of cycle 23. The dimension of the attractor, DA, was the used parameter to characterize each attractor. Knowing that the electron density variation of the ionosphere depends critically on the Sun radiation, we selected the same season, winter. Table 1 summarize the used data and the obtainedvalue for the dimension of the attractors. We apply the time series analysis developed in the theory of non-linear dynamics systems. Assuming that a single time series contains information on the entire system it originates from, the dynamics of such system can be reconstructed in its state-space (Takens 1981). Figure 1 and 2 shows respectively the profile of the f0F2 fluctuations and the reconstructed state-space for the period Winter

31 1997-1998 of f0F2 ionospheric hourly data aswell as. The presence of an attractor region can be inferred from the state-space. In order to measure the strangeness of the attractors, the estimation of the correlation dimension DA is useful. DA is related to the scaling properties of spatial correlations between attractor points, and it is used to investigate how deterministic the process is. The correlation dimension DA is determined from the Grassberger-Procaccia algorithm (Grassberger and Procaccia 1983) via the correlation integral, which estimates the probability that two randomlyselected points from the attractor are closer than an arbitrary distance r. The results show a difference between the values of the dimension of the attractors DA, that is, different strangeness of the attractors. It is attractive for us, to find such a difference for the two f0F2 profiles corresponding to different phases of the solar cycles also with different rising and descending slopes. This fact can be an indicator of a natural phenomenon (fluctuations of the free electron density in the f0F2 ionospheric layer) with a sensitive dependence on the solar cycle stage, in this case, different ascending and descending phases of the solar cycles 22 and 23. This can be in consonance with many cited and controversial papers regarding the strong connection between the solar cycles’ factors and its influence in the Earth environment (example Friss-Christensen and Lassen, 1991). The dynamics underlying the time series associated with the variation of the ionospheric f0F2 layer studied in this work, can be characterized by a low dimensional chaotic process (dimension of order less than 3). It means a non-deterministic behavior with sensitive dependence on initial conditions. The obtained values indicate a relatively low degree of freedomsufficient to describe the dynamics of the system and consequently a relatively low minimum number of independent non-linear equations needed to specify the evolution of the f0F2. That means at least three non-linear equations are necessary to describe the process generating the fluctuations values in the electron density in the f0F2 profiles considered in this work.

Conclusion The creation of the “Poincare Group for the Studies on Nonlinear Dynamical Systems” inMiami Dade College-Padron Campus, was the result of the attempt to introduce the studies of chaotic behavior in time series describing natural phenomena in undergraduate programs. The course “Introductory Lectures to Nonlinear Dynamical Systems” has been fundamental for that purpose. As consequence, notable results have been obtained in the study of a particular dynamical system: the response of the ionosphere to different stage of the solar activity.Currently, the group is working in other subjects like stock markets

32 and solar burst with time finestructures. This work was done under the Project “Detecting Chaotic Behavior in NaturalPhenomena” of Miami Dade College-Padron Campus.

Acknowledgements The Poincare Group for the Studies on Nonlinear Dynamical Systems wants to thanks toMath and Natural Sciences Department of Miami Dade College-Padron Campus, the support at any time despite the uncommon working conditions due the Covid-19 pandemic. Also, we want to thanks to FURC Organizing Committee and the Florida State University for the opportunity topresent our results. The authors are thankful to the editor-in-Chief and Reviewer for their constructive and valuable suggestions, which considerably improved the presentation of the paper.

REFERENCES [1] P. H. Borcherds: The butterfly that stamped: a brief introduction to nonlinear dynamics and chaos. Physics Education 30 (1995), 372-381. [2] E. Friis-Christiansen, K. Lassen: Length of the Solar Cycle: An Indicator of Solar Activity Closely Associated with Climate, Science, 254 (1991), 698-700. [3] P. Grassberger, I. Procaccia: Characterization of strange attractors. Physical Review Letters 50 (1983), 346-349. [4] E. N., Lorenz: Deterministic nonperiodic flow. Journal of Atmospheric Science 20 (1963), 130- 41. [5] M. Perc: Introducing nonlinear time series analysis in undergraduate courses. Fizika A, 15 (2006), 91112. [6] G. J. Rodgers: From order into chaos. Physics Education 27 (1992), 14-17. [7] F. Takens: Detecting strange attractors in turbulence, Lectured Notes on Math, 898 (1981), 366- 381. [8] Tien-Yien Li and J. A. Yorke: Period three implies chaos. The American Mathematical Monthly 82 (1975), 985-992.

Appendix

Table 1. Used data and calculated dimension of the attractor, DA Solar cycle 22 23

Solar cycle Phase Ascending Descending

Slope 8.5 units 3.4 units

f0F2 Winter 1987-1988 Winter 2002-2003

DA 2.401 ± 0.199 1.842 ± 0.164

Figure 1. Profile of the f0F2 fluctuations (a) and the reconstructed state-space (t is the time delay) for the period Winter 1997-1998 of f0F2 ionospheric hourly data.

Figure 2. Reconstructed state-space (t is the time delay) of f0F2 ionospheric hourly data showed in figure 1.

An Exploratory Statistical Data Analysis of Some Covid-19 Death Data M. Shakil, Ph.D. Dept. of Math, Liberal Arts & Sciences Miami-Dade College, Hialeah Campus, Fl., USA, E-mail: mshakil@mdc.edu

Abstract As one of the many factors affecting the human being is the death due to the covid-19, the study of the daily death due to the covid-19 also becomes necessary which may be helpful in many problems related to the covid-19. The statistical analysis of the daily death data due to the covid-19 is therefore very crucial, and plays an important role in many studies relating to the covid-19. In this paper, we propose to conduct an exploratory data analysis of daily covid-19 death data recorded from January 24, 2020 to June 06, 2020, as reported by an international website “Worldometer”. It is hoped that our study may be helpful in predicting the probability or forecasting the frequency of occurrence of the daily covid-19 death during the current pandemic, and planning beforehand, and also in many problems related to covid-19 and other applied research. 2010 Mathematics Subject Classifications: 62C12, 62F03, 62N02, 62N03, 62-07 Keywords: Descriptive Statistic, Exploratory Data Analysis (EDA), Covid-19

35 Introduction The present crisis due the covid-19 pandemic is an issue of emerging international importance and significance. As we observe, the covid-19 pandemic has created a great crisis at this time and has affected all spheres of our life, such as economic, social, health, political, psychological, and environmental, among others. Whether it is health or economic or social or political or environmental, almost all countries of the world are facing these problems due to the covid-19 pandemic crisis. There appears to be complete chaos and disorder. Millions of people have become unemployed and poor, thus creating great health crisis, economic inequality and social injustice. It has therefore become very necessary that we must take some measures for our economic development to overcome poverty. We need to take measures for the protection of our environment to overcome health crisis. There is a great need of economic equality and social justice, the lack of which is also a major cause of our sufferings. Since the covid-19 pandemic crisis started, considerable research into various aspects of issues related to the covid-19 pandemic has been conducted by many authors and researchers. For example, recently, Bantan et al (2020) has studied the covid-19 cases in Pakistan using an exponentiated M family of continuous distributions. For M family of distributions, see Kumar et al (2017). The interested readers are also referred to Chen et al (2020), where the authors have studied the clinical characteristics of 145 patients with corona virus disease 2019 (COVID-19) in Taizhou, Zhejiang, China. The very fast spread of covid-19, resulting in a gradual increase in the daily death of human being, is an important issue and area of research. There is a rising trend of average daily death due to the covid-19 over recent months. Scientists, medical doctors, politicians, almost everyone, around the world are concerned about the covid-19 pandemic. There are many causes and effects of covid-19. One possible effect is the death due to the covid-19. As one of the many factors affecting the human being is the death due to the covid-19, the study of the daily death due to the covid-19 also becomes necessary which may be helpful in many problems related to the covid-19. The statistical analysis of the daily death data due to the covid-19 is therefore very crucial, and plays an important role in many studies relating to the covid19. Such studies may be helpful in predicting the probability or forecasting the frequency of occurrence of the daily death data due to the covid-19, and planning beforehand. As such, motivated by the importance of the study of the daily death data due to the covid-19, we conduct an exploratory data analysis (EDA) for the statistical analysis of some world daily covid-19 death data recorded from January 24, 2020 to June 06, 2020, as reported by an international website “Worldometer”. The organization of the paper is as follows: In Section 2, we discuss the methodology. The results and discussions are provided in Section 3. We provide concluding remarks in Section 4.

36 Methodology In this section, we will investigate the statistical analysis of the daily death data due to thecovid19. For this, we have considered some world daily covid-19 death data recorded from January 24, 2020 to June 06, 2020, as reported by an international website “Worldometer”. For the sake of completeness, these data are provided in Table 1 below.

Table I TABLE 1 Daily Deaths due to COVID-19 (SOURCE: https://www.worldometers.info/coronavirus/) Date Jun. 6 Jun. 5 Jun. 4 Jun. 3 Jun. 2 Jun. 1 May. 31 May. 30 May. 29 May. 28 May. 27 May. 26 May. 25 May. 24 May. 23 May. 22 May. 21 May. 20 May. 19 May. 18 May. 17 May. 16 May. 15 May. 14 May. 13 May. 12 May. 11 May. 10 May. 9 May. 8 May. 7 May. 6 May. 5 May. 4 May. 3 May. 2 May. 1

Daily Deaths 4,253 4,906 5,512 4,929 4,671 3,054 3,190 4,097 4,923 4,650 5,307 4,051 1,180 3,147 4,183 5,258 4,930 4,687 4,594 3,446 3,618 4,362 5,081 5,358 5,366 5,566 3,452 3,509 4,255 5,552 5,593 6,814 5,788 4,100 3,481 5,224 5,626

Date Apr. 30 Apr. 29 Apr. 28 Apr. 27 Apr. 26 Apr. 25 Apr. 24 Apr. 23 Apr. 22 Apr. 21 Apr. 20 Apr. 19 Apr. 18 Apr. 17 Apr. 16 Apr. 15 Apr. 14 Apr. 13 Apr. 12 Apr. 11 Apr. 10 Apr. 9 Apr. 8 Apr. 7 Apr. 6 Apr. 5 Apr. 4 Apr. 3 Apr. 2 Apr. 1 Mar. 31 Mar. 30 Mar. 29 Mar. 28 Mar. 27 Mar. 26 Mar. 25

Daily Death s 5,800 6,597 6,695 4,513 3,759 6,109 6,422 6,712 6,703 7,294 5,492 4,898 6,679 8,435 7,005 8,197 7,415 5,644 5,569 6,213 7,356 7,671 6,740 7,897 5,611 5,007 6,069 5,965 6,273 5,193 4,712 4,162 3,344 3,672 3,470 2,946 2,590

Date Mar. 24 Mar. 23 Mar. 22 Mar. 21 Mar. 20 Mar. 19 Mar. 18 Mar. 17 Mar. 16 Mar. 15 Mar. 14 Mar. 13 Mar. 12 Mar. 11 Mar. 10 Mar. 9 Mar. 8 Mar. 7 Mar. 6 Mar. 5 Mar. 4 Mar. 3 Mar. 1 Mar. 2 Feb. 29 Feb. 28 Feb. 27 Feb. 26 Feb. 25 Feb. 24 Feb. 23 Feb. 22 Feb. 21 Feb. 20 Feb. 19 Feb. 18 Feb. 17

Daily Deaths 2,486 1,932 1,638 1,644 1,380 1,094 983 820 648 691 414 447 353 330 274 197 228 105 106 102 83 85 73 67 54 65 58 37 64 81 158 100 113 121 117 136 98

Date Feb. 16 Feb. 15 Feb. 14 Feb. 13 Feb. 12 Feb. 11 Feb. 10 Feb. 9 Feb. 8 Feb. 7 Feb. 6 Feb. 5 Feb. 4 Feb. 3 Feb. 2 Feb. 1 Jan. 31 Jan. 30 Jan. 29 Jan. 28 Jan. 27 Jan. 26 Jan. 25 Jan. 24

Daily Deaths 106 143 143 122 146 97 108 97 89 86 73 73 66 64 58 45 46 43 38 26 26 24 15 16

38 The descriptive statistics of the daily covid-19 death data are computed in Table 2.

Table 2 (Descriptive Statistics) Statistic Sample Size Range Mean Mode Variance Std. Deviation Coef. Of Variation Std. Error Skewness Excess Kurtosis

Value

135 8420 2975.4 73 7.1280E+6 2669.8 0.89731 229.78 0.20633 -1.4524

Percentile

Min 5% 10% 25% (Q1) 50% (Median) 75% (Q3) 90% 95% Max

Value

15 37.8 61.6 106 3344 5358 6685.4 7306.4 8435

Using the software Statdisk and MiniTab, we have tested the normality of the daily covid- 19 death data by Ryan-Joiner Test (Similar to Shapiro-Wilk Test), along with drawing a histogram of the data, which are given in Figure 1 (a, b, c) and Table 3 below.

Figure 1 (a): Histogram

Figure 1 (b): Normality Assessment

Figure 1 (c): Histogram and Normality Assessment

Table 3 (Ryan-Joiner Test of Normality Assessment) Ryan-Joiner Test (Similar to Shapiro-Wilk Test) Test statistic, Rp: 0.9321 Critical value for 0.05 significance level: 0.9891 Critical value for 0.01 significance level: 0.9848 Reject normality with a 0.05 significance level. Reject normality with a 0.01 significance level. Possible Outliers Number of data values below Q1 by more than 1.5 IQR: 0 Number of data values above Q3 by more than 1.5 IQR: 0 From Figure 1 (a, c) of histogram and Table 3 of the Ryan-Joiner Test of Normality Assessment of the daily covid-19 death data, it is obvious that the shape of the precipitation data is skewed to the right. This is also confirmed from the skewness of the precipitation data as computed in Table 2. Since fitting of a probability distribution to the daily covid-19 death data may be helpful in predicting the probability or forecasting the frequency of occurrence of the daily covid-19 death, this suggests that y, the daily covid-19 death data, could possibly be modeled by some skewed distributions. As such the students their more advanced statistics courses in future could tested the fitting of the generalized extreme value, Gumbel minimum, log-gamma, log-logistic and Weibull distributions based on their goodness of fit to the daily covid-19 death data as given in Table 1. For this, they could use several software such as the Easyfit software for estimating the parameters of these distributions and the goodness of fit (GOF) tests, namely, Kolmogorov-Smirnov, Anderson-Darling, and Chi-Squared tests for goodness-of-fit. For the parameters estimated as such, the generalized extreme value, Gumbel minimum, log-gamma, log-logistic and Weibull distributions respectively could be superimposedon the histogram of the daily covid-19 death data. For these distributions, we could also plot the cumulative distribution function, survival function, hazard function and P-P plot respectively.

Results and Discussions The descriptive statistics of the daily covid-19 death data (Table 1) are provided in Table 2 above. From Table 3 of Ryan-Joiner Test of Normality Assessment and Figure 1 (histogram) ofthe daily covid19 death data, it is obvious that the shape of the daily covid-19 death data is skewed to the right. This is also confirmed from the skewness of the daily covid-19 death data ascomputed in Table 3.

41 Concluding Remarks In many research problems of the covid-19, fitting of a probability distribution to the daily death data due to the covid-19 may be helpful in predicting the probability or forecasting the frequency of occurrence of the daily death data due to the covid-19, and planning beforehand. Motivated by the importance of the study of the daily death data due to the covid-19,we develop a lesson plan where the students will conduct their research on a statistical analysis of some world daily covid-19 death data recorded from January 24, 2020 to June 06, 2020, as reported by an international website “Worldometer”. By transforming the considered data in the paper appropriately, the students in their more advanced statistics courses in future could also investigate the applicability of the generalized extreme value, Gumbel minimum, log-gamma, log-logistic and Weibull distributions and test their best fit to these data based on the well-knowngoodness of fit (GOF) tests, namely, Kolmogorov-Smirnov, Anderson-Darling, and Chi-Squaredtests. Moreover, it is hoped that this study will be helpful in many problems of research related tothe covid-19.

Acknowledgments First, the author is thankful to the reviewer for his valuable and constructive suggestionswhich considerably improved the presentation of the paper. Further, the author is thankful to theEditorial Board of Miami Dade College Hialeah Campus Electronic Journal, Polygon, for accepting this paper for its publication in their 2021 issue. The author would like to thank the Earth Ethics Institute (EEI) of Miami Dade College for providing him an opportunity to attend the online EEI1026-1 workshop on “The Earth Charter at 20”, through Blackboard Collaborate Ultra, where this research was conducted. The author would also like to express his thanks to Miami Dade College for providing him an opportunity to serve as a mathematics faculty in thecollege at its Hialeah Campus, without which it was impossible to conduct my research and complete this paper.

REFERENCES [1] Bantan, R.A.R.; Chesneau, C.; Jamal, F.; Elgarhy, M. On the Analysis of New COVID-19Cases in Pakistan Using an Exponentiated Version of the M Family of Distributions. Mathematics 2020, 8, 953. [2] Chen, Q., Zheng, Z., Zhang, C. et al. Clinical characteristics of 145 patients with coronavirus disease 2019 (COVID-19) in Taizhou, Zhejiang, China. Infection (2020). https://doi.org/10.1007/s15010-02001432-5

42 [3] Kumar, D., Singh, U., Singh, S.K., and Mukherjee, S. The new probability distribution: Anaspect to a Life time distribution. Math. Sci. Lett. 2017, 6, 35–42. [4] https://www.worldometers.info/coronavirus

A Statistical Analysis of Students’ Opinions towards the Best Practices for Online Teaching and Learning Approaches of Instructions *M. Shakil, Ph.D., and **Subhojit Majumdar, Ph.D. *Department of Mathematics **Department of Chemistry Liberal Arts and Sciences, Miami Dade CollegeHialeah Campus, FL 33012, USA Emails: *mshakil@mdc.edu; **smajumda@mdc.edu

Abstract Classroom Assessment Techniques are designed to help teachers measure the effectiveness of their teaching by finding out what students are learning in the classroom and how well they are learning it. In recent years, there has been a great emphasis on “Remote Online Teaching and Learning Approaches of Instructions” in various disciplines. This paper deals with “A Statistical Analysis of Students’ Opinions towards the Best Practices for OnlineTeaching and Learning Approaches of Instructions through Blackboard and Blackboard Collaborate Ultra.” Keywords: Blackboard, Classroom assessment techniques, Best Practices for Online Teaching and Learning.

44 Introduction In recent years, there has been a great emphasis on “Remote Online Teaching and Learning Approaches of Instructions” using different learning management systems. For example, Miami-Dade College has been using, for some years, the learning management system (LMS) called “Blackboard”, for its remote online teaching and learning approaches of instructions. Recently, for its remote online and blended instructions, the college has also integrated “Blackboard Collaborate Ultra”, which has many features of delivering lectures remotely and is being used by the college faculty for remote online lectures and instructions. In addition to “Blackboard Collaborate Ultra”, the learning management system, “Blackboard”, hasmany other tools and features which are being used to deliver high quality online and blended instructions and as a means of assessment to evaluate student performance in all courses taught by Miami-Dade College faculty. As pointed out by Krutt (2008), “online instruction is defined asan educational process in which Internet technology is used to facilitate a student’s ability to access and interact with course content and activities, and to communicate and interact with the instructor and other students. Communication can take place asynchronously (not in real time, such as discussion boards, blogs, journals, etc.) or synchronously (in real time, such as online chats).” It appears from the literature that the education is imparted through distance education orlong-distance learning to the students when they are not physically present at a school. Furthermore, it has been observed that some of the recent developments in online or distance education are usually involving correspondence courses and either hybrid, blended or 100% distance learning, including massive open online courses (MOOCs), offering large-scale interactive participation and open access through the World Wide Web (WWW) or other network technologies. In literature, some other terms used for distance education are distributed learning, e-learning, online learning, etc. According to Krutt (2008), “online instruction is defined as an educational process in which Internet technology is used to facilitate a student’s ability to access and interact with course content and activities, and to communicate and interact with the instructor and other students. Communication can take place asynchronously (not in realtime, such as discussion boards, blogs, journals, etc.) or synchronously (in real time, such as online chats).” The interested readers are also referred to Keengwe and Kidd (2010) and Ko and Rossen (2017), among others. According to Merriam-Webster Dictionary (2019), “Pedagogy is defined as the art,science, or profession of teaching; especially: education.” Furthermore, as pointed out by Krutt (2008), “Pedagogy is defined as the methods, strategies, and underlying epistemology of an approach to teaching. An instructor’s skills, training An instructor’s skills, training, and commitment are critical to the implementation of an effective online pedagogy.”

45 Since, in recent years, there has been a great emphasis on “Remote Online Teaching and Learning Approaches of Instructions”, it is evident from the above theories that online learning and teaching approaches of instructions in higher education are student-centered, and, at the same time, focus on cooperative learning. For details on student-centered and cooperative learning approaches of instructions, the interested readers are referred to Slavin (1995), Timpson and Bendel-Simso (2003), Johnson et al. (2008), and Eggen and Kauchak (2010), among others. As stated above, the effects of online learning and teaching approaches of instructions in higher education on students’ learning have been studied and analyzed by many researchers. As such, motivated by the importance of the online learning and teaching approaches of instructions in higher education, in this paper we have conducted a survey on students’ opinions towards the best practices for online teaching and learning approaches of instructions in some mathematics and chemistry classes during Fall term 2020, and data has been analyzed statistically. The organization of the paper is as follows: In section 2, we have described the problems for the study and the methodology used. Section 3 contains the analysis and discussions of results. Some concluding remarks are given in Section 4.

Description of The Problems Used for The Study and The Methodology Education is a purposeful activity. Various disciplines taught at Miami Dade College have their own identity, importance and educational values. Besides Utilitarian, Disciplinary, andCultural values and aims of the teaching of these disciplines, another important objective is to develop in our students the quantitative analytic, critical thinking, communication and technological skills to evaluate and process numerical data, which belong to the followingGeneral Education Learning Outcomes as defined by the Miami Dade College: •

Communicate effectively using listening, speaking, reading, and writing skills.

•

Use quantitative analytical skills to evaluate and process numerical data.

•

Solve problems using critical and creative thinking and scientific reasoning.

•

Formulate strategies to locate, evaluate, and apply information.

•

Use computer and emerging technologies effectively.

Besides student success, our concern is also “how to incorporate the general education (learning) outcomes into a course.” In order to achieve these goals, it is understood that all the instructors at Miami

46 Dade College have been incorporating the various general education learning outcomes into their classes, in one way or another. As stated above, Miami-Dade College has been using, for some years, the learning management system (LMS) called “Blackboard”, for its remote online teaching and learning approaches of instructions. Recently, for its remote online and blended instructions, the college has also integrated “Blackboard Collaborate Ultra”, which has many features of delivering lectures remotely and is being used bythe college faculty for remote online lectures and instructions. In addition to “Blackboard Collaborate Ultra”, the learning management system, “Blackboard”, has many other tools and features which are being used to deliver high quality online and blended instructions and as a means of assessment to evaluate student performance in all courses taught by Miami-Dade College faculty. As such, , in view of the importance of the above-stated general education (learning) outcomes, and in order to achieve these goals, and at the same time motivated by the importance of the online learning and teaching approaches of instructions in higher education, in this paper we have conducted a survey on students’ opinions towards the best practices for onlineteaching and learning approaches of instructions in some mathematics and chemistry classes during the Fall Term 2020, and data has been analyzed statistically. These survey questions weresame for each class, and were posted online in the Blackboard Course Learning Management System, as described below. Question 1: Which of the following Online Teaching and Learning Approaches throughBlackboard Collaborate Ultra did you like most? A. Sharing Whiteboard (Solving Problems, etc.) B. Sharing Application / Screen (Textbook Video and Resource Library(Multimedia Library), Videos, YouTube, etc.) C. Sharing Files (Uploaded Lectures, Image, PowerPoint, or PDF Files, etc.) D. Tutoring through Blackboard Collaborate Ultra E. All of the above F. None of the above

Question 2: Which of the following Online Teaching and Learning Approaches throughBlackboard Collaborate Ultra did you find complicated? A. B. C. D.

Tutoring through Blackboard Collaborate Ultra None of the above All of the above Sharing Application / Screen (Textbook Video and Resource Library(Multimedia Library), Videos, YouTube, etc.) E. Sharing Whiteboard (Solving Problems, etc.) F. Sharing Files (Uploaded Lectures, Image, PowerPoint, or PDF Files, etc.)

Question 3: Which of the following Online Teaching and Learning Approaches throughBlackboard Collaborate Ultra did you find user friendly? A. B. C. D. E.

All of the above Tutoring through Blackboard Collaborate Ultra None of the above Sharing Whiteboard (Solving Problems, etc.) Sharing Application / Screen (Textbook Video and Resource Library(Multimedia Library), Videos, YouTube, etc.) F. Sharing Files (Uploaded Lectures, Image, PowerPoint, or PDF Files, etc.)

Question 4: In addition to the above, which of the following Online Teaching and LearningApproaches through Blackboard did you find most helpful in your field of studies? A. B. C. D. E. F. G. H. I.

Using Blackboard Grade Roster (For Early Alerts, etc.) Using Blackboard Attendance Roster (For Early Alerts, etc.) Using Blackboard Home Page (Announcements, etc.) Using Blackboard MDC Library (Learning Resource, Library, etc.) Using Blackboard Content (Instructor’s Uploaded Course Tests, Files, PowerPoint, PDF Files, Videos, etc.) Using Blackboard Resources (Instructor’s Uploaded Course Files, PowerPoint, PDF Files,Videos, etc.) Using Blackboard technology (e.g., Blackboard E-mail, Meeting Instructor through Blackboard Collaborate Ultra, etc.) All of the above None of the above

Question 5: Did you find the above Online Teaching and Learning Approaches through Blackboard and Blackboard Collaborate Ultra helpful in your field of studies? A. Yes B. No Question 6: Choose one of the following rating scales for the above Online Teaching and Learning Approaches through Blackboard and Blackboard Collaborate Ultra. A. B. C. D.

Excellent Good Average None of the above

48 The students’ responses on the above six survey questions and data analysis are provided in Section 3 below.

DISCUSSIONS OF RESULTS As pointed above, during the Fall Term 2020, we conducted a survey on students’ opinions towards the best practices for online teaching and learning approaches of instructions in some mathematics and chemistry classes. The students were asked to complete the online survey questions, as stated in Section 2 above, about their opinions towards the best practices for online teaching and learning approaches of instructions. A total of 240 students combined from both mathematics and chemistry 11 classes participated in the survey and completed it online in the Blackboard Course Management within the specified time without any difficulty. The students’ responses on the above six survey questions and data analysis are provided in Figures 1-3 and Tables 1-7 below. The “TWO-WAY ANOVA: STUDENTS’ RESPONSE versus QUESTIONS (# 1, 2, 3), QUESTION (# 4), and QUESTION (#5), including INTERACTION PLOTS (DATA MEANS)” are also provided; see Tables 8, 9, and 10 respectively, and Figures 4, 5, and 6 respectively. These tables and figures are self-explanatory. One can easily draw inferences from the statistical analysis of students’ opinions towards the best practices for online teaching and learning approaches of instructions implemented in some mathematics and chemistry courses during Fall 2020 Term. From the interaction plots as provided below (Figures 4, 5, and 6), one can also observe some interaction between different factors.

TABLE 1 STUDENTS’ RESPONSE versus QUESTIONS (# 1, 2, 3)

QUESTIONS

1. Which of the following Online Teaching and Learning Approaches through Blackboard Collaborate Ultra did you like most? 2. Which of the following Online Teaching and Learning Approaches through Blackboard Collaborate Ultra did you find complicated? 3. Which of the following Online Teaching and Learning Approaches through Blackboard Collaborate Ultra did you find user friendly?

STUDENTS’ RESPONSE Sharing Application / Sharing Files Sharing Screen (Textbook (Uploaded Whiteboard Video and Resource Lectures, Image, (Solving Library, Multimedia PowerPoint, or Problems, Library, Videos, PDF Files, etc.) etc.) YouTube, etc.)

Tutoring through All of the Blackboard above Collaborate Ultra

None of the above

TOTAL RESPONSES

115

429

152

286

114

377

TABLE 2 Q.1: Which of the following Online Teaching and Learning Approaches through Blackboard Collaborate Ultra did you like most?

STA2023-2207-4842

Sharing Application/Screen (Textbook Video and Resource Library, Multimedia Library, Videos, YouTube, etc.) 8

STA2023-2207-18408

MAC2311-2207-5333

MAC2233-2207-4880 MAC1147-2207-4789

2 5

5 8

4 6

2 4

8 12

0 1

21 36

MAC1147-2207-5326 CHM1025-2207-2174

7 8

6 10

10 7

6 4

6 13

0 1

35 43

CHM1025-2207-8333

CHM1033-2207-2188

CHM1045-2207-7752

CHM2210-2207-19032

TOTAL RESPONSES

115

429

COURSE

Sharing Whiteboard (Solving Problems, etc.)

Sharing Files (Uploaded Lectures, Image, PowerPoint, or PDF Files, etc.) 8

Tutoring through Blackboard Collaborate Ultra

All of the above

None of the above

TOTAL RESPONSES

TABLE 3 Q.2: Which of the following Online Teaching and Learning Approaches through Blackboard Collaborate Ultra did you find complicated?

COURSE

Sharing Whiteboard (Solving Problems, etc.)

Sharing Application/Screen (Textbook Video and Resource Library, Multimedia Library, Videos, YouTube, etc.)

Sharing Files (Uploaded Lectures, Image, PowerPoint, or PDF Files, etc.)

Tutoring through Blackboard Collaborate Ultra

All of the above

None of the above

TOTAL RESPONSES

STA2023- 2207-4842

STA2023- 2207-18408

MAC2311-2207-5333

MAC2233-2207-4880

MAC1147-2207-4789

MAC1147-2207-5326

CHM1025-2207-2174

CHM1025-2207-8333

CHM1033-2207-2188

CHM1045-2207-7752

CHM2210-2207-19032

TOTAL RESPONSES

152

286

TABLE 4 Q.3: Which of the following Online Teaching and Learning Approaches through Blackboard Collaborate Ultra did you find user friendly? Sharing Files (Uploaded Lectures, Image, PowerPoint, or PDF Files, etc.)

Sharing Whiteboard (Solving Problems, etc.)

Sharing Application/Screen (Textbook Video and Resource Library, Multimedia Library, Videos, YouTube, etc.)

STA2023-2207-4842

STA2023-2207-18408

MAC2311-2207-5333

MAC2233-2207-4880

MAC1147-2207-4789

MAC1147-2207-5326

CHM1025-2207-2174

CHM1025-2207-8333

CHM1033-2207-2188

CHM1045-2207-7752 CHM2210-2207-19032

12 8

8 13

9 10

6 3

12 11

0 0

47 45

TOTAL RESPONSES

114

377

COURSE

Tutoring through Blackboard Collaborate Ultra

All of the above

None of the above

TOTAL RESPONSES

TABLE 5 Q.4: In addition to the above, which of the following Online Teaching and Learning Approaches through Blackboard did you find most helpful in your field of studies?

Using Blackboard Grade Roster (For Early Alerts, etc.)

Using Blackboard Attendance Roster (For Early Alerts, etc.)

Using Blackboard Home Page (Announce ments, etc.)

Using Blackboard MDC Library (Learning Resource, Library, etc.)

STA2023-2207-4842

Using Blackboard technology (e.g., Blackboard E-mail, Meeting Instructor through Blackboard Collaborate Ultra, etc.) 8

STA2023-2207-18408

MAC2311-2207-5333

MAC2233-2207-4880

MAC1147-2207-4789

MAC1147-2207-5326

CHM1025-2207-2174

CHM1025-2207-8333

Using Blackboard Content (Instructor’ s Uploaded Course Tests, Files, PowerPoint , PDF Files, Videos, etc.)

Using Blackboard Resources (Instructor’ s Uploaded Course Files, PowerPoint , PDF Files, Videos, etc.)

All of the above

None of the above

TOTAL RESPONSES

CHM1033-2207-2188

CHM1045-2207-7752

CHM2210-2207-19032

TOTAL RESPONSES

116

105

653

COURSE

TABLE 6 Q. 5: Did you find the above Online Teaching and Learning Approaches through Blackboard and Blackboard Collaborate Ultra helpful in your field of studies? COURSE

Yes

TOTAL RESPONSES

STA2023-2207-4842 STA2023-2207-18408 MAC2311-2207-5333 MAC2233-2207-4880 MAC1147-2207-4789 MAC1147-2207-5326 CHM1025-2207-2174 CHM1025-2207-8333 CHM1033-2207-2188 CHM1045-2207-7752 CHM2210-2207-19032 TOTAL RESPONSES

20 19 12 15 19 17 25 17 25 26 26 221

1 0 4 0 1 3 2 1 2 1 2 17

21 19 16 15 20 20 27 18 27 27 28 238

TABLE 7 Q. 6: Choose one of the following rating scales for the above Online Teaching and Learning Approaches through Blackboard and Blackboard Collaborate Ultra. TOTAL COURSE Excellent Good Average None of the above RESPONSES STA2023-2207-4842 11 9 1 0 21 STA2023-2207-18408 11 6 2 0 19 MAC2311-2207-5333 6 9 1 2 18 MAC2233-2207-4880 8 8 0 0 16 MAC1147-2207-4789 12 6 2 0 20 MAC1147-2207-5326 8 9 4 0 21 CHM1025-2207-2174 10 12 4 1 27 CHM1025-2207-8333 10 7 1 0 18 CHM1033-2207-2188 17 9 1 0 27 CHM1045-2207-7752 14 11 2 0 27 CHM2210-2207-19032 20 8 0 0 28 TOTAL RESPONSES 127 94 18 3 242

FIGURE 1: Percentage of Students’ Response towards Questions # (1, 2, 3)

FIGURE 2: Percentage of Students’ Response towards Question # 5

FIGURE 3: Percentage of Students’ Response towards Question # 6

TABLE 7 Two-way ANOVA: RESPONSE versus QUESTIONS (1, 2, 3), OPINION Source QUESTION OPINION Error Total

DF 2 5 10 17

SS 1746.6 2572.7 25433.0 29752.0

S = 50.43

R-Sq = 14.52%

MS F 873.17 0.34 514.53 0.20 2543.30

P 0.717 0.954

R-Sq(adj) = 0.00%

FIGURE 4: Interaction Plot (data means) for RESPONSE - QUESTIONS (# 1, 2, 3)

58 A) Hypothesis Test: As a consequence of the results in Table 7 and Figure 4, using the P-value approach, we can draw the following conclusion from the hypothesis test among the means for the main effect due to the Survey Questions as follows: •

Conclusion: Since the P-value (0.717) > 0.05, we fail to reject the null hypothesis. That is, at the 5% level of significance, we cannot conclude that the average ofthe students’ response for the three survey questions is significantly different from each other.

B) Hypothesis Test: As a consequence of the results in Table 7 and Figure 4, using the P-valueapproach, we can draw the following conclusion from the hypothesis test among the means for the main effect due to the Students’ Opinions as follows: •

Conclusion Since the P-value (0.954) > 0.05, we fail to reject the null hypothesis. That is, at the 5% level of significance, we cannot conclude that the average of the students’ response for the five opinions issignificantly different from each other.

TABLE 8 Two-way ANOVA: RESPONSE versus QUESTION (5), OPINION Source QUESTION OPINION Error Total

DF 10 1 10 21

SS 114.27 1854.73 120.27 2089.27

S = 3.468

R-Sq = 94.24%

MS F P 11.43 0.95 0.531 1854.73 154.21 0.000 12.03

R-Sq(adj) = 87.91%

FIGURE 5: Interaction Plot (data means) for RESPONSE - QUESTION (# 5)

TABLE 9 Two-way ANOVA: RESPONSE versus Q.6, OPINION Source QUESTION OPINION Error Total

DF 10 3 30 43

SS 48.50 968.82 177.68 1195.00

S = 2.434

R-Sq = 85.13%

MS F 4.850 0.82 322.939 54.53 5.923

P 0.613 0.000

R-Sq(adj) = 78.69%

FIGURE 6: Interaction Plot (data means) for RESPONSE - QUESTION (# 6)

Note: Hypothesis Test: Similar to the Table 7 and Figure 4, Tables 8 and 9, and Figures 5 and 6 are also self-explanatory. As a consequence of the results in Tables 8 and 9, and Figures 5 and 6, using the P-value approach, one can easily draw the conclusions from the hypothesis tests among the means for the main effect due to the Survey Questions and Students’ Opinions, similar to the Table 7.

CONCLUDING REMARKS Based on our observations and analysis, it is evident that “Remote Online Teaching and Learning Approaches of Instructions” are most important in mathematics and chemistry classes. Incorporating these approaches of instructions in various mathematics and chemistry classes can help teachers to measure the effectiveness of their teaching by finding out what students are learning in the remotely online delivered classroom and how well they are learning. In addition, these techniques can provide an efficient avenue of input and a high information return to the instructor without spending much time and energy. It is recommended that, in future, much better practices for remote online teaching and learning approaches of instructions using differentlearning management systems be developed and implemented in

62 various disciplines for better learning and more effective teaching.

Acknowledgment First, the authors are thankful to the reviewer for his valuable and constructive suggestions which considerably improved the presentation of the paper. The authors would alsolike to thank the Editorial Committee of Polygon for accepting this paper for publication in Polygon. Also, the authors are thankful to their institution, Miami Dade College, for providing them an opportunity to serve it, and allowing them to teach various courses in their disciplines, which helped them to write this research paper. Further, the authors would like to thank their family for their patience and perseverance for the period during which this paper was prepared.Lastly, the first author would like to dedicate this paper to his late parents.

References [1] Eggen, P., and Kauchak, D. (2010). Educational Psychology: Windows on Classrooms, 8thEdition. Pearson Education, Inc., Upper Saddle River, NJ, USA. [2] Johnson, D. W., Johnson, R. T., and Holubec, E. J. (2008). Cooperation in the classroom, 8thEdition. Interaction Book Co., Edina, MN, USA. [3] Keengwe, J., and Kidd, T. T. (2010). Towards best practices in online learning and teaching inhigher education. MERLOT Journal of Online Learning and Teaching, 6(2), 533-541. [4] Krutt, T. (2008). Best Practices of Teaching in Web-Enhanced, Hybrid & Online Classes. Technological Tools & Training, Connecticut Community Colleges, System Office, Connecticut, USA. [5] Ko, S., and Rossen, S. (2017). Teaching Online: A Practical Guide, Routledge, New York, USA. [6] Slavin, R. E. (1995). Cooperative learning theory, research and practice. Allyn & Bacon,Boston, USA. [7] The Merriam-Webster Dictionary (2019). Merriam - Webster Inc., Springfield, MA, USA. Timpson, W., and Bendel-Simso, P. (2003). Concepts and Choices FOR TEACHING. Atwood Publishing, Madison, WI, USA

Narrative Memory: The Poetic Response to the Aporia Between Personal and Collective Memory In Ricoeur’s Hermeneutics Professor Kristofer C Arca Department of Arts and Philosophy Miami Dade College Kendall Campus 11011 SW 104 Street, Miami, FL 33176 E-mail: karca@mdc.edu

ABSTRACT In this paper, I propose and develop a poetic response to one of the major aporias of memory developed by Ricoeur in Memory, History, Forgetting—i.e. that between personal and collective memory. My contention is that the structure of this aporia is parallel to that between phenomenological and cosmological time found in Time and Narrative. As such, the poetic response to the aporia between personal and collective memory is already prefigured in the pagesof Time and Narrative. Similarly, to the way that poetically responding to the aporia of time required utilizing the resources of narrativity to develop a third, intermediary notion of time—i.e.‘historical’ or ‘human’ time—I propose that poetically responding to the aporia between personaland collective memory requires utilizing the resources of narrativity to develop a third, intermediary notion of memory, which I dub ‘narrative’ or ‘narrated’ memory. KEY WORDS: Personal Memory, Collective Memory, Narrative/Narrated Memory, Narrative Identity, Narrativity

64 INTRODUCTION: THE APORIA BETWEEN PERSONAL AND COLLECTIVE MEMORY I would like to begin with a thought experiment. Suppose you have a friend named Maria. You have been friends since childhood, and find that whenever the both of you spend time together, you both inevitably share childhood memories with one another. Suppose that one day, while meeting over lunch, Maria shares a memory of helping her mother make flan—a traditional Latin American dessert—for Christmas. She lights up as she loses herself in the details—recalling how her mother learned how to cook flan from Maria’s great grandmother; how her mother would teach Maria that the secret to a great flan could never be found in a recipe book; why this particular dish was exclusively reserved for instances of mother-daughter bonding; and why this particular recipe—a cheese flan—was made only during Christmas time. Maria’s memory is quite vivid, coherent, and meaningful—especially its emotional undertones. You cannot help but to wonder aloud as to what makes sense of these qualities.i Fortunately for everyone, Maria is a phenomenologist. As such, she responds that the intentional structure of this rememorative experience is one where the memory she is recalling is immediately given to her as belonging to her. She is not confused about who is the true owner of this experience; the memory is hers. Moreover, she also has no doubt that this is a memory that she is recalling, and not rather a fantasy. This experience is clearly of the past. Lastly, the coherence and meaningfulness of this particular memory stems from the nature and structure of internal time consciousness, and the vast myriad of passive syntheses that ensure that the ‘stream’ of consciousness is able to integrate and organize itself. Given all this, she reassures you that a phenomenological analysis can address any and all questions concerning the way in which one experiences and understands a memory. That seems to settle all matters. Or does it? I neglected to mention that, while Maria is a phenomenologist, you are a sociologist. After a careful pause, you respond that you disagree. The coherency, and meaningfulness of Maria’s memory is due, not to a phenomenological account, but to a sociological one. The memory is Maria’s, to be sure, but it is also her mother’s; and had human living not been fundamentally intersubjective, deeply organized into an established social order involving a large network of concepts and relationships—i.e. “family”, “mother”, “daughter”, “holidays”, etc.—and permeated by language, this memory, and those like it, could never be formed or shared. Further, how could internal time consciousness, all by itself, grasp the significance of this flan—a cultural artifact with a rich social history—only being cooked around Christmas time—a specific holiday, the significance of which is the product of cultural belonging? These two things—the flan and the holiday—are highly symbolic in nature. Is it not the case that their underlying symbolic significance exceeds the boundaries of the rudimentary intentional structure of perceptual experience? It is clear to you that sociology can better address these pesky questions concerning the way one experiences and understands memory. In fact, you

65 eloquently say, one might go one step further and add: The trouble with phenomenology is that while it claims to offer, on the grounds of disclosing the intentional structure of perception and perceptual experience, the most primary source from which all propositional thought can be understood and derived, it fails to consider that its analyses are only made possible by recognizing the greater fundamental truths found in the sociological sciences. Phenomenology rests on sociology. Maria pauses. You do have a point. However, after some thought, she retorts that the same argumentative structure you have used against phenomenology—that x presupposes and rests on y—can be used against sociology. Is it not the case that sociology presupposes and, therefore, rests on phenomenology? The symbolic networks that organize humanity’s social lives cannot exist by themselves. A society without any social agents is a dead one. Society requires agents of action, and is made possible by them. If so, do we not need to understand ‘who’ these beings are? If we should understand these beings, would it not be the case that an analysis of them would be incomplete without a phenomenological one? Further, why should this analysis not elucidate upon a set of the most foundational kinds of experience—perception, imagination, memory? After all, sociology is not the condition of possibility of these sorts of experiences; it requires that social beings are capable of them in the first place. It seems that before sociology can become an issue, phenomenology must first prevail. Thus, sociology presupposes and rests on phenomenology. You pause. She does have a point. However, after some thought, you begin again. The discussion continues. You both go on to counter each other’s position while clarifying your own. It is to no avail. By the end of the discussion, the only thing that can be agreed upon is that it seems both sides— phenomenology and sociology—mutually assert their primacy over the other, while at the same time implicitly borrow from the conceptual apparatuses of the other. There goes a perfectly good lunch. To the best of my knowledge, the above is illustrative of the fundamental structure of the aporia concerning the attribution of memory as Ricoeur presents it in Memory, History, Forgetting.ii This aporia emerges upon Ricoeur’s inquiry into whether memory is primarily a personal phenomenon—i.e. it is individuals who remember, and thus, understanding the subject of memory (the ‘who’ that remembers) ought to be confined to a phenomenological investigation—or whether it is a collective phenomenon—i.e. it is cultures and societies that remember, and thus, understanding the subject of memory ought to be confined to a sociological investigation. Yet, upon closer analysis of each side’s respective arguments, it only becomes more evident that each side borrows from, at the same time that it denies, the other— creating a rather vicious circle.iii It is to this aporia that I would like to respond within the confines of this paper. I would like to propose that the underlying structure of this aporia is not new. It has a parallel

66 structure to the central aporia of time that Ricoeur developed in Time and Narrative: the aporia between phenomenological time and cosmological time.iv Though there are key differences between the aporia of time in Time and Narrative, and the aporia between personal and collective memory in Memory, History, Forgetting, my contention is that the underlying similarity in their structures—that of the mutual assertion of the primacy of one over the other, while at the same time surreptitiously presupposing the other— suggests a fruitful avenue to which the aporia between personal and collective memory can be addressed.v As such, the poetic response to the aporia between personal and collective memory is already prefigured in the pages of Time and Narrative. By the term “poetic response”, I mean one that employs the creative capacity of language in order to go beyond the confines of pure description.vi Poetically responding to the aporia between phenomenological and cosmological time required utilizing the resources of narrativity to develop a third, intermediary notion of time—i.e. ‘historical’ or ‘human’ time. Similarly, I propose that poetically responding to the aporia between personal and collective memory requires utilizing the resources of narrativity to develop a third, intermediary notion of memory—which I am calling ‘narrative’ or ‘narrated’ memory.vii Thus, the overarching goal of this paper is to develop an account of narrative memory as a way of testing its legitimacy within Ricoeurian hermeneutics, and as a way of preparing for a further analysis of the concept.viii This paper will be organized into four major sections. The first three sections will each respectively recapitulate three major components of Time and Narrative: 1) The structure of narrativity; 2) the structure of the aporia of time; and 3) the way in which narrativity refigures time to poetically ‘resolve’ the aporia. These first three sections serve two major roles. First, they more greatly show the parallel between the aporia of time in Time and Narrative and that of personal and collective memory in Memory, History, Forgetting. Second, they will culminate with an analysis of a concept that will be central to the development of the notion of narrative memory—namely, the idea that human subjects are always, already ‘being-affected’ by the past, which Ricoeur developed at the conclusion of Time and Narrative. The notion of being-affected by the past will allow me to argue that memories are subject to interpretation. If they must be interpreted, then they require narrativity. Thus, in the fourth section of this paper, I will develop the notion of narrative memory. In order to state clearly what a narrated memory properly ‘is’, I will base my analysis off of Ricoeur’s notion of a ‘happy memory’—which is implicated throughout the pages of Memory, History, Forgetting. This analysis will require developing the essential features of a happy memory—a task that Ricoeur only sketched out in his work—and from there, demonstrating how the poetic capacity of narrativity reconfigures each essential feature so as to arrive at the concept of narrative memory.

67 NARRATIVITY AS THE ACTIVITY OF EMPLOTMENT I shall begin by recapitulating the nature of narrative within Ricoeur’s hermeneutics. To do so, I shall incorporate elements of Ricoeur’s essay “Life in Quest of Narrative”, as the account he provides therein elegantly prefigures the aporia of time in Time and Narrative.ix According to Ricoeur, the basis of narrativity stems from the ancient Greek notion of muthos, specifically, the Aristotelian configuration of the term, indicating what he calls emplotment.x Ricoeur’s preference of the term ‘emplotment’—over that of ‘plot’, ‘narrative’, or ‘story’—stems from the term’s double-meaning.xi On the one hand, the term could refer to the structure of emplotment, i.e. the dialectic between Mimesis1, Mimesis2, and Mimesis3.xii On the other hand, it could refer to the dynamic activity of emplotment as such, which is made possible by the dialectical mimetic structure of narrativity. For my purposes, I am referring to emplotment as an activity. If the activity of emplotment stems from the dialectic of Mimesis1, Mimesis2, and Mimesis3, then emplotment is a synthetic activity.xiii As a synthetic activity, emplotment recontextualizes three phenomena. First, emplotment recontextualizes the notion of an event. Out of many, divergent events, emplotment is capable of weaving a coherent story.xiv As Ricoeur states, “an event is more than an occurrence… it is what contributes to the progress of the narrative as well as to its beginning and to its end.”xv The notion of an event—and other notions weaved into its conceptual network—is augmented from the synthetic act of emplotment. Second, emplotment synthesizes the complicated topography between agents and patients, as well as the reversals of fortune that mediate between the two: acting and suffering, chance encounters and inevitable confrontations, conflict and collaboration, etc.xvi It is here where stochastic ‘happenings’ become ordered and necessary for the entirety of the story told—hence Ricoeur’s description of emplotment as discordant concordance. Lastly, emplotment is capable of poetically weaving together two distinct notions of temporality. On the one hand, through a story’s ordering of events and the series of actions and reversals of fortunes contained therein, emplotment relies upon and makes use of temporality as a succession of events, as a ‘now’ and ‘later’, a ‘before’ and ‘after’.xvii On the other hand, a story taken as a complete work incorporates an understanding of the permanence of time; events begin and end, but time endures— as do the stories we tell.xviii Narratives do not simply exist in a vacuum, nor do they form a closed system upon themselves. Narratives are a form of discourse; they, as Ricoeur often repeated, say something about something to someone.xix As discursive, narratives belong to a tradition that contextualizes the way in which a particular narrative is received. I will touch upon this more when I highlight the way in which emplotment poetically resolves the aporia of time. Further, as discursive, a narrative is not truly complete until its

68 encounter with an audience—whether that audience is simply a single reader or an entire population of readers. It is in this encounter that the world of the text collides with that of the reader, and from this collision emerges a ‘fusion of horizons’.xx By ‘world of the text’, Ricoeur means a possible horizon of experience to and for the reader; a horizon that opens one to a possible world different from one’s own, but similar enough that it offers itself as a realm of imaginative engagement—hence Ricoeur’s fondness to metaphorically refer to the world of the text as a laboratory of action and experimentation.xxi Finally, as Ricoeur goes on to explain, the fusion of horizons places a text—a story, a narrative—in a threefold intermediary relationship between the reader and 1) the world; 2) others; and 3) herself.xxii The text has the capacity to transform the reader’s understanding of each of these relationships. With regard to the world, the fusion of horizons nourishes an understanding of it beyond pure description—think of the child who (re-)kindles their sense of wonder in the world around them through the Harry Potter series. With others, the fusion of horizons augments our empathetic relations, allowing for greater understanding between people. Lastly, as Blamey has argued, the fusion of horizons discloses a relationship to oneself that is purged of egotistical desires of mastery, to make a space for self-understanding guided by open and honest self-interpretation.xxiii

THE STRUCTURE OF THE APORIA OF TIME IN TIME AND NARRATIVE In the opening pages of the third volume of Time and Narrative, Ricoeur states rather plainly that what animates his analysis is the conviction that the synthetic activity of emplotment is able to creatively respond to the aporia of time, which emerges from the unbridgeable gulf between phenomenological and cosmological time.xxiv Indeed, it is interesting to note that Ricoeur’s treatment of emplotment in “Life in Quest of Narrative” already anticipates this aporia, as well as its creative resolution. One of the synthetic elements of emplotment, we noted above, revolves around bringing together and creatively interweaving two seemingly conflicting characteristics of time—that it, first, flows; and second, that it endures. My goal here is not to painstakingly recount the aporia, but rather to elucidate upon its structure. I do so for two reasons: 1) to more clearly show how narrativity responds to this aporia; and more importantly 2) to show that it has a parallel structure to that between personal and collective memory. Ricoeur dedicates three chapters to the aporia of time, and each chapter serves not to develop three differing aporias, but to deepen one central aporia. The aporia stems from two notions of time: a phenomenological one and a cosmological one. From the perspective of the phenomenological notion of time, the constitution of time stems from conscious lived experience and the structure of the first-person perspective—or from dasein’s being-in-the-world.xxv From the perspective of the cosmological notion, time is part of the fabric of the cosmos. The issue is not that there are two competing mutually exclusive

69 theses on the constitution and nature of time. If that were the case, there would be no aporia; there would only be a debate between two competing positions, where the best argument—or the best arguer—wins. The issue is that both phenomenological and cosmological accounts of time simultaneously rely on each other, while at the same time, claim to be more originary to and more fundamental than the other. Stevens presents the most succinct and clear explanation: Philosophical speculation on time leads to the irreconcilable contrast between a phenomenological perspective… and a cosmological perspective... Ricoeur shows that each perspective relies on the presupposition of its opposite while, altogether, concealing it: cosmological time, while aiming at the rejection of any subjectivity, cannot be measured without being perceived by a contingent subject; phenomenological temporality, on the other hand, while trying to present itself as the source of time, cannot create its own conceptuality without referring to an objective preconcept of time.xxvi As a brief illustration, consider the aporia as it manifests itself in both Husserl and Kant. On the Husserlian side of the equation, Ricoeur painstakingly retraces the steps involved in Husserl’s analysis of internal time consciousness. Here, the object is to make time itself, as flux, appear; and to do so, Husserl must perform two phenomenological reductions: The first on world time, where Husserl brackets four a priori truths of time;xxvii the second on the “objectified time of tempo-objects” (e.g. a tone, a recited poem, etc.).xxviii Yet, Ricoeur’s analysis suggests that, in order for Husserl to finalize his argument concerning the self-constitution of the temporal flux, he surreptitiously has to rely on the objectified time that was the target of the second reduction.xxix Even further, the constitution of the unity of the flux of time requires a conception of time which endures—and such a conception is precisely that which Kant holds as a necessary condition of possibility. If this conception of time is a necessary condition of possibility for experience, then this conception of time cannot itself be directly experienced. Thus, we see how the phenomenological conception relies on and excludes the cosmological. The Kantian route commits the same crime. Kant, contra Husserl, maintained that time cannot appear, and that one has no recourse to time through the first-person perspective; rather, it is a condition of possibility of experience as such. Yet, it seems that Kant is incapable of truly committing to his transcendental route without implicitly borrowing from the first-person perspective. As Godlove eloquently puts it: Here, too, there is no dispute about how Kant must argue if he is to maintain a transcendental stance: all agree that he must presuppose rather than perceive the permanence of objects of experience. But, if what recommends objects of experience as models for the permanence of time is the perceivability of their permanence, then we ought to conclude that, in this instance, Kant

70 cannot keep to the transcendental path; indeed, it is his failure to do so at precisely this point that Ricoeur claims to document.xxx Thus, the structure of the aporia of time is more clearly apparent. On the one hand, there is mutual borrowing between phenomenology and cosmology; on the other, mutual exclusion.xxxi We can see, then, that the aporia of time in Time and Narrative has a similar structure as the aporia of the subjective analysis of memory in Memory, History, Forgetting, as it was developed in introduction of this paper; phenomenology requires, but brackets, the rich social world to which one belongs in order to claim that the foundation of memory is personal, whereas sociology also requires, but brackets, the rich inner life of individuals in order to claim that the foundation of memory is collective.

THE POETIC RESPONSE TO THE APORIA OF TIME What remains to be shown is how narrative, as developed by Ricoeur, is able to poetically resolve the aporia of time, and from this, whether the rubric through which narrative is capable of responding to the aporia of time can be transposed to that of memory. First, however, I should highlight the nature of Ricoeur’s method for responding to the aporias he develops. Ricoeur’s proposed ‘resolutions’ to these aporias are poetic—they involve the creative capacity of language to go beyond the realm of physical or pure description; they make use of the creative tropes and resources upon which both Western philosophy, the sciences, and fiction rest. As such, Ricoeur’s way of responding to philosophical aporias is ‘jury-rigged’, imperfect. It is not uncommon for Ricoeur to state that his goal is not to resolve or dissolve a philosophical problem, but to make that problem “work”.xxxii Without question Ricoeur is capable of responding to the aporias he uncovers, but only with respect to certain limits. It is up to each generation of philosophers, then, to disclose these limits, reignite the aporias, and to also formulate new, more original ways of responding to them. Philosophical progress may be slow, careful, unsteady—but it is still progress. With that in mind, to the aporia between phenomenological time and cosmological time, Ricoeur proposes an intermediary term: historical time—also sometimes referred to as human time, or even, narrated time.xxxiii Narrative’s capacity to interweave and reconfigure events, human action, interaction, and suffering, along with various characteristics of temporality make it ripe with creative resources to respond to the aporia of time. Through the analysis of the features of historical time, Ricoeur is able to show how history blends both phenomenological and cosmological time. Historical time has three features: 1) calendar time; 2) the succession of generations; and 3) the historical trace.xxxiv I shall speak only briefly about each. In calendar time, we see quite plainly the

71 interweaving of phenomenology and cosmology. From phenomenology stems the more pragmatic reappropriation of within timeness: today, tomorrow, yesterday, etc. History is the horizon from which one resolutely pursues one’s projects—and to devoting oneself to losing, finding, unmaking, and remaking oneself through these projects.xxxv From cosmology, we have the overall organization of the calendar revolving around astronomy.xxxvi Further, Ricoeur points out that calendar time, inasmuch as it interweaves phenomenology and cosmology, also interweaves history with fiction. Holidays punctuate the calendar year, offering people opportunities to pause and reflect on the circumstances of their lives, as well as offering entire communities to connect and reconnect with a community’s constitutive founding moments—moments that have the tendency of being elevated to mythic proportions: The signing of the Declaration of Independence, El Grito de Dolores, Armistice Day, etc. The interweaving of ‘lived’ and ‘universal’ time continues with the succession of generations. Here we see that the biological reality that underlines our being-towards-death open itself to, and becomes fused with, our sociality. Through the succession of generations, the living replace the dead, predecessors ‘pass the baton’ to their successors, and contemporaries act and suffer together—in cooperation and conflict—in order to respond to the ethico-politico task of human living.xxxvii There is much that narrativity has to offer here, as the succession of generations is itself mediated by the dialectic of innovation and sedimentation. Each member of a new generation is already the result of innovation— albeit at the genetic and biological level. Each generation of people, further, work from within the context of the tradition to which they belong, modifying it as time goes by, to allow human existence to continue to unfold, chronicled by the stories we tell. Last is the historical trace—by which Ricoeur means a residue that leaves a ‘mark’ on the social world.xxxviii I will limit my treatment of the historical trace to a few remarks. The first is the figurative nature of the trace. As Ricoeur notes, the historical trace can be understood either as a mark—a streak, a groove—or as a passage.xxxix However it is understood, the figurative nature of the trace announces its discursivity. It communicates that something happened. Further, taking the trace as a passage indicates that following the trace might reveal what happened, but determining what happened requires interpretation, narration, argumentation, etc.xl Secondly, as figurative and discursive, the trace also reveals something else: the extent to which we are at time’s mercy. Ricoeur’s position is that human beings are always already being-affected by the past.xli Through the notion of being-affected by the past, Ricoeur’s hermeneutics comes into contact, however briefly, with Gadamer’s hermeneutics. Specifically, the notion of being-affected by the past is a modification of Gadamer’s Wirkungsgeschichtliches Bewusstein,xlii by which Ricoeur understands “consciousness of being exposed to the efficacity of history”.xliii Others have translated it as our

72 ‘historically affected consciousness’.xliv I shall use both expressions as I see fit. As I just mentioned, Ricoeur’s notion of being-affected by the past is a modification of Gadamer’s historically affected consciousness. Ricoeur specifically modifies the intermediary notion of tradition. Within the confines of Time and Narrative, traditionality is primarily used to clarify the concept of being-affected by the past by articulating its dialectical structure, which necessitates mediation and interpretation.xlv The central dialectic of being-affected by the past is that of belongingess and distanciation.xlvi Human beings are deeply social creatures, and our sociality carries with it a shared history that becomes furcated through the prism of traditionality. Indeed, the issue here is not which tradition one belongs to, or identifies with, but that our being-in-the-world is always, already demarcated by a historicity that conditions the range of meaningful actions on which we can rely to respond to the particularities of our existential situation. In other words, from Ricoeur’s perspective, it is a given—a necessary condition of possibility—that human beings belong to, before one can begin to question and criticize, a tradition of some sort or another. “The past questions us and calls us into question,” Ricoeur contends, “before we question it or call it into question.”xlvii Humanity’s belongingess to (some such) tradition is what Ricoeur means when he uses the term ‘traditionality’.xlviii Traditionality as such humanizes the past and the present—or better, it modifies the relationship between the past and the present. Through the intermediary concept of traditionality, the past ought not be understood as something that is ‘over and done with’, no longer existent, “a dead interval”, or “an inert deposit”.xlix Neither should it be taken as being contemporaneously fused with the present.l There is still a temporal gap between the past and the present, however, this gap is bridged by traditionality, for through it, the past is able to ‘transmit’ a wealth of meaning-potential that every present generation—or every individual of a present generation—may (or may not) actualize.li Through traditionality, then, a vast network of symbolic meaning is ‘handed down’ and given to those in the lived present, and those in the lived present receive and take upon the task of unfolding this symbolic network of meaning.lii As Ricoeur states, traditionality “proceeds from the tension, at the very heart of what we call experience, between the efficacity of the past we undergo and the reception of the past we bring about.”liii To attempt to articulate this more clearly, between the past and the present, there is a fusion of horizons.liv This fusion of horizons is a combination of our passivity to history—we always already dwell within circumstances we have not made, and have had no part inlv—as well as our capability of ‘making’ history. Between this passivity and activity is traditionality. The tradition to which one belongs grants one a vast symbolic network that can be utilized to 1) understand the past and its relationship with the present; and 2) use this understanding to formulate plans of action geared towards the future. Consider, for instance, the person who justifies her volunteer work to help the poor as being ‘the Christian thing to do’,

73 or the person who cheerfully insists that developing a strong work ethic hinged upon self-reliance and industriousness is ‘the American way(!)’. These two examples might be rather kitschy, but they do get the point across. They also allow me to stress another point. Namely, that the relation one has with one’s tradition is not direct. It is symbolically mediated, and as such, the fusion of horizons between the past and present is one marked by interpretation. Consider the following quotations by Ricoeur: [Traditionality] is not a separating interval, but a process of mediation staked out by the chain of interpretations and reinterpretations.lvi And Before being an inert deposit, tradition is an operation that can only make sense dialectically through the exchange between the interpreted past and the interpreting present.lvii To return to my examples, this is precisely why it is possible for different people to have staggeringly different ideas as to what, exactly the ‘Christian thing to do’ or ‘the American way(!)’ is to begin with. To put it differently, Ricoeur’s concept of being-affected by the past suggests that, metaphorically, the humanized past ‘speaks’ to us; it has a discursive reality. But I have to be careful. The discursivity of the past is not like that of a dialogue. It lacks both the symmetry of Buber’s I-Thou relation, as well as the asymmetry of Levinas’s face-to-face.lviii Rather, the discourse is like that between a text and its readers. The nature of discourse is best incapsulated by the expression of which Ricoeur is so fond. Discourse entails someone saying something about something to someone else.lix From this, discourse has three major traits: a speaker, a topic of discussion situated within a worldly (or social) context, and an interlocutor.lx To these three, a fourth can be added, i.e. a temporal dimension through which discourse unfolds.lxi Written or textual discourse modifies all four traits. The temporal: whereas spoken discourse takes the character of a fleeting event—two friends meet, catch up, and then go their separate ways— written discourse inscribes what is said such that its meaning—“the noema of speaking”lxii— is retrievable. In other words, in speaking, saying something to someone is an event with a beginning, middle, and end. Whereas in writing, that which is said remains; it becomes an artifact. The speaker: In spoken discourse, the meaning of what one is saying overlaps with the speaker’s intention. As Ricoeur states, “it is almost the same thing to ask, what do you mean? What does that mean?”lxiii In written discourse, there is a break between the author’s intention and what is written; a phenomenon the Ricoeur has elsewhere called “semantic autonomy”.lxiv Understanding the meaning of a

74 text, then, is not about inquiring into the psychological state of its author—this would be to reduce the meaning of a text to a form of psychologism. Understanding the meaning of a text, then, requires allowing the text to ‘speak for itself’: “What the text says now matters more than what the author meant to say”.lxv The meaning of the text can only be discovered by reading the text. The worldly context: In spoken discourse, the interlocutors are situated within a shared social context, a “situation”, as Ricoeur describes it.lxvi As such, the dialogical event has a direct reference. In written discourse—as is the case with important works of philosophy, history, or literature—the reference is not direct, but rather discloses a possible world laden with meaning—enough so that it can augment one’s own being-in-the-world. Thus we speak about the “world of Greece”, not to designate any more what were the situations for those who lived them, but to designate the nonsituational references that outline the effacement of the first and that henceforth are offered as possible modes of being, as symbolic dimensions of our being-in-the-world.lxvii In reading a work of literature, such as 1984, one also gains a richer symbolic relation with one’s own worldly context; the world of the reader collides with the world of the text, unlocking new meaning-potentials—new ways of relating to, understanding, and interpreting the world. The interlocutor/reader: The dialogical, face-to-face relation is one wherein which the interlocutors are present to each other. However, textual discourse entails a double absence. The writer is writing to and for an audience, but this audience is invisible to the author. Further, the reader receives the text, and as was suggested earlier, the matter is no longer the author’s intent, but the text itself. Hence, the double absence is that of the writer and the audience. More radically, the reader need not even belong to the same worldly situation or sociological context as the author; the temporal distance between the two can be of several lifespans. Yet, as Ricoeur argued in the first volume of Time and Narrative, it is through the reader that the text is realized, actualized.lxviii I would like to add one more thought to the relationship between the reader and the text. Namely, the reader’s capacity, in actualizing the text, to discover—in a moment of interpretative innovation—a possible meaning that exceeds the historical boundaries of the text (e.g. to see in one of the works of William Shakespeare an analogy of our current scientific understanding of memory, say). In sum, the relationship between the reader and the text imbues texts with a “peculiarity”: The peculiarity of the literary work, and indeed of the work as such, is nevertheless to transcend its own psychosociological conditions of production and thereby to open itself to an unlimited series of readings, themselves situated in sociocultural contexts that are always different. In short, the work decontextualizes itself, from the sociological as well as the psychological point of view,

75 and is able to recontextualize itself differently in the act of reading.lxix By now, it ought to be clear that the proposed metaphor between one’s relationship with the past—via being-affected by the past and via traditionality—and the relationship of the text and its reader is a healthy metaphor. In the same way that a text lends itself to be read and understood through a fusion of horizons between the ‘world’ of the text and the world of the reader, so too does tradition grant one a manner of being-in-the-world that transforms one’s worldly social context or situation. In the same way that one actualizes and revitalizes the meaning of a text through interpretation, so too does one actualize and revitalize the meaning of their historical belonging to a tradition. In the same way that one may break from interpretative orthodoxy with a text and discover a new meaning-potential, one may break from the orthodoxy of one’s tradition, innovating upon the level of receptivity of the past. In these three features, we find the fullness of the dialectical relation between belongingness and distanciation that is at the heart of being-affected by the past. To return to the aporia of time: between phenomenological and cosmological time, the resources of narrativity allowed Ricoeur to posit historical, humanized time. Historical time weaves together features of both phenomenological and cosmological time. It also transcends both accounts of time, becoming its own paradigm. Within this paradigm, we find that time affects us. In order to work through this passivity with regard to temporality, we must refer to our inherent traditionality. Through this, we discover our belongingness to and distanciation from the historical past. Our belongingness to history, through tradition, contextualizes how we live in the present. Our distance allows us to break from the chains of the past, and act for the sake of a hope towards a better future.

NARRATIVE MEMORY: BETWEEN PERSONAL AND COLLECTIVE MEMORY In the closing of the first part of Memory, History, Forgetting, Ricoeur returns to the aporia between personal and collective memory. Within these pages, Ricoeur offers a brief remark as to that which the hermeneutic response to this aporia consists. Ricoeur’s gesture comes in the form of an open question: Does there not exist an intermediate level of reference between the poles of individual memory and collective memory, where concrete exchanges operate between the living memory of individual persons and the public memory of the communities to which we belong?lxx Accordingly, it is in one’s shared life “with and for others”lxxi where we can find the poetic resolution to the aporia—a phenomenology open to social reality, a sociology capable of taking into account social agents and patients, acting and suffering.lxxii

76 In gesturing that the response to the aporia between personal and collective memory lies in one’s intersubjective relation(s) with others, we are transposed back to the relationship between narrativity and selfhood in Oneself as Another, insofar as (narrative) selfhood necessarily requires intersubjectivity as a condition of possibility. In Oneself as Another, Ricoeur argues that selfhood emerges out of the dialectical relationships between narrativity and idem identity, on the one hand, and narrativity and ipse identity, on the other.lxxiii Between narrative and idem, we find the annunciation of ‘who’ one is through ‘what’ one is—i.e. the ability to put into words the rich and often complex history of one’s character. Between narrative and ipse, we find the demand for self-constancy through the concrete, face-to-face relation with another—whether this relation is symmetrical or asymmetrical, or with a predecessor, successor, or contemporary. It is because of others that fidelity and authenticity become a concern for me. It is to the other that I attest this fidelity. It is with others that I become a self, in the fullest sense of the word. With the reality and intricacy of the intersubjective relation in mind, I would like to initiate the response to the aporia between personal and collective memory. Between these two forms of memory, I propose a third, intermediary form: narrative memory. To develop this intermediary form of memory, I will analyze more closely Ricoeur’s notion of a ‘happy memory’—to which he refers throughout Memory, History, Forgetting. I will demonstrate that in order for any memory to meet the criteria required to be designated as a happy memory, it is necessary to appropriate from the structure and form of emplotment, narrativity. In Ricoeur’s hermeneutics, a happy memory, then, is one that can be put into words, articulated to oneself and to others. By Ricoeur’s own admission, the notion of the happy memory is one of the guiding principles of his analysis of memory and mnemonic phenomena in Memory, History, Forgetting.lxxiv Indeed, the notion of the happy memory is invoked no less than seventeen times during his rigorous analysis of memory. Despite its centrality to his analysis of memory, Ricoeur does not develop the concept in a coherent manner. I shall attempt to do so here by developing four features of a happy memory. I shall base these features off of the way in which Ricoeur utilized the notion of a happy memory throughout Memory, History, Forgetting. The first feature of a happy memory is that it is nonpathological.lxxv By “nonpathological”, I mean two different interpretative meanings of the word. The first is that a happy memory is not an unhealthy one—where the reinvigoration of a traumatic event’s mnemonic trace, for example, causes, not a recollection of the event, but its repetition. A happy memory is not necessarily a pleasant memory, but it is one that lends itself to recollection as recollection. Secondly, as nonpathological, a happy memory is not one that emerges from a suspicious analysis of mnemonic phenomena—suspicious, namely of the aporia between memory and imagination.lxxvi

77 The first feature of a happy memory tells us only what it is not. The following three will sketch out more clearly what a happy memory is. The second feature of a happy memory is that it is accessible.lxxvii Here, Ricoeur has in mind what he sometimes referred to as the “work” of memory—the effort it takes for one to successfully recall a specific memory, a specific moment. There is a quasieconomic rule that underlies the accessibility of a happy memory: the less effort required to bring a memory to consciousness, the more accessible it is. Thus, a happy memory is not simply one that lends itself to recollection; it does so with ease. A happy memory is, third, recognizable.lxxviii Phenomenologically, recognition can be understood as perceptual or mnemonic. Whether perceptual or mnemonic, recognition has a similar phenomenological structure: appearance, disappearance, reappearance. In terms of mnemonic recognition, recognition is made possible through the “quasi-hallucinatory” capacity of the imagination.lxxix The remembered event is superimposed on top of the mnemonic trace in a way that is analogous to the perceived object being ‘squared’ with its numerous sides, profiles, and adumbrations. The recognized memory is recognized as a memory; phenomenologically, it is (re)presented alongside with “the seal of anteriority”.lxxx Every happy memory is always already given as being “of the past”.lxxxi If the concept of a happy memory is nonpathological, accessible, and recognizable, then Ricoeur would maintain that it is, fourthly and finally, discursive.lxxxii If memory is discursive, then Ricoeur’s hermeneutic analysis of memory is consistent with one of the central theses of the entirety of his hermeneutics—i.e. what I have dubbed the “descriptive inescapability”lxxxiii of experience: Experience in all its fullness… has an expressibility [disibilité] in principle. Experience can be said, it demands to be said. To bring it to language is not to change it into something else, but in articulating and developing it, to make it become itself.lxxxiv The discursivity of memory can be understood in two ways, and whichever way it is understood, therein lies the necessity to couple memory with narrativity. Memory “demands to be said”. First and foremost, the discursive nature of a happy memory means that one is capable of sharing one’s memories with others. Sharing one’s memories with others necessarily entails appropriating from the triadic structure of narrativity. The lived experiences one recounts to others are disclosed in the form of a life story, resting on the threefold relation of prefiguration, configuration, and refiguration. Secondly, prior to an instance wherein one shares a life story with others, memory is discursive in another capacity. As discursive, one’s memories metaphorically ‘speak’ to the subject to whom the memory belongs. Memory itself places on the subject the “demand to be said”. In other words, to understand a memory, to understand the meaning of a past lived experience, to understand the meaning of

78 one’s present in relation to the past, one must interpret one’s memories. To be clear, what I am describing as the ‘discursivity’ of memory is not meant to imply that memory as such is ‘always, already’ in a narrative form, or that, as human beings, that which we experience is ‘naturally’ or ‘ordinarily’ organized by consciousness as a narrative. Rather, in an effort to better understand the experiences that one has endured, one must appropriate features of narrativity. As I have stated elsewhere, one’s recourse to narrativity does not designate a psychological phenomenon, but an ontological condition of possibility.lxxxv I shall add here that the possibility is that of interpreting one’s life with the view of gaining a better understanding of who one is. Such a task requires that one borrow from narrativity. Such a task requires, then, the middle concept of narrative memory. Narrative memory relies on both personal and collective memory. Personal: Any recounted memory is one that is narrated by someone. The activity of recounting a memory contains a claim concerning the veracity of the experience; the memory has fidelity to the past. In recounting a memory to my best friend, I attest to him that this really happened to me. Making this attestation necessarily relies on the mineness of memory—the narrated memory conveys that there was something it was like for me to endure the experience being remembered, recounted. Collective: In order for a memory to be recounted— and in order for the recounted memory to be understood by others—it must appropriate features of narrativity, and these features are conditioned by the tradition to which one belongs, whichever specific tradition it may be. Beyond this, it may also be said that collective entities—such as governments, institutions, or organizations—‘have’ memories, and these memories may help shape their underlying values, may help determine the relationship they have with the society in which they operate. To the extent that this is the case, a narrated memory can convey or further articulate the ‘meaning’ that these memories have for the way in which a collective entity ‘understands’ itself.lxxxvi Through narrative memory, the discursive nature of memory refigures the other three features of a happy memory. Working backwards, the notion of narrative memory refigures recognition. I stated earlier that, phenomenologically, a recognized memory is recognized as a memory because it is constituted as being of the past. Through the resources of narrative, the pastness of one’s past becomes analogously similar to the pastness of one’s tradition. In the same way that the relationship one has with one’s tradition is marked by belongingness and distanciation, so too can we find belongingness and distanciation with regard to the relationship with one’s past.lxxxvii As such, my past ‘belongs’ to me, and I to it. Yet, I am capable—through the process of interpreting my life—to discover, uncover, recover, and create meaning that deepens or transcends a pure description of the circumstances of my life—and the same goes for those with whom I share my life story. They are just as capable of discovering meaning that is consistent with—or in conflict with—my own interpretation of my life story.

79 Through narrative memory, an accessible memory is no longer one that is simply easily recalled. It is one that is more fully integrated into one’s coherent life story. When recounting such an integrated memory, one can understand more deeply where it ‘fits’ with regard to one’s identity. Think back, for instance, to Maria from this paper’s introduction. Her memory of learning to make flan with her mother was not simply a detached ‘episode’ from her life—with little to no bearing on the way in which she conceives herself. Rather, this memory has meaning to her; it ‘factors’ in to her life story; it gives her a sense of ‘who’ she is, as well as her ‘place’ within her family, as she continues to live out and express her family’s traditions. Narrative memory, then, has the capacity to illustrate who one was, who one currently is, and who one may become. Through the synthetic capacity of narrative, a happy memory refigures its nonpathological characteristic by putting the aporia between memory and imagination to use. In this sense, the imagination is no longer reducible to its hallucinatory capabilities—as Sartre emphasized.lxxxviiiThe understanding of the imagination upon which the aporia rests is no longer strictly phenomenological; it is hermeneutic. As Amalric has argued, Riceour’s hermeneutic understanding of the imagination is poetic, rather than perceptual; it grants to the subject the capacity to synthesize multiple interpretations of an event, phenomena, or state of affairs, and to put that synthesis into action.lxxxix Taken in this light, the nonpathological nature of a happy memory ought to be reframed. That memory requires the resources of the (hermeneutic) imagination entails that memory, first and foremost, is not an epistemological issue—as in, “how do I know that this memory is true?” Memory is, primarily, a theme in philosophical anthropology. The issue is not necessarily about the veracity of one’s memories, but about whether one is being faithful to the events and the experiences of one’s past. To designate a memory as a happy memory is to also attest to one’s existential authenticity.

CONCLUSION I shall conclude by clarifying the underlying argumentative arc of this paper. Given that the aporia between personal and collective memory is structured similarly to that of the aporia between phenomenological and cosmological time, Ricoeur’s theory of narrativity—in addition to other constitutive elements of his hermeneutic philosophy (e.g. being-affected by the past, traditionality)—is capable of responding to the aporia of the subject of memory similarly to how it responds to the aporia of time. Responding to the aporia of time required developing a third, mediating concept of time—historical, or narrated, time. The historical understanding of time weaved together both phenomenological and cosmological accounts of time. Historical time was also capable of transcending the limits of both phenomenological and cosmological time. In other words, historical time becomes its own paradigm—

80 capable of being understood on its own terms. From this emerged Ricoeur’s thesis of being-affected by the past, as well as the dialectic of belongingness and distanciation. Human beings belong to a historical past, and this past both informs the way in which humanity receives the present, while also at the same time sketching out a horizon for future action (and suffering). However, there is also a distance that demarcates humanity’s relationship with the past—a temporal fission. This allows humanity to reinterpret its own past, alter the meaning-potential that the past has to offer, and thus, alter the course of human history. Yet, reinterpreting the past necessitates that we are beings capable of utilizing the resources of narrativity in order to uncover or recover the various meaning-potentials contained within the past. History, as I articulated throughout this paper, has a discursive element. Being-affected by the past does not only describe humanity’s relationship with time, it also describes each individual’s relationship with their own life story. In the same way that human beings simultaneously belong to and are distant from human history via the intermediary network of traditionality, individuals belong to and are distant from their own past. In the same way, then, that one may interpret and reinterpret (human) history, one may interpret and reinterpret one’s own history, one’s own past. Memories lend themselves to this interpretive process, and are that upon which the stories one tells about oneself—or that others tell about oneself—are based. It is not enough, then, for memory to be viewed or investigated purely from the lens of phenomenology (personal memory) or solely from that of sociology (collective memory). Memory—human memory—is a matter of hermeneutic concern. Human memory is narrated memory. A narrated memory is one that is integrated into a coherent life story, and a coherent life story is made possible by the intersubjective nature of human existence.

81 i The

following analysis is based on Ricoeur, Memory, History, Forgetting, pp. 93 – 132. should note that the aporia between personal and collective memory is one of two aporias that Ricoeur develops in Memory, History, Forgetting. The other aporia is that between memory and imagination. As Ricoeur frames it, the central issue here is the epistemic problem posed by memory’s reliance on the imagination in order for a past lived experience to be recalled. That memory requires the imagination means that memory is fallible, and this fallibility is an inescapable fact of memory as such. From my own reading, Ricoeur privileges this aporia to such an extent that the profundity of—as well as the poetic response to—that between personal and collective memory is occluded, hence the undertaking of this paper. iii Consider Ricoeur’s own description on p. 95 of Memory, History, Forgetting: “In this intensely polemical situation, which opposes a younger tradition of objectivity [sociology] to the ancient tradition of reflexivity [philosophy], individual memory and collective memory are placed in a position of rivalry. However, they do not oppose one another on the same plane, but occupy universes of discourse that have become estranged from each other.” iv I should note that I am phrasing the aporia as “the central aporia of time” carefully, as it is not the only aporia. Indeed, Ricoeur goes through great lengths in the third volume of Time and Narrative to show that Husserl’s account of internal time consciousness can create and multiply its own set of aporias with regard to time. Even further, Ricoeur’s critical assessment of internal time consciousness continues in Memory, History, Forgetting, specifically with regard to the first aporia of memory, that of memory and imagination, to which I refer in the previous footnote. v Indeed, though phenomenology plays a central role in both the aporia of time in Time and Narrative, and of personal and collective memory in Memory, History, Forgetting, it is important to note that the respective ‘other’ to phenomenology in each aporia is a strikingly different branch of science—cosmology, on the side of time, and sociology, on the side of memory. There is, thus, an intellectual risk that I am undertaking in pursuing the avenue of thought on which I am traveling. However, it strikes me as a necessary risk, as one of the guiding insights that I have in this paper is that, while the first aporia between memory and imagination is rigorously developed and addressed, that between personal and collective memory remains much less so. This paper is an attempt to address what seems to be an aporia that is just as important as that which is internal to the phenomenology of memory. vi I shall develop the notion of a ‘poetic response’ at the beginning of the third section of this paper. vii I shall treat the two terms as being interchangeable with each other. viii Significant portions of this paper are based off of a chapter I am writing for my dissertation at the Katholieke Universiteit Leuven. My dissertation, as a whole, is an investigation of the intersections between Ricoeur’s account of narrative selfhood and memory. In this much larger work, I am weaving a thread that attempts to unite the later works of Ricoeur, from Time and Narrative to Memory, History, Forgetting through the subjectivity of the human individual. ix Ricoeur, Paul. “Life in Quest of Narrative.” In On Paul Ricoeur: Narrative and Interpretation, pp. 20 – 33. New York: Routledge, 1991. x Ricoeur, “Life in Quest of Narrative”, pp. 20 – 21. xi According to Ihde, it is characteristic of the ‘middle Ricoeur’ to analyze phenomena that have double- or triplemeanings. See Ihde, Don. “Paul Ricoeur’s Place in the Hermeneutic Tradition”. In The Philosophy of Paul Ricoeur, pp. 59 – 70. Chicago: Open Court, 1995. xii Ricoeur, Paul. Time and Narrative. Translated by Kathleen McLaughlin and David Pellauer. Vol. 1 - 3. Chicago: University of Chicago Press, 1988 xiii See Ihde, “Paul Ricoeur’s Place in the Hermeneutic Tradition”, as well as Bourgeois, Patrick, “The Limits of Ricoeur’s Hermeneutics of Existence” in The Philosophy of Paul Ricoeur, pp. 549 – 566, and Michel, Johann. Ricoeur and The Post-Structuralists. New York: Rowman and Littlefield, 2015. xiv Ricoeur, “Life in Quest of Narrative”, p. 21. xv Ibid. xvi Ibid. xvii Ibid., 22. xviii Ibid. xix See, for instance, Ricoeur, Paul, “What is a Text?” In From Text to Action: Essays in Hermeneutics, II, pp. 105 – 124. Evanston: Northwestern University Press, 2007. ii I

82 xx Ricoeur, “Life

in Quest of Narrative”, p. 26. “Hermeneutics and the Critique of Ideology”, p. 298. xxii Ricoeur, “Life in Quest of Narrative”, p. 26. xxiii Blamey, Kathleen, “From the Ego to the Self: A Philosophical Itinerary”. In The Philosophy of Paul Ricoeur, pp. 571 – 603. xxiv Ricoeur, Time and Narrative Vol. III, p. 3. xxv I am switching between a Husserlian and Heideggarian vocabulary out of fidelity to Ricoeur’s analysis of the aporia of time, which, from the phenomenological perspective, entails the philosophies of Augustine, Husserl, and Heidegger. xxvi Stevens, Bernard, “On Ricoeur’s Analysis of Time and Narration”. In The Philosophy of Paul Ricoeur, pp. 499 – 506. xxvii Ricoeur, Time and Narrative Vol. III, p. 25. The a priori truths of time are: 1) That the temporal order is fixed and two dimensional; 2) that two different temporal points can never coincide; 3) that the relationship between two distinct temporal points is that of non-simultaneity; and 4) that time is organized by an ‘earlier’ and a ‘later’. xxviii Ricoeur, Time and Narrative, p. 44. xxix Ibid. xxx Godlove, Jr., Terry. “Ricoeur, Kant, and the Permanence of Time.” In The Philosophy of Paul Ricoeur, pp. 399 415. Chicago: Open Court, 1995. xxxi Ricoeur, Time and Narrative Vol. III, p. 57. xxxii See, Ricoeur, Time and Narrative Vol. III, p. 4, where he states, “My aim will be to discover what resources a poetics of narrative possesses for, if not resolving, at least making this aporia work for us.” (Italics mine). As Michel has argued, though Ricoeur himself never had the opportunity to more fully engage with American pragmatism, his manner of responding to aporias certainly has pragmatic undertones. See: Michel, “Anthropology of Homo Interpretans,” p. 17. xxxiii Ricoeur, Time and Narrative Vol. III, p. 104. xxxiv Ibid, p. 105, 109, 116, respectively. xxxv Ibid, p. 107. xxxvi Ibid. xxxvii Ibid, p 110. xxxviii The historical trace ought not be confused with Ricoeur’s notion of the mnemonic trace, which he develops in Memory, History, Forgetting. There, Ricoeur’s position was that the mnemonic trace is that residue upon which memory must have recourse to the imagination in order for one to recollect, reminisce, or remember. In terms of historical time, the historical trace is a similar phenomenon. Whereas the mnemonic trace required the resources of the imagination, the historical trace de facto lends itself to narrativity. Later, I will show how the mnemonic trace also requires enrichment from narrative, and thus, must go beyond Ricoeur’s phenomenological analysis of memory. xxxix Ibid, pp. 119 – 120. xl Ibid. xli Zimmerman, Jens. Hermeneutics. Oxford: Oxford University Press, 2015. According to Zimmerman, the notion of being-affected by the past is one of the chief positions that unites all of the 20th century and contemporary hermeneutic philosophers. xlii Gadamer, Hans-Georg. Truth and Method. Translated by Joel Weinsheimer and Donald G. Marshall. London: Continuum, 2004. xliii Ricoeur, Time and Narrative Vol. III, p. 217. xliv Zimmerman, Hermeneutics, p. 40. xlv I should add that Ricoeur’s clarification of traditionality also served to show that hermeneutics is not susceptible to the fallacy of the appeal to tradition, which was one of the dominant criticisms of hermeneutics at the time that Time and Narrative was published. As I will later show, Ricoeur’s position is that one always already belongs to and is distant from one’s tradition—and this relationship of distanciation entails the capacity to critique and break from the confines of the more morally repugnant features of one’s tradition. See, Ricoeur, Paul, “Hermeneutics and the Critique of Ideology.” In From Text to Action, pp. 270 - 307. Evanston: Northwestern University Press, 2007. xxi Ricoeur, Paul,

83 xlvi Ricoeur, “Hermeneutics and the Critique of Ideology”, pp. 294 – 301. This is a similar dialectic, I should note, to that of innovation and sedimentation that we see in narrative and in selfhood (habit formation). xlvii Ricoeur, Time and Narrative Vol. III, p. 222. xlviii Ibid, p. 221. xlix Ibid, p. 220. l Ibid. li Ricoeur favors understanding the present as a lived-present, as it shifts our focus away from a ‘philosophical optics’—that is, our tendency to understand the present through a phenomenology of perception. Ricoeur’s view emphasizes understanding the present as it relates to a philosophy of action. lii Ricoeur, Time and Narrative Vol. III, pp. 220 - 221. liii Ibid, p. 220. liv Ibid. lv Ibid, p. 216. lvi Ibid, p. 220. lvii Ibid, p. 221. lviii Buber, Martin. I and Thou. Translated by RG Smith. New York: Scribner, 1958. Levinas, Emmanuel. Totality and Infinity. Translated by Alphonso Lingis. Pittsburgh: Duquesne University Press, 2004. lix Ricoeur, “What is a Text?” p. 108. lx Ricoeur, “Hermeneutics and the Critique of Ideology”, p. 298. lxi Ricoeur, “The Model of the Text”, p. 145. lxii Ibid, p. 146. lxiii Ibid, p. 148, emphasis mine. lxiv Ricoeur, Paul, “Explanation and Understanding” In From Text to Action: Essays in Hermeneutics, II, pp. 125 143. Evanston: Northwestern University Press, 2007 lxv Ricoeur, “The Model of the Text”, p. 148. lxvi Ibid. lxvii Ibid, 149. lxviii I am alluding to the section in Vol. I of Time and Narrative on Mimesis3. As Ricoeur states, “it is the reader who completes the work inasmuch as… the written work is a sketch for reading.” Ricoeur even goes on to say that in some cases, the reader’s role is to carry “the burden of emplotment”. Time and Narrative Volume I, p. 77. lxix Ricoeur, “Hermeneutics and the Critique of Ideology”, p. 298. lxx Ricoeur, Memory, History, Forgetting, p. 131. lxxi Ricoeur, Oneself as Another, p. 172. lxxii Ricoeur, Memory, History, Forgetting, p. 130. lxxiii Ricoeur, Oneself as Another, pp. 88 – 168. lxxiv Ricoeur, Memory, History, Forgetting, p. 494. lxxv Ricoeur makes explicit reference to the nonpathological nature of a happy memory on p. 37 and 412 of Memory, History, Forgetting. lxxvi While a fuller treatment of this aporia would be beneficial to my analysis, doing so would certainly be beyond the confines of this paper. I shall simply refer the reader back to the sketch of the aporia provided in endnote 2. lxxvii The accessibility of a happy memory is referenced on pages 58, 65, 77,98, and 99 of Memory, History, Forgetting. lxxviii Ibid, pages 391, 414, 429. lxxix Ibid, p. 54. lxxx Ibid, p. 494. lxxxi Ibid, p. 15. lxxxii Ibid, pages 143, 494 - 496.

84 lxxxiii Arca, Kris, “Opaque Selves: A Ricoeurian Response to Galen Strawson’s Anti-Narrative Arguments.” In Études Ricoeuriennes/Ricoeur Studies, Vol. 9, No. 1 (2018), p. 74. lxxxiv Ricoeur, "Phenomenology and Hermeneutics," p 39. lxxxv Arca, Kris, “Opaque Selves”, p. 84. lxxxvi Though, I should also hasten to add that, in order for any such collective entity to utilize the capacity of narrativity, it is necessary for someone, that is, a person, to put that memory into words. So we see here an intermingling of both the personal and the collective. lxxxvii Ricoeur, Memory, History, Forgetting, p. 496. lxxxviii Sartre,

Jean-Paul. The Psychology of Imagination. New York: Citadel, 1965. 86

lxxxix Amalric, Jean-Luc, “L’imagination poético-pratique dans l’identité narrative,” in Études Ricoeuriennes/Ricoeur Studies 3, No. 2 (2012): 110 – 127

Acknowledgment The author is thankful to the reviewer’s valuable and constructive suggestions whichconsiderably improved the presentation of the paper.

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