Editorial Note:
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. In this issue, we find seven articles that celebrate the scholarship of teaching
and learning from different academic disciplines. As we cannot understand a polygon merely by contemplating its sides, our goal
is to present work that represents the campus as a whole. We encourage our colleagues to send in submissions for the next issue of
Polygon. The editorial committee and reviewers would like to thank Dr. Goonen, Dr. Bradley-Hess, Dr. Castro, and Prof. Jofre for
their unwavering support. Also, we would like to thank Mr. Samuel Hidalgo and Mr. John Munoz of Media Services for their
work on the design of the journal. In addition, the committee would like to thank the contributors for making this edition possible.
It is our hope that you, our colleagues, continue to contribute and support the mission of the journal.
Sincerely, The Polygon Editorial Committee The Editorial Committee: Dr. Mohammad Shakil - Editor-in-Chief Dr. Jaime Bestard Prof. Victor Calderin
Patrons: Dr. Norma M. Goonen, Campus President Dr. Ana Maria Bradley-Hess, Academic Dean Dr. Caridad Castro, Chair of Arts and Sciences Prof. Maria Jofre, Chair of EAP and Foreign Languages
Reviewers: Prof. Steve Strizver-Munoz Prof. Joseph Wirtel
Mission of Miami Dade College The mission of the College is to provide accessible, affordable, high-quality education that keeps the learner’s needs at the center of the decision-making process.
Miami Dade College District Board of Trustees Helen Aguirre Ferré, Chair Peter W. Roulhac, Vice Chair Armando J. Bucelo Jr. Marielena A. Villamil Mirta "Mikki" Canton Benjamin León III Robert H. Fernandez Eduardo J. Padrón, College President
Editorial Notes
i
Guidelines for Submission
ii-iii
Waiting for a Pattern in Coin Tossing
1-5
Common Mistakes Made by Native Spanish Speakers
6-10
The Importance of the Study of Evolution in the Course PSC1515 "Energy in the Natural Environment"
11-14
A. Rodriguez
On an Iterative Algorithm in Multiobjective Optimization
15-26
J.A. Serpa
African-Americans in Mathematical Sciences - A Chronological Introduction
27-42
M. Shakil
Survey of Students' Familiarity with Grammar and Mechanics of English Language - An Exploratory Analysis
43-55
M. Shakil, V. Calderin, and L. Pierre-Phillip
Effects of Developmental Courses on Students' Use of Writing Strategies on the Florida College Basic Skills Exit Test
56-80
M. L. Varela
Comments about Polygon
81-82
M. Andreoli M. Orro
Disclaimer: The views and perspectives presented in these articles do not represent those of Miami Dade College. Â
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POLYGON: Many Corners, Many Faces (POMM) A premier professional refereed multi-disciplinary electronic journal 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 increase information dissemination. It is published by MDC Hialeah Campus Arts and Sciences Department.
Editorial Committee: Dr. Mohammad Shakil (Mathematics), Editor-in-Chief Dr. Jaime Bestard (Mathematics), Editor Prof. Victor Calderin (English), Editor
Manuscript Submission Guidelines: Welcome from the POLYGON Editorial Team: The Department of Arts and Sciences at the Miami Dade College–Hialeah Campus and the new 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 increase information dissemination. We are pleased to have the opportunity to continue the publication of the POLYGON, which will be anually during the Spring term 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 the submission 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 10-11. 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.
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 readers to 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 submitted to either
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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 150 words 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 the editorial office of any changes to the authorship, securing written permission (via email) from each co-author to sign the copyright agreement 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 warranty listed in the agreement, you will be the sole author indemnifying the publisher and the editor of the journal against such 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.
Polygon Spring 2010 Vol. 4, 1-5
WAITING FOR A PATTERN IN COIN TOSSING "
M. Andreoli" Department of Mathematicsß Miami-Dade College, North Campusß Miami, FL 33167ß USA, Email: mandreol@mdc.edu ABSTRACT
Two commonly held misconceptions regarding a sequence of tosses of a fair coin are addressed. The reasons for the misconceptions are discussed, and the correct analysis is provided. The results are somewhat surprising to most people. The mathematical derivation of the correct results is followed by a discussion of why our intuition may have initially misled us. Suggestions for various generalizations of the problem follow. KEYWORDS: Probability, conditional expectation, waiting times. Mathematics Subject Classification: 60C05, 65C50. 1. INTRODUCTION The Problem: Consider a sequence of independent tosses of a fair coin. Suppose we are waiting for a certain pattern to occur for the first time, say HHTT. We invite the reader to consider the following two questions, and guess the answers before reading on. Q1: Which pattern requires a longer expected time to occur: HH or TH? Q2: Which pattern has a higher probability of occurring first: HHH or THH? Many, if not most people answer the questions as follows: A1: A2:
"The expected times are the same for each pattern." "Each pattern has an equal chance of occurring first."
How many readers answered this way? This certainly seems reasonable, since we have assumed the coin is fair. Unfortunately, as we propose to show in this note, both answers are incorrect. We will prove this by explicitly computing the relevant expectations and probabilities. 2. NOTATION AND PRELIMINARIES We use standard notation, where T ÐEÑ denotes the probability that event E occurs. T ÐElFÑ denotes the probability that event E occurs, given that event F has occurred. The mean, or expected value of a random variable \ is denoted IÐ\ÑÞ The conditional expectation, denoted IÐ\l] Ñ, is the expected value of \ given ] ß and is a function of ] Þ We will need the following results, the proofs of which can be found in almost any introductory probability text. My personal favorite is [1].
© 2010 Polygon
1
Waiting for a patterná PROPOSITION 1.1 If \ and ] are discrete random variables with finite expectation, then IÐ\Ñ œ " IÐ\l] Ñ T Ð] œ CÑÞ C
See [1, p.335] for a proof. PROPOSITION 1.2 In a sequence of independent trials, each of which has probability : of success, with ! : "ß the expected number of trials until a success is first observed is "Î:Þ See [1, p.168] for a proof. The latter proposition gives the mean of the geometric distribution. In particular, when tossing a fair coin, the expected number of tosses required to observe heads is 2. 3. COMPUTING THE EXPECTED TIMES Let RE denote the time (number of tosses) required to observe the first occurrence of HH in a sequence of tosses of a fair coin. Conditioning on the outcomes of the first two tosses, we have Ú2
IÐRE lfirst two tossesÑ œ Û # IÐRE Ñ Ü " IÐRE Ñ
first two tosses are HH, w.p. "Î% first two tosses are HTß w.p. "Î% . first toss is T, w.p. 1/2
Unconditioning, that is, applying Proposition 1.1, we have IÐRE Ñ œ # † Ð"Î%Ñ Ò# IÐRE ÑÓ † Ð"Î%Ñ Ò" IÐREÑÓ † Ð"Î#ÑÞ Solving for IÐRE Ñ yields IÐRE Ñ œ 'Þ Now let RF denote the number of tosses required to observe TH. Calculation of the expected time is a bit simpler. IÐRF lfirst tossÑ œ œ
" IÐRF Ñ first toss is H, w.p. "Î# . " IÐtime to first H) first toss is T, w.p. 1/2
Unconditioning, and recalling that IÐtime to first HÑ œ #ß we have IÐRF Ñ œ Ò" IÐRF ÑÓ † Ð"Î#Ñ $Î#ß and solving for IÐRF Ñ yields IÐRF Ñ œ %Þ
2
Andreoli
To summarize: IÐtime to first occurrence of HHÑ œ '. Ð"Ñ IÐtime to first occurrence of TH) œ %Þ We must conclude then, that IÐtime to first occurrence of HHÑ Á IÐtime to first occurrence of TH), a result many people find counterintuitive.
4. COMPUTING THE PROBABILITY THAT ONE PATTERN PRECEDES ANOTHER Let E and F respectively denote the sequences HHH and THT. Define the following random variables. RE œ the number of tosses until E appears. RF œ the number of tosses until F appears. RElF œ the additional number of tosses for E to appear after F has appeared. RFlE œ the additional number of tosses for F to appear after E has appeared. Q œ minÐRE ß RF ÑÞ Finally, let TE denote the probability that pattern E occurs before pattern FÞ Our goal in this section is to find TE Þ As a bonus we will also find IÐQ ÑÞ We begin by computing IÐRE Ñ œ IÐRElF ÑÞ Note that for pattern E to occur, the pattern HH must occur first. Conditioning on the result of the toss immediately following the first occurrence of HH, we have, in view of (1), IÐRE lnext toss after HHÑ œ ' œ
if next toss is H, w.p. 1/2 " Þ 1 IÐRE Ñ if next toss is T, w.p. 1/2
Unconditioning, IÐRE Ñ œ ( Ð"Î#ÑIÐRE Ñß and we conclude that IÐRE Ñ œ IÐRElF Ñ œ "%Þ In the same way we can compute IÐRF Ñß and we find that IÐRF Ñ œ IÐRFlE Ñ œ "!Þ Moreover, following Ross [2 p.232], we have IÐRE Ñ œ IÐQ Ñ IÐRE Q Ñ œ IÐQ Ñ IÒRE Q l F before EÓÐ" TE Ñ œ IÐQ Ñ Ð" TE ÑIÐRElF ÑÞ 3
Waiting for a patterná Similarly, IÐRF Ñ œ IÐQ Ñ TE IÐRFlE ÑÞ Solving these equations yields TE œ
IÐRF Ñ IÐRElF Ñ IÐRE Ñ ß IÐRFlE Ñ IÐRElF Ñ
and IÐQ Ñ œ IÐRF Ñ IÐRFlE Ñ TEÞ For the particular case at hand, TE œ
"! "% "% & œ ß "! "% "#
IÐQ Ñ œ "! "!Ð
& $& Ñœ Þ "# '
In particular, we note that TE œ T ÐE occurs before FÑ "Î#ß a result many people find counterintuitive.
5. INTUITION ADJUSTMENT When faced with a counterintuitive result, most of us scrutinize what went wrong with our intuition, and try to improve it. We offer the following scenario as an aid to "intuition adjustment". Suppose we are to observe independent tosses of a fair coin and are to be awarded a large sum of money when the pattern HH first occurs. When the first heads occurs, our pulse quickens. Suppose alas, that the next toss is tails. We are discouraged, for now we must start from scratch. On the other hand, suppose we are to be awarded a large sum of money when the pattern TH first occurs. When the first tails appears, our pulse quickens, but suppose, alas, that the next toss is tails. We are disappointed, of course, but things are not so bad. We need not start from scratch, in fact we may win on the very next toss. In view of these considerations, perhaps the results we have derived in this note do not seem so surprising. Yet, the heuristic argument above is of no help in actually computing the expected time for a pattern to occur, or in computing the probability that one pattern precedes another. 6. GENERALIZATIONS Many generalizations to the questions addressed in this note suggest themselves. In the first place, the coin might be biasedß where the probability of getting heads on a single toss is :ß and the probability of tails is ; œ " :Þ Actually this does not present any substantial difficulty if the length of the patterns involved is relatively small, say two or three as considered above. The reader is encouraged to work out the answers to Q1 and Q2 for a biased coin. A far more serious drawback to the methods presented here comes about when we consider longer patterns, such as computing the expected time required to observe the pattern HHHTHTHHH. 4
Andreoli The reason is obvious if one recalls that to compute the expected time to HHH, we needed to first derive the expected time to HH. The amount of calculation for long patterns grows daunting in a hurry. Then there is the issue of generalizing the results to an experiment where a single trial may result in 8 # possible outcomes, where outcome 3 occurs with probability :3 Þ Imagine tossing a "ten sided biased coin" for example, and trying to compute the expected time until some pattern of length 30 appears. Fortunately, the problem has been solved in complete generality. The interested reader may consult Ross [2, pp. 231-233] for one method of doing so. Ross uses the theory of Martingales in his analysis. While he only works out two specific examples, these examples make it clear how to proceed to the general case, with only a modest amount of calculation. Ross uses a completely different method than the one used here, except as noted in section 3. ACKNOWLEDGMENT I am indebted to Ross for bringing this type of problem to my attention in the first place. I took the liberty of using Ross' notation, where the symbols RE ß RFlE and TE are employed. REFERENCES 1. Sheldon Ross, E J 3<=> G9?<=/ 38 T <9,+,363>C , 4th ed., Macmillan, New York, 1994. 2. Sheldon M. Ross, W>9-2+=>3- T <9-/==/=ß Wiley, New York, 1983.
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Polygon Spring 2010 Vol. 4, 6-10 COMMON MISTAKES MADE BY NATIVE SPANISH SPEAKERS
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M. Orro1 Department of ESL and Foreign Languages, Miami Dade College, North Campus, Miami, FL 33167, USA. Email: morro1@mdc.edu
ABSTRACT Language errors are quite common in any language, so it shouldn't come as a surprise that native speakers of Spanish would make mistakes when speaking their language, and although they generally aren't the same mistakes that are likely to arise in English, they are probably as common. This paper presents a sample of some of the most common errors made by native speakers of Spanish. Such mistakes are addressed in the courses SPN2340 and SPN2341 [Spanish for Native Speakers I and II] at Miami Dade College. Both courses also satisfy several of the Learning Outcomes of MDC, most notably #1 [Communicate effectively using listening, speaking, reading, and writing skills], and #5 [Demonstrate knowledge of diverse cultures, including global and historical perspectives]. KEYWORDS Spanish, lexical variations, common mistakes, spelling, grammar.
1. INTRODUCTION
Unless you're an incessant perfectionist for grammatical details, chances are you could make dozens of errors each day in the way you speak. And you might not notice until you're told that a sentence, or a word wrongly said, is enough to make some language perfectionists grit their teeth.
Since language errors are so common in English, it shouldn't be surprising that Spanish speakers often make their share of mistakes too when speaking their language. Mistakes, particularly in grammar, are probably every bit as common in Spanish as they are in English.
In many instances, there is no such thing as right or wrong when it comes to language, only differences in how various word usages might be perceived. For example, there are
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lexical variations noted in many standard Spanish words such as ‘piscina’ (swimming pool), that in Mexico is referred to as ‘alberca’, but in Argentina is ‘pileta’, or ‘frijoles’ (beans) which in Venezuela are called ‘caraotas’, in Puerto Rico ‘habichuelas’, and in Argentina ‘porotos’, and also ‘campesino’ (country person), which in Cuba is named ‘guajiro’, but in Chile is known as ‘huaso’, and in Puerto Rico ‘jíbaro’. There are also cases in which one word may have different meanings, depending on the region where it is used, as is the example of the slang word ‘guagua,’ which in the Caribbean is a bus, but in the Andes region is a baby, or the verb ‘coger’ (to catch, to get), which in most parts is used in its proper meaning, but in some other places carries a vulgar connotation. I could go on and on citing many other similar examples, but that would be the topic for another article. The point I wanted to bring across in presenting the few examples above is that, although there is generally a standard lexicon used in all Spanish-speaking countries, nonstandard varieties should not be dismissed as useless or undesirable mistakes,
but
rather
as
different
uses
of
the
same
word.
When it comes to grammar though, the situation is quite different because in this case, it’s not a matter of simply dealing with lexical variety, but with mistakes regarded as ‘unacceptable’ by most educated people.
2. Most Common Errors Made by Spanish Speakers Following is a list of some of the most common errors that Spanish speakers often make; several of them are so common, they even have names to refer to them. Although some speakers, especially in informal contexts, may find these mistakes acceptable, most grammarians and language purists view them as uneducated or plain wrong. So then, since there isn't unanimous agreement in all cases about what is to be considered correct in language usage, some of the examples presented below will be referred to as “improper” rather than as "incorrect".
Dequeísmo — In some areas, the use of de que in lieu of que has become so common, that it is on the verge of being considered a regional variant, but in other areas it is strongly looked down on as being the mark of an inadequate education.
Improper: No creo de que Pedro sea mentiroso.
Proper: No creo que Pedro sea mentiroso. (I don’t believe Pedro is a liar.)
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Loísmo and laísmo — Le is the correct pronoun to use as the indirect object meaning "to/for him" or " to/for her." However, lo is sometimes used for the male indirect object pronoun, particularly in some parts of Latin America, and la for the female indirect object pronoun, especially in certain parts of Spain.
Improper: La envié una carta. Lo escribí.
Proper: Le envié una carta (a ella). Le escribí (a él). (I sent her a letter. I wrote to him.)
Leísmo — On the other hand, lo is the correct pronoun to use as the direct object meaning “him.” However, le is sometimes used for the masculine direct object, although mainly in Spain.
Improper: Le vi ayer.
Proper: Lo vi ayer. (I saw him yesterday)
Quesuismo — Cuyo is often the Spanish equivalent of the adjective "whose," but it is used infrequently in speech. One quite popular alternative is the use of que su.
Improper: Conocí a una señora que su gato estaba muy enfermo.
Proper: Conocí a una señora cuyo gato estaba muy enfermo. (I met a lady whose cat was very sick.)
Plural use of existential haber — In the present tense, there is practically no confusion in the use of haber in a sentence such as "hay una silla" ("there is one chair") and "hay tres sillas" ("there are three chairs"). In all other tenses, the rule is the same — the singular conjugated form of haber is used for both singular and plural subjects. However, in most of Latin America, and also in some parts of Spain, plural forms are often heard and are sometimes simply considered as a regional variant.
Improper: Habían tres sillas.
Proper: Había tres sillas. (There were three chairs.)
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Misuse of the gerund — The Spanish gerund (the verb form ending in -ando or -iendo, generally the equivalent of the English verb form ending in "-ing") should generally be used to refer to another verb, not to nouns as can be done in English. Yet, it appears to be increasingly common to use gerunds to anchor adjectival phrases.
Improper: No conozco al hombre hablando con Teresa.
Proper: No conozco al hombre que habla con Teresa. (I don't know the man speaking with Teresa.)
Errors in verb conjugation — There are numerous mistakes made when conjugating verbs in different tenses. One of the most recurrent gaffes made in this category is the addition of an the letter ‘s’ to the second person singular form (tú) of verbs in the preterit tense, for example: hablastes instead of hablaste (you spoke); or the improper usage of irregular verbs in either the preterit or the subjunctive, such as: conducí instead of conduje (I drove), and indució instead of indujo (he/she induced), or haiga instead of haya (there is/there are) and satisfazca instead of satisfaga (satisfy); last, but not least, the common use nowadays of the non-standard past participle rompido instead of the standard roto (broken).
Spelling mistakes — Since Spanish is a very phonetic language, it is normal to think that mistakes in spelling should be unusual. However, while the pronunciation of most words can almost always be deduced from their spelling (the main exceptions are words of foreign origin), the reverse isn't always true. Native speakers frequently mix up the identically pronounced b and v, or y and ll, for example, and occasionally add a silent h where it doesn't belong or vice versa. It isn't unusual either for native speakers of Spanish to be confused on the use of orthographic accents, that is, they may mistake aun (even) with aún (still), el (the) with él (he), mas (but) with más (more), mi (my) with mí (me), que (that) with qué (what), si (if) with sí (yes), solo (alone) with sólo (only), or tu (your) with tú (you), which are pronounced identically.
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3. CONCLUSION
SPN2340 and SPN2341, two courses offered at MDC specifically designed for native speakers of Spanish, provide our considerably large population of bilingual students with the opportunity, not only to learn about all the common mistakes presented above (and many more), but to develop and improve their communicative skills [LO#1]. These courses also expose students to the history, literature, films and current events of the Hispanic world, thus expanding their cultural horizons and encouraging them to explore other corners of the world in a different light [LO#5].
REFERENCES
Marqués, Sarah (2005). La lengua que heredamos. Curso de español para bilingües. (5th Ed.) New Jersey: John Wiley & Sons, Inc.
Ortega, Wenceslao (1988). Redacción y composición. Técnicas y prácticas. Mexico: McGraw-Hill. Valdés, G., Dvorak, T., & Pagán-Hannum, T. (2008). Composición. síntesis. (5th Ed.) New York: McGraw-Hill Higher Education.
Proceso y
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Polygon Spring 2010 Vol. 4, 11-14 THE IMPORTANCE OF THE STUDY OF EVOLUTION IN THE COURSE PSC1515 “ENERGY IN THE NATURAL ENVIROMENT”
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A. Rodriguez 1 Department of of Chemistry/Physics/ Earth Sciences, Miami Dade College, North Campus, Miami, FL 33167, USA. Email: arodri10@mdc.edu ABSTRACT
This paper demonstrates the importance and relevance of the PSC 1515 course for the students pursuing an Associate in Arts Degree at Miami Dade College (MDC). This course not only provides a general overview of the scientific method but also of the different physical, natural and earth sciences. Of particular relevance is the study of evolution, which is a recurrent controversial topic in our society because of the apparent conflict between the scientific and religious points of view. In this paper, it is demonstrated that this controversy is mostly limited only to the United States, although to some degree, it is also expanding to the United Kingdom and other parts of Europe due to the American influence in that part of the world. This course, PSC1515 also satisfies several of the Learning Outcomes (LO) received by MDC’s graduates, particularly LO #3, #6 and #10. KEYWORDS Evolution, creationism, intelligent design, science, religion, and scientific method.
INTRODUCTION One of the most popular courses taken by Miami Dade College (MDC) students, as part of the General Education Requirements for the Associate in Arts Degree, is PSC 1515 “Energy in the Natural Environment”. This course is included in the Natural Science section, Group B – Physical Sciences of the General Education Requirements. In the College Catalog, it appears in the Physics section, as one of the Physical Sciences with a Multidisciplinary approach. The course description in the Catalog portrays it as an “Investigation of the physical Environment using energy as a theme to demonstrate the impact of science and technology on the environment and on the lives of people”. This course satisfies several of the General Education Learning Outcomes (LO) that demonstrate the knowledge acquired by MDC’s students, regardless of their major, particularly Learning Outcomes #3, #6 & #10. Learning Outcome #3 establishes the following: “As graduates of MDC, students will be able to solve problems using critical and creative thinking and scientific reasoning”. This LO is approached since the first
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chapter, in which the Scientific Method is discussed, and it is pursued throughout the entire course content. LO #10 establishes “how natural systems function and recognize the impact of humans in the environment”. The goal of this LO is achieved throughout multiple chapters in the course that discuss energy and its interrelationship with natural systems, as well as the impact of human activities in the environment; special emphasis is placed on global warming and its countless negative impacts in the environment and society, ranging from the impacts on the ecosystems, health, the economy and –even- national security. The importance of LO #6 cannot be highlighted enough. This outcome “creates strategies that can be used to fulfill personal, civic and social responsibilities”. The issues that are discussed in the course, like evolution, global warming, and others will help our students make informed decisions, as members of our society in many personal, civic and social aspects, like voting for the appropriate candidate elections at different levels, and also choosing the correct organizations to be involved with; and these are decisions that reflect what is important, useful and necessary for the well-being of our nation. To fully understand the great importance of the depth of the scientific knowledge that the learning of evolution provides to our students, we must consider the results of the public opinion poll released by the Pew Forum on Religion and Public Life on August 30, 2005, which reveals that “nearly two thirds of Americans want both creationism… to be taught along with evolution in public schools. Fewer than half of Americans – 48% accept any form of evolution… and just 26% accept Darwin’s theory of evolution by means of natural selection. Fully 42% say that all living beings, including humans have existed in their present form since the beginning of time” (cited by Jacoby, 2008). According to Jacoby, 2008, this level of scientific unawareness cannot be blamed solely on the low level of science education in American elementary and secondary schools, as well as in many community colleges. In her book The Age of American Unreason, Jacoby clearly states: “Only 27% of college graduates believe that living beings have always existed in their present form, but 42% of Americans with only a partial college education and half of high school graduates adhere to the creationist viewpoint that organic life has remained unchanged throughout the ages. A third of Americans mistakenly believe that there is substantial disagreement about evolution among scientists – a conviction reinforcing and reflecting… that evolution is “just a theory” (Jacoby, 2008). The graduates of Miami Dade College who take the PSC1515 course, will not be caught in the “just a theory” argument, because the first chapter of this course is dedicated to the study of science and the scientific method, as well as the relationship between science and religion. In this chapter, the students learn the scientific definition of theory. To our students, a theory is ‘a synthesis of a large body of information that encompasses well-tested hypotheses about certain aspects of the natural world’. Thus,
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after taking the PSC1515 course, students of Miami Dade College become part of a considerable percentage of college-educated Americans who will be thoroughly informed about this transcendental scientific theory. 1. CREATIONISM Advocates of the opposition to the study of evolution have attempted to substitute the study of this theory, with the study of the afore cited theory of creationism, which can be briefly defined as the religious belief that human life, the Earth and the Universe were created in some form by a supernatural being, a God. For the Christian religion, creationism is usually based on a literal interpretation of the book of Genesis in the Bible. 2. INTELLIGENT DESIGN The concept of intelligent design was developed by a group of American creationists who reformulated their argument in the creation-evolution controversy to evade court rulings that ban the teaching of creationism as science. Intelligent design is the allegation that some features of the universe (and of living things) are best explained by an intelligent cause, not an undirected process such as natural selection. It is a more contemporary form of the conventional teleological argument for the existence of God, but without specifying the nature or identity of the ‘designer’, or creator. The discussion about intelligent design must start by indicating that most of the scientific community has rejected this idea. The U.S. National Academy of Sciences, the U.S. National Science Teachers Association, and the American Association for the Advancement of Sciences have all denounced intelligent design as a pseudoscience, because it is not testable according to the principles and methods of science. In a statement adopted on July 2003 by the Board of Directors of the National Science Teachers Association, we can read: “The National Science Teachers Association (NSTA) strongly supports the position that evolution is a major unifying concept in science and should be included in the K-12 science education frameworks and curricula. Furthermore, if evolution is not taught, students will not achieve the level of scientific literacy they need”. 3. EVOLUTION In his book, Richard Dawkins states: “all except the woefully uninformed are forced to accept the fact of evolution”, adding to his statement that “…no reputable scientist disputes it [evolution]” (Dawkins, 2009). The National Academy of Science (NAS) and the Institute of Medicine (IOM) released Science, Evolution and Creationism in 2008, where the importance of the teaching of evolution in the science classroom was emphasized, or as the President of the National Academy of Science, Ralph Cicerone, states: “The study of evolution remains one of the most active, robust, and useful fields in science” (Cicerone, NAS, 2008).
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The President of the Institute of Medicine, Dr. Harvey Fineberg, says: “Understanding evolution is essential to identifying and treating disease. For example, the SARS virus evolved from an ancestor virus that was discovered by DNA sequencing. Learning about SARS’ genetic similarities and mutations has helped scientists understand how the virus evolved. This kind of knowledge can help us anticipate and contain infections that emerge in the future” (Fineberg, NAS, 2008). The same could even be said today about the H1N1 virus causing the swine flu. CONCLUSIONS The importance of the study of PSC 1515 [Energy in the Natural Environment] is such, that this class is at the basis of the scientific literacy acquired by the graduates of Miami Dade College, and encompasses many of the Learning Outcomes that form the core of a college education. In PSC1515 students learn about science and the scientific method, and the basic elements of evolutionary biology, in contrast to creationism and intelligent design. The most important aspect of the study of evolution in this course is that our students are not mandated to accept it or believe in it. They are given the elements of the three approaches, and then are allowed to draw their own conclusions based on what they have learned about the scientific method. The study of the chapter on evolution is complemented with the study of the Universe and the Solar System, which includes the theory of the Big Bang, the Nebular Theory and the evolution of the Universe and our Solar System. This class should be recommended to all MDC students, and the chapter on evolution in particular must be considered of high relevance in the teaching of the course.
REFERENCES Dawkins, Richard (2009). The Greatest Show on Earth. The Evidence for Evolution. New York: Free Press Jacoby, Susan (2008). The Age of American Unreason. New York: Pantheon Books National Academy of Sciences/Institute of Medicine [NSTA/IOM] (2008). Science, Evolution and Creationism. Retrieved January 9, 2008 from http://www.8.nationalacademies.org/onpineews/newsitem.aspx?RecordID=11876 National Science Teachers Association [NSTA] (2007). Teaching of Evolution. The NSTA Position Statement. Retrieved February 23, 2007 from www.nsta.org/positionstatement&psid=10.
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Polygon Spring 2010 Vol. 4, 15-26 ON AN ITERATIVE ALGORITHM IN MULTIOBJECTIVE OPTIMIZATION
1
J. A. Serpa 1 Department of Mathematics, Miami Dade College, Inter-American Campus, Miami, FL 33135, USA. Email: jserpa@mdc.edu ABSTRACT
Multiobjective optimization is commonly used in every field where decisions are made to determine optimal values for a given object or process. Itâ&#x20AC;&#x2122;s been particularly expanded in management and business and a wide variety of methods has been developed. In this paper an original iterative algorithm is presented which takes into account the difficulties for decision-maker to mathematically formalize priorities on the functions vector.
KEYWORDS
Multiobjective optimization, mathematical programming, decision-maker, Paretooptimal solutions, iterative algorithms, adaptability depth.
AMS Subject Classification: 90C11, 90C29, 90B50, 90C31, 90C80
1. INTRODUCTION
Multiobjective Optimization Problem (MOP) arises more often than we could think. Optimization as it is understood in Mathematical Programming is reduced to the maximization (minimization) of an Objective Function where the Domain of possible solutions (alternatives) is given by a set of inequalities and equations. Defining one single Objective Function is often too risky, since other parameters for the given system could result with very undesirable values. The presence of multiple conflicting goals causes the necessity of a new approach: Multiobjective Optimization. Different methods have been developed: optimizing one single objective while on the other objectives constraints are
15
imposed; defining a global function as a combination of all objective functions; iterative algorithms; and more recently evolutionary algorithms. Iterative algorithms are particularly useful in situations where MOP regularly has to be solved and the task for decision-maker to formalize the priorities on the functions vector becomes too hard and eventually impossible. We show below some aspects of an original iterative algorithm where optimization occurs after several runs of the mathematical model. On each step the Domain is reduced to a subset within the set of Pareto-optimal solutions by following an evaluation rule and eventually a single solution is obtained.
2. MULTIOBJECTIVE OPTIMIZATION 2.1 THE PROBLEM
Let’s define MOP as follows:
F ( f1 ( x), f 2 ( x),..., f m ( x)) min,
(1)
x
m where
is the number of Objective Functions, and the Domain
linear inequalities and equations defined on the variable
is given by
x . A trivial solution is
obtained when the optimum occurs simultaneously for all functions. This rarely happens in real-world problems.
2.2 THE SOLUTION
Basic Principles of the Algorithm
The algorithm is based on the following statements:
I p,I p I
I Let
(
fib , i I p I \ I p
- the set of the Objective Functions) and let
be given boundary values.
16
Let’s define preference relation
P such that xPy
if
f i ( x ) f i ( y ), i I p ,
(2)
i and for at least one value
the inequality is strict and, in addition
f i ( x) f i b , i I p
(3)
Then the idea of narrowing the Pareto-Optimal Solutions set ( as follows. Let the point
y is
T ) can be executed
fixed and ‘’preferable’’ rather than any
z according to decision-maker’s evaluation rule, z : z T , z p , region
p is defined by inequalities (2)-(3) .
In the region
T p is executed the optimization. This resembles the idea of
set of ‘’individuals’’ after selection process and prior to ‘’recombination’’ and ‘’mutation’’ in Evolutionary Algorithms [1],[5].
Given
I p and
y , found after initial approximation, the optimization is carried out
according to the principle of minimum deviation from
fi ( y ), i I p
. As a rule
minimal deviation is not obtained simultaneously for all mentioned functions. Then principle of best guaranteed value is applied, i.e. minmax principle. Let
functions
f i ( x), i I
are transformed to dimensionless functions
Wi ( f i ( x)) keeping preference order of the original functions vector.
W {Wi }, i 1,..., m functions,
Let
are defined on
Wd W
region of transformed
Wd .
w s be an intermediate solution (at iteration s ), f s w s . 17
At every iteration of the algorithm, the decision-maker redefines the preference
vector based on the obtained intermediate alternative.
I s is defined as the set of
functions to be submitted to ‘’improvement’’ on the given iteration.
Boundary values on the iteration (
f i bs , i I s , s 2 )
are determined by
recurring relations:
bs
fi
f i b ( s 1) ( s 2) fi
, i I ( s 1) , i I ( s 1)
On iteration s , ( s 1) the problem is reduced to:
ws arg min max (wi wi( s 1) ) w Wds i I s
here
(4)
Wds : w Wds / w W d , wi wi( s 1) , i I s and at least i
for one value
the inequality is strict,
wi wibs , i I s
I s : I s I , I s , I s I \ I s Statement I : if
w s is unique solution to problem (4) in Wd , then it is Pareto-
Optimal. Proof by contradiction:
Let
w s be unique solution but not Pareto-Optimal, then there exists w ' Wd
such that
wi' wis , i I
(5)
18
i and for one value of
From
wis 1 0
the inequality is strict.
we have
wi' wi( s 1) wis wi( s 1) , i I max ( wi' wi( s 1) ) max ( wis wi( s 1) ) min max ( wi wi( s 1) ) iIs iIs w W ds i I s
from
w s Wds
and (5) follows
w ' Wds
(6)
ws and either
is not unique
solution of (4) , what happens for strict inequality at (6), either
w ' arg min max ( wi wi( s 1) ) w Wds i I s then
w s is not unique solution.
Statement (I) is proved.
In case of not uniqueness of solution in (4) the following problem is solved:
Wi ( x) min iIs
(7)
Wi ( x) max ( wis wi( s 1) ) , i I s iIs
(8)
Wi ( x) Wds , i I
(9)
Initialization (iteration ‘’0’’):
19
From extreme values of Objective Functions in *
*
b1
f i b1 , i I ( f w , f Weighing coefficients vector
is defined
f * { f i * } and
w b1 ) .
{i } is defined [2] according to:
* i
w jI j i
i * i
(10)
w qI jI j i
The problem at this step is reduced to
w0 arg min max i wi w Wd0 i I
s0 The consistency of the problem at
is given by
Wds [0, wis ] Wd iI
The parallelepiped is generated from
wi0 wib1
s 1: and for
wi( s 1) , i I s wi bs s w , i I i Inconsistency in the Domain of alternatives can be overcome by introducing
auxiliary variables
yi to weaken the constraints at step ‘’0’’:
h ci yi min
(11)
iI
f i ( x) h( f i max f i min ) / i f i min , i I
(12)
20
f i ( x ) y i f i b1 , i I
(13)
yi 0
(14)
x (15) And ci 0 are such penalties that worsening of function as
yi
increases is more
h significant rather than its improvement at
worsening.
Solution to (11)-(12) allows correction of boundary values of Objective Functions
using
yi
in case of inconsistency. On the other hand if the system is consistent
then the auxiliary variables are ‘’0’’ and no correction is needed.
At iteration ‘’s’’ the MOP (4) becomes:
l min
(16)
f i ( x ) l ( f i max f i min ) f i ( s1) , i I s
(17)
f i ( x) k i f i ( s 1) , i I s
(18)
f i ( x ) fi bs , i I s
(19)
x (20) Here
k i 0, i I s
i are set conveniently small and at least for one value
applies strict inequality. It serves the fast convergence of the algorithm.
f i min , f i max
are minimum and maximum respectively of functions in
.
Suggested transformation of functions:
f i ( x) f i min Wi ( f i ( x)) max ,i I f i f i min 21
We need to prove the following statement.
Statement II:
w r Wds , w s w r there
i' I s can
be
found
such
that
wis' wir' . Proof:
For
I s {1} it is obvious.
From
w r Wds
we have
max ( wis wi( s 1) ) max ( wir wi( s 1) ) iIs iIs
(21)
In case of strict inequality in (21) then at least for
i ' : ( wir wi( s 1) ) max ( wir wi( s 1) ) iIs
In case of equation at (21), then
applies
wis' wir'
w s is solution to (7)-(9). Let’s prove this part of
the statement by contradiction:
Let
wir wi( s 1) wis wi( s 1) , i I s , then
( wir wi( s 1) ) (wis wi( s 1) ) iIs i Is
(22)
Inequality (22) contradicts (7)-(9). Statement II is proved.
22
Fast convergence of the algorithm demands carefully handling the set
Is.
In this
regard the following statement is useful:
Statement III: If
I ( s 1) I s , then [0, wis ] Wd
i I
and MOP
min w Wd( s 1)
max ( wi wis ) has no solution. iIs
Proof by contradiction:
w ( s 1) Let
w
be such that
( s1) i
wis ( s1) wi
, i I s i I ( s1) , i I ( s1)
wi( s 1) wis , i I s From
wd( s 1) wds
(23)
follows
w ( s 1) Wds
(24)
But (23)-(24) contradict ‘’Statement II’’ . Statement III is proved.
Evaluation rule
Search for solution of MOP stops at iteration ‘’s’’ if one of the following conditions applies: 1.
The solution satisfies evaluation rule.
23
Ability to react changing conditions of preferences over the objective functions in the search of solution to MOP can be measured with ‘’adaptability depth’’
H , its
maximization serves as evaluation rule:
H
H 1 H
H
1 m i H i' m i1
H ,
1 m i H i' m i1
f i * f i ** , i I1 * f i f *i ' H i 1 ** f i f *i , i I 2 f i * f *i
I1 , I 2
are the sets of functions to maximize and minimize respectively.
f i** f i ( x* ), i 1,..., m f i * max f i ( x), i 1,..., m, x
f *i min f i ( x), i 1,..., m, x The decision-maker reconsiders the functions to be improved at this iteration by measuring
H i' i Hi H i' i i
i , i are boundary values of vector {i } To determine
I s , it is solved:
24
'
'
i * (i * / i* H i(*s 1) min i
H i( s1) , i I ) '
2. Decision-maker attempts to continue the search, however
(25) '
I s , I s I it turns
'
out
Wds . Hence
w ( s 1) is the solution to MOP.
Formal Algorithm
The algorithm is performed following the steps:
1. Single optimization problems are solved for all functions: f i min, max
2. Decision-maker defines
f i b1 , i I
Functions are transformed into
and ‘’ideal’’ alternative
f * { f i* } .
Wi ( f i ( x )) , and vector {i }
is defined as
per (10). Initialization
s 0.
3. The problem (11)-(15) is solved. If the solution satisfies evaluation rule go to the end.
4.
s s 1 . By solving (25) state I s
5. Solve (16)-(20). In case of not uniqueness solve (7)-(9). If conditions 1 or 2 are satisfied, go to end, otherwise go to 4.
6. End.
3. CONCLUSIONS
An algorithm for the solution of MOP has been presented. The algorithm consists of an iterative process. At each iteration, according to an evaluation rule, the set of
25
alternatives is reduced to ‘’more preferable’’ points. Narrowing the searching Domain serves the approximation to the ‘’ideal’’ alternative, a point that rarely in practice is achieved. Some statements have been proved to show convergence of the algorithm and Pareto-Optimal character of the solution. Decision-maker deals directly with objective functions vector, which has considerably lower dimension rather than the Domain of alternatives.
REFERENCES
Coello, C. A. (2004). Applications of Multiobjective Evolutionary Algorithms. MexicoUSA.
Mikhalevich, V. S, and Volkovitch, V. L. (1982). Computational Methods of Researching and Designing Complex Systems, Moscow (in Russian).
Petrenko, V. L., Mirzoakhmedov F., Nguyen, V. H., and Serpa, J. (1987). An Approach to Solving Multiobjective Optimization Problems in Adaptable Planning Systems. Operations Research and Automated Management Systems, Kiev, Ukraine (in Russian).
Serpa, J. (1988). Modeling in Short-term Management of Seaports. Doctoral Thesis, Donetsk, Ukraine (in Russian).
Zitzler, E. (1999). Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications. Doctoral Thesis, Zurich.
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Polygon Spring 2010 Vol. 4, 27-42
AFRICAN-AMERICANS IN MATHEMATICAL SCIENCES A CHRONOLOGICAL INTRODUCTION
1
M. Shakil1 Department of Mathematics, Miami Dade College, Hialeah Campus, Hialeah, FL 33012, USA. Email: mshakil@mdc.edu ABSTRACT
In this paper, a chronological introduction of African-Americans in the field of Mathematical Sciences is presented. KEYWORDS African-Americans, mathematical sciences. AMS Subject Classification: 01A05; 01A07; 01A70; 01A85
1. INTRODUCTION
The accomplishments of the past and present can serve as pathfinders to present and future mathematicians. African- American mathematicians have contributed in both large and small ways that has been overlooked when chronicling the history of science. By describing the scientific history of selected African-American men and women within mathematical sciences we can see how the efforts of individuals have advanced human understanding in the world around us. The abilities and accomplishments of these AfroAmerican scholars of science and mathematics cannot be underrated. History bears testimony to their achievements. The purpose of this paper is to highlight and exhibit the accomplishments of African-Americans within the Mathematical Sciences. The materials presented are based on the “Mathematicians of the African Diaspora”, (www.math.buffalo.edu/mad/index.html). The organization of this paper is as follows. Section 2 contains a Tree Diagram of African-Americans in the mathematical sciences by dividing it into four different periods, beginning from 18th century to present. These periods have been further classified indexed by year. In Section 3, a chronology of African-Americans in mathematical sciences is presented. The statistics on the numbers of African-Americans receiving Ph.D.’s in mathematics, during the period 1925 – 2004, have been presented in Section 4. The achievements of African-Americans in the mathematical sciences are highlighted in section 5. The concluding remarks are presented in Section 6.
27
2. A TREE DIAGRAM The following is a Tree Diagram depicting the different periods of African-Americans in Mathematical Sciences.
African-American Mathematicians
19th Century
20th Century
18th Century
21st Century
2000 - 2004 1925 - 1999 1700 - 1799
1800 - 1899
3. A CHRONOLOGY OF AFRICAN-AMERICANS IN MATHEMATICAL SCIENCES The following is a chronology of African-Americans in mathematical sciences.
3.1 AFRICAN-AMERICAN MATHEMATICIANS OF 18TH CENTURY The names of the following African-Americans of 18th century are available through historical records, who have contributed in the field of mathematical sciences:
(i) (ii) (iii)
Muhammad ibn Muhammad (16?? - 1741) Thomas Fuller (1710 - 1790) Benjamin Banneker (1731 - 1806)
Development of African-American influence in mathematical sciences began with the work of Benjamin Banneker, who used the method of doubling sequences to generate an estimate for the method of false position. Benjamin Banneker is often recognized as the first African American mathematician. However, the names of ex-slave Thomas Fuller and the Nigerian Muhammad ibn Muhammad also appear in history, whose mathematical
28
activities predate Benjamin Banneker. It is interesting to note that none of these men had formal degrees.
3.2 AFRICAN-AMERICAN MATHEMATICIANS OF 19TH CENTURY Below is the list of three African-American mathematicians of 19th century, who are prominent for their contribution to the knowledge and advancement of mathematical sciences. (i) Charles Reason (1814 - 1893) is considered to be the first African-American to receive a faculty position in mathematics, in the year 1849, at a predominantly white institution - Central College in Cortland County, New York.
(ii) Edward Alexander Bouchet was the first African-American to earn a Ph.D. in Physics (Science), in the year 1878, from Yale University, and only the sixth American to possess a Ph.D. in Physics. It should be noted that Yale University became the first United States of America institution, in the year 1862, to award a Ph.D. in mathematics.
(iii) Kelly Miller was the first African American to study graduate mathematics, in the year 1886, at Johns Hopkins University. It will be interesting to note that Johns Hopkins University was the first American University to offer a program in graduate mathematics.
3.3 AFRICAN-AMERICAN MATHEMATICIANS OF 20TH CENTURY The list of African-American mathematicians of 20th century is very exhaustive. In the following paragraph, a chronology of African-Americans, who have excelled and contributed to the knowledge and advancement of mathematical sciences, during the period 1900 – 1999, is presented, (see, for example, the “Mathematicians of the African Diaspora” website created and maintained by Professor Dr. Scott W. Williams, Professor of Mathematics University at Buffalo, SUNY, among others).
(1) 1925: Elbert Frank Cox was the first African-American to earn a Ph.D. in Mathematics in 1925 from Cornell University. There were 28 Ph.D.'s awarded in the United States that year.
(2) 1928: Dudley Weldon Woodard was the second African-American to earn a Ph.D. in Mathematics in 1928 from the University of Pennsylvania. (4) 1933: William Schieffelin Claytor was the third African-American to earn a Ph.D. in Mathematics (University of Pennsylvania). Dr. Claytor had an extraordinary promise as a mathematician. (5) 1934: Walter R. Talbot was the fourth African-American to earn a Ph.D. in Mathematics (University of Pittsburgh).
29
(6) 1938: Ruben R. McDaniel (Cornell University), and Joesph Pierce (University of Michigan) were the fifth and sixth African-Americans to earn a Ph.D. in Mathematics in the year 1938. (7) 1941: David Blackwell was the seventh African-American to earn a Ph.D. in Mathematics, in the year 1941, from the University of Illinois. Dr. Blackwell earned his Ph.D. at the age of 22. He is regarded as one of the greatest African-American mathematician of the 20th century. Dr. Blackwell is famous and well-known in the world of mathematics for his seminal “Rao-Blackwell Theorem” which gives a technique for obtaining unbiased estimators with minimum variance with the help of sufficient statistics (see, for example, Dudewicz and Mishra (1988), Kapur (1999), and Rohatgi and Saleh (2001), among others). In 1954, Dr. David Blackwell became the first AfricanAmerican to hold a permanent position at one the major universities, University of California at Berkley.
(8) 1942: J. Ernest Wilkins became the eighth African-American to earn a Ph.D. in Mathematics, in the year 1942, from the University of Chicago. Dr. Wilkins earned his Ph.D. at the age of 19. He is also regarded as one of the greatest and rarest AfricanAmerican mathematician of the 20th century
(9) 1943: Euphemia Lofton Haynes (Catholic University), the first African -American woman, and Clarence F. Stephens (University of Michigan) were the ninth and tenth African-Americans, respectively, to earn a Ph.D. in Mathematics (see, for example, the websites “Black Women in Mathematics” and “Timeline of African American Ph.D.'s in Mathematics,” among others). The Morgan-Potsdam Model is the name given to a method of the teaching of mathematics developed by Dr. Clarence F. Stephens at Morgan State University and refined at the State University of New York College at Potsdam. Dr. Clarence F. Stephens also received the Mathematical Association of America Gung-Hu Award for the Pottsdam Miracle. Under the direction of Dr. Clarence Stephens, Morgan State University became the first institution to have three African-Americans of the same graduating class (1964), who obtained a Ph.D. in Mathematics. These people were Dr. Earl Barnes (University of Maryland, 1968), Dr. Arthur Grainger (University of Maryland, 1972), and Dr. Scott Williams (Lehigh University, 1969). This is still a record that stands among all U.S. universities and colleges.
(10) 1944: This is the year when the eleventh, twelfth and thirteenth African- Americans, Joseph J. Dennis (from Northwestern University), Wade Ellis, Sr. and Warren Hill Brothers (both from University of Michigan), respectively, earned a Ph.D. in Mathematics.
(11) 1945: Jeremiah Certaine was the fourteenth African-American to earn a Ph.D. in Mathematics, in the year 1945, from the University of Michigan.
30
(12) 1949: Evelyn Boyd Granville was the fifteenth African-American and the second African-American Woman to earn a Ph.D. in Mathematics, in the year 1949, from Yale University. (13) 1950: Marjorie Lee Browne (University of Michigan), the third African-American Woman, and George H. Butcher (University of Pennsylvania) were the sixteenth and seventeenth African-Americans, respectively, to earn a Ph.D. in Mathematics, in the year 1950. (14) 1953: Luna I. Mishoe was the eighteenth African-American to earn a Ph.D. in Mathematics from New York University. (15) 1954: Charles Bell was the nineteenth African-American to earn a Ph.D. Mathematics from the University of Notre Dame.
in
(16) 1955: Vincent McRea (Catholic University) and Lonnie Cross (Cornell University) were the twentieth and twenty-first African-Americans to earn a Ph.D. in Mathematics.
(17) 1956: Lloyd K. Williams (University of California at Berkeley) and Henry M. Elridge (University of Pittsburgh) were the twenty-second and twenty-third AfricanAmericans to earn a Ph.D. in Mathematics in the year 1956.
(18) 1957: Eugene A. Graham, Jr. (University of Turin in Italy) and Elgy S. Johnson (Catholic University) were the twenty-fourth and twenty-fifth African-Americans to earn a Ph.D. in Mathematics in the year 1957. Dr. Graham, probably, was the first AfricanAmerican earning a Mathematics Ph.D. outside the U.S.
(19) 1959: Laurence Harper, Jr. (University of Chicago) was the twenty-sixth AfricanAmerican Ph.D. in Mathematics.
(20) 1960 – 1999: Above, we have tried to enlist the African-Americans in the field of mathematical sciences from 1900 to 1959. It is gratifying to note that a number of African-Americans earned their Ph.D.’s in the field of Mathematical Sciences from 1960 to 1999, (see, for example, the website “http://www.math.buffalo.edu/mad/yearindex.html,” for details). For the interest of the readers, their names are presented below in chronological order.
(i) 1960: Charles G. Costley; Joshua Leslie; Argelia Velez-Rodriguez
(ii) 1961: Jesse P. Clay; Sadie Gasaway; John Gilmore; Rogers Newman (iii) 1962: Robert O. Abernathy; Joseph Battle; John Henry Bennett; Gloria Conyers Hewitt; Georgia Caldwell Smith; Louise Nixon Sutton; Theodore R. Sykes
31
(iv) 1963: Simmie S. Blakney; Earl O. Embree; William A. McWorter
(v) 1964: Louis C. Marshall; Alfred D. Stewart; Mary C. Wardrop-Embry
(vi) 1965: James A. Donaldson; Beryl E. Hunte; John H. McAlpin
(vii) 1966: John A. Ewell III; William T. Fletcher; Eleanor Dawley Jones; Eugene W. Madison; Vivienne Malone Mayes; Shirley Mathis McBay; Charles E. Morris (viii) 1967: Harvey T. Banks; Llayron L. Clarkson; Geraldine Darden; Samuel H. Douglas; Annie M. Watkins Garraway; Melvin Heard; Percy A. Pierre; Thyrsa Anne Frazier Svager; Ewart A. C. Thomas; Ralph B. Turner; Irving E. Vance (ix) 1968: Earl R. Barnes; Dennis D. Clayton; Mary Deconge-Watson; Lloyd Demetrius; Milton A. Gordon; Velmer Headley; Guy T. Hogan; Phillip E. McNeil; Ronald E. Mickens; Wilbur L. Smith; Donald F. St.Mary; Donald Weddington; James H. White (x) 1969: Boniface Eke; David M. Ellis; Etta Falconer; Fannie Ruth Gee; Raymond L. Johnson; Wendell P. Jones; Benjamin J. Martin; Robert Smith; Scott W. Williams; Vernon Williams (xi) 1970: John C. Amazigo; Dean R. Brown; Japeth Hall, jr.; Lonnie W. Keith; Curtis S. Means; Mutio Nguthu; G. Edward Njock; Sonde Nwankpa; Winston A. Richards; Nathan F. Simms, Jr.; Eddie R. Williams (xii) 1971: Roosevelt Calbert; Joella Hardeman Gipson; Orville Edward Kean; Hugh G.R. Millington; Dolores Spikes (xiii) 1972: Ethelbert Nwakuche Chukwu; Oscar H. Criner, III; Carlos Ford-Livene; Christopher Olutunde Imoru; C. Dwight Lahr; John Nguthu Mutio; James A. White; Floyd L. Williams (xiii) 1973: Annas Aytch; Garth A. Baker; Robert Bozeman; Therese H. Braithwaite; Lloyd Gavin; Seyoum Getu; James E. Ginn; Isom H. Herron; Frank A. James; Manuel Keepler; Clement McCalla; Michael Payne; Evelyn Thornton; Hampton Wright (xiv) 1974: Elayne Arrington; Della D. Bell; Roosevelt Gentry; Tepper L. Gill; Johnny L. Houston; Arthur M. Jones; Nathaniel Knox; Rada Higgins McCreadie; Kevin Osondu; Chester C. Seabury; Willie E. Taylor; Alton S. Wallace; Harriet R. Junior Walton
(xv) 1975: Bola Olujide Balogun; Arthur D. Grainger; Roy King; James Nelson, Jr; Wandera Ogana; Osborne Parchment
32
(xvi) 1976: David I. Adu; James Howard Curry; David Green, Jr; Leon B. Hardy; SalahEldin A Mohammed; Lawrence R. Williams (xvii) 1977: Eddie Boyd Jr.; Gerald R. Chachere; Louis Dale; Ebenezer O. George; Theodore R. Hatcher; David M. James; Carl L. Prather (xviii) 1978: Reuben O. Ayeni; Clifton Edgar Ealy; Carroll J. Guillory; Fern Y. Hunt; Karolyn Ann Morgan; Jonathan Chukwuemeka Nkwuo; Donald St. P. Richards; Wesley Thompson; Henry N. Tisdale (xix) 1979: Samuel Omoloye Ajala; Gary S. Anderson; Johnny E. Brown; Emma R. Fenceroy; R. Charles Hagwood; Walker Eugene Hunt; Donald R.King; Keith Mitchell; Claude Packer; George A. Roberts (xx) 1980: Curtiss A. Barefoot; Robert M. Bell; Ronald Biggers; Sylvia T. Bozeman; Suzanne Craig; Gaston M. N'guĂŠrĂŠkata; James E. Robinson; Daniel Arthur Williams
(xxi) 1981: Overtoun M. Jenda; Corlis P. Johnson; William A. Massey; David O. Olagunju; Gabriel A. Oyibo
(xxii) 1982: William A. Hawkins jr.; Peter D. Nash; Janice B. Walker
(xxiii) 1983: Melvin R. Currie; Carolyn Mahoney; Bernard A. Mair; Bessie L. Tucker
(xiv) 1984: Abdulkeni Zekeria; Curtis Clark; Carl Graham; Kevin Oden; Alade Tokuda
(xv) 1985: Darry Andrews; Donald Ray Cole; Ibula Ntantu; Ronald Patterson; Bonita V. Saunders; Daphne Letitia Smith (xvi) 1986: Semere Arai; Stella R. Ashford; Busiso Chisala; Kevin Corlette; Arouna Davies; Lorenzo O. Hilliard; Iris Marie Mack; Walter M. Miller; Denise M. StephensonHawk; James C. Turner (xvii) 1987: Richard Lance Baker; Shiferaw Berhanu; Dennis Davenport; Nathaniel Dean; George Edmunds; Dawit Getachew; Amos Olagunju; DeJuran Richardson; Hanson Umoh; Nathaniel Whitaker (xviii) 1988: Emery Neal Brown; Dominic P. Clemence; Vanere Goodwin; Abdulcadir Issa; Amha Tume Lisan; Frank Albert Odoom; Kweku-Muata Agyei Osei (Noel Bryson); Wanda Patterson; Lemuel Riggins; Elaine Smith; Gregory Smith; Vernise Steadman; Leon Woodson; Roselyn Elaine Williams; Leon C. Woodson; Paul E. Wright
(xix) 1989: Tor A. Kwembe; Joan Sterling Langdon; Jean-Bernard Nestor; Abdul-Aziz Yakubu
33
(xx) 1990: Gideon Abay Asmerom; Teresa Edwards; Rodney Kirby; Janis Oldham; Michael M. Tom (xxi) 1991: Harun Adongo; Adebisi Agboola; Patricia Beaulieu; Aniekan A. Ebiefung; Jacqueline M. Hughes-Oliver; Sizwe G. Mabizela; Katherine Okikiolu; Yewande Olubummo; Broderick O. Oluyede; Arlie O. Petters; Philippe Rukimbira (FIU) (xxii) 1992: Evans Afenya; Gerald Yinkefe Agbegha; Donald Martin; Bi Roubolo Vona (xxiii) 1993: Halima Ali; Danielle Carr; Duane Anthony Cooper; Koffi Fadimba; Stanley Einstein-Matthews; Abba Gumel; Lancelot F. James; Camille A. McKayle; Christine McMillan; Tonya M. Smoot (xxiv) 1994: Kokou Y. Abalo; Patty Anthony; Ron Buckmire; Dawn Lott; Zephyrinus Okonkwo; Gregory Smith; Frederick J. Semwogerere; Barama Toni
(xxv) 1995: Joseph Apaloo; Gregory Battle; Kossi Edo; Suzanne L. Weekes (xxvi) 1996: Randolph G. Cooper III; Neil Flowers; Henry Gore; Errol Rowe; Temba Shonhiwa; Aissa Wade (xxvii) 1997: Afi Davis Harrington; Francis Y. Jackson; Michael Keeve; Tuwaner Lamar; Alfred Noël; Richard F. Patterson; Sonya Stephens; Asamoah Nkwanta; Remi Ombolo; Elaine Terry; Alain Togbe; Enoch Z. Xaba (xxviii) 1998: Paulette Ceesay; Terrence Edwards; Neal Jeffries; Julie S. Ivy; Trachette Jackson; Mark Lewis; Lemuel Riggins; Rhonda Sharpe; Monica Y. Stephens; Kim Y. Ward; Pamela J. Williams
(xxix)1999: Garikai Campbell; Gelonia Dent; Berhane T. Ghaim; Edray H. Goins; Daniel Lee Hunt; Anthony D. Jones; Alvina M. Johnson; Chawne Monique Kimber; Kathryn M. Lewis; Cassandra McZeal; Desmond Stephens; Peter Stephens; Shree Whitaker 3.4 AFRICAN-AMERICAN MATHEMATICIANS OF 21ST CENTURY (2000 – 2004) The names of African-American mathematicians, for the period 2000 - 2004, are presented below in chronological order.
(i) 2000: Kim Woodson Barnette; Serge A. Bernard; Shea Burns; Illya V. Hicks; Keith E. Howard; Tasha Inniss; Otis B. Jennings; Sean Paul; Selemon Getachew; Sherry Scott; Talitha M. Washington; Kimberly Weems
(ii) 2001: Jamylle L. Carter; Naiomi T. Cameron; Shurron M. Farmer; Jeffery Fleming; Russell Goward; Leona Harris; Rudy Horne, Jr.; Clifford Johnson; Daniel R.Krashen;
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Lynnell Matthews; Jillian McLeod; Shona Davidson Morgan; Kimberly Flagg Sellers; Idris Stoval; Craig Sutton; Talitha M. Washington (iii) 2002: Gabriel Ayine; Martial Marie-Paul Agueh; Louis Beaugris; Nancy Glenn; Jean-Michelet Jean-Michel; Djivede A. Kelome; Lynelle Matthews; Jillian McLeod; Iris Gugu Moche; Tolu Okusanya; Jean M. Tchuenche; Howard Thompson; Gikiri Thuo; Donald C. Williams (iv) 2003: Sammani D. Abdullahi; Gerard M. Awanou; Sharon Clarke; Berhane T. Ghaim; Jean-Michelet Jean-Michel; Llolsten Kaonga; Nolan MacMurray; Monica Jackson; Kasso Okoudjou; Miranda I. Teboh-Ewungkem; Archie Wilmer III (v) 2004: Milton H. Nash; Donald Outing; Rachel E. Vincent
4. STATISTICS OF AFRICAN-AMERICAN Ph.D.’s IN MATHEMATICAL SCIENCES (1925 – 2004) According to the list as presented in Section 3 above, it is interesting to note that a total of 392 African-Americans had received a Ph.D. in mathematics during the period 1925 – 2004. For the sake of our statistical computations, we have divided this period into four different sub-periods: 1925 – 1944, 1945 – 1964, 1965 – 1984, and 1985 – 2004. Out of 392 African-American Ph.D.’s in mathematics, 3.32 % received their Ph.D.’s during the period 1925 – 1944, 8.42 % received their Ph.D.’s during the period 1945 – 1964, 40.05 % received their Ph.D.’s during the period 1965 – 1984, and 48.21 % received their Ph.D.’s during the period 1985 – 2004. From the analysis presented here, it is easily seen that the maximum number of African-Americans receiving Ph.D.’s in mathematics was during the period 1985 – 2004. The statistics on the numbers of African-Americans receiving Ph.D.’s in mathematics, during the period 1925 – 2004, have been presented inthe Figure 4.1 below.
# African-Americans Ph.D.'s in the Mathematical Sciences 1925 - 2004 Total: 392
Ph.D.'s in Mathematics (%)
60.00%
50.00%
40.00% # African-Americans Ph.D.'s in the Mathematical Sciences
30.00%
20.00%
10.00%
0.00% 1925 - 1944 1945 - 1964 1965 - 1984 1985 - 2004 YEAR
Figure 4.1: African-American Ph.D.’s in Mathematical Sciences (1925 – 2004)
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5. HIGHLIGHTS ON THE ACHIEVEMENTS OF AFRICAN-AMERICANS IN MATHEMATICAL SCIENCES In the following paragraphs, achievements of some African-Americans in the field of mathematical sciences are highlighted. It is interesting to note that, during the period 1925 - 1947, 12 AfricanAmericans earned a Ph.D. in Mathematics. Furthermore, half of all African-Americans who had earned their Ph.D.'s in Mathematics, by the time of the year 1945, were students of the University of Michigan. During the period 1943 - 1969, thirteen African-American women earned a Ph.D. in Mathematics. It is also interesting to know that one of the most important landmarks and rarest achievements in the field of mathematical sciences was when three African-American Women, Drs. Tasha Innis, Kimberly Weems, and Sherry Scott, received the Ph.D. in mathematics, in the same year 2000, from the same university, University of Maryland, College Park, Maryland. In 1929, Dr. Dudley Woodard was the first African-American to publish a research paper in mathematical sciences in an accredited mathematics journal, entitled, “On two dimensional analysis situs with special reference to the Jordan Curve Theorem,” Fundamenta Mathematicae, 13 (1929), 121-145. The first African American publication in a top research journal was Dr. William W. S. Claytor's Topological Immersian of Peanian Continua in a Spherical Surface, Annals of Mathematics, 35 (1934), 809-835. Dr. Gloria Ford Gilmer is considered to be the first African-American woman to publish the first two (non-Ph.D.-thesis) mathematics research papers, jointly with another African-American, Dr. Luna I. Mishoe, in the year 1956, entitled: (a) “On the limit of the coefficients of the eigenfunction series associated with a certain non-self-adjoint differential system”, Proc. Amer. Math. Soc. 7 (1956), 260-266. (b) “On the uniform convergence of a certain eigenfunction series”, Pacific J. Math. 6 (1956), 271-278.
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The second joint research paper by two African-Americans, Charles Bell and David Blackwell, in collaboration with Leo Breiman, was published in the year 1960, entitled “On the completeness of order statistics,” Ann. Math. Stat., 31, 1960, 794-797. In 1961, Dr. Lonnie Cross shocked the African-American and mathematics community by changing his name to Abdulalim Shabbazz, and becoming the first African-American scientist to embrace the followers of Elijah Mohammed, the leader of the AfricanAmerican Moslem community. In 1963, Dr. Grace Lele Williams became the first Nigerian woman to earn a Ph.D. in Mathematics from the University of Chicago. In 1964, Dr. David Blackwell became the first African-American mathematician to Chair a department, Department of Statistics, at one of the major universities, University of California at Berkeley. In 1965, Dr. David Blackwell became the first African-American named to The National Academy of Sciences. From 1968 to 1969, Dr. Percy A. Pierre was White House Fellow for the Executive Office of the President of the United States. In 1969, Clarence Ellis became the first African-American to earn a Ph.D. in Computer Science from the University of Illinois. Two mathematics graduate students, Johnny Houston and Scott Williams, at the January 1969 Annual Meeting of The American Mathematical Society, called together a group of African-American mathematicians, and begat an adhoc organization, called “Black and Third World Mathematicians,” which, in 1971, changed its name to The National Association of Mathematicians (NAM). In 1969, the book “Negroes in Science - Natural Science Doctorates” by James M. Jay was published by the Balamp Company. In 1972, Professor Morris Sika Alala became the first Kenyan African Full Professor of Mathematics at the University of Nairobi. In 1974, Dr. J. Ernest Wilkins, Jr., became the President of the American Nuclear Society. Alton Wallace became the first African-American to earn a Ph.D. in mathematics, in the year 1974, under the direction of an AfricanAmerican thesis advisor, Dr. Raymond L. Johnson, at the University
37
of Maryland. The African Mathematical Union (AMU) was founded in Africa In 1975. Its first president was a Cameroonian mathematician, Professor Henri Hogbe Nlend. The first AMU Pan-African Congress of Mathematicians was held in Rabat, Morocco, in the year 1976. In 1976, Dr. J. Ernest Wilkins, Jr., became a member of The National Academy of Engineers. Howard University established the first Ph.D. program in Mathematics at a Historically Black University and College (HCBU), in the year 1976, under the guidance of Dr. James Donaldson, the Chair of its Mathematics Department, and Dr. J. Ernest Wilkins, Jr., then a member of its Physics Department. In 1979, Dr. David Blackwell won the von Neumann Theory Prize of the Operations Research Society of America. The National Association of Mathematicians (NAM) inaugurated the first Claytor Lecture, in 1980, with Professor James Josephs as the speaker. In 1980, the first book on African American Mathematicians, “Black Mathematicians and their Works,” by V. K. Newell, J. H. Gipson, L. W. Rich, and B. Stubblefield, was published by Dorrance & Company.
The Southern African Mathematical Sciences Association (SAMSA) was founded among the 12 countries of Southern Africa in 1980.
In 1981, Dr. C. Dwight Lahr became the first African-American to get tenure in a department of mathematics of an Ivy League School. In 1984, Dr. C. Dwight Lahr became the first African-American to become Full Professor in a department of mathematics of an Ivy League School. In 1986, the first issue of the African Mathematical Union's Commission on the History of Mathematics in Africa (AMUCHA) was presented. In 1990, the African Mathematical Union Commission on Women in Mathematics in Africa (AMUCWMA) was founded with Dr.
38
Grace Lele Williams as its Chairman. In 1992, Dr. Gloria Gilmer became the first woman to deliver a major the National Association of Mathematicians (NAM) lecture. In 1995, the first Conference for African American Researchers in the Mathematical Sciences (CAARMS1) was held at the Mathematical Sciences Research Institute (MSRI), University of California, Berkeley. The conference was organized by three prominent African-American mathematicians, Drs. Raymond Johnson, William Massey, and James Turner, in collaboration with Dr. William Thurston. Since then CAARMS has been held each year. In 1997, Dr. Katherine Okikiolu became the first African-American to win Mathematics' most prestigious young person's award, the Sloan Research Fellowship. She also was awarded the new $500,000 Presidential Early Career Awards for Scientists and Engineers. In 1997, the organization Council for African American Researchers in the Mathematical Sciences (CAARMS) was formed to oversee the CAARMS conferences and to aid African Americans interested in research in mathematics. Also in 1997, Nathaniel Dean's book “African American Mathematicians” was published by the American Mathematical Society. In 2001, Dr. William A. Massey became the first African-American Full Professor (Edwin S. Wilsey Professor) of Operations Research and Financial Engineering at Princeton University. The following is the list of some articles published in best and reputed mathematics journals of high quality by African-American mathematicians: Schiefelin Claytor, Topological Immersion of Peanian Continua in a Spherical Surface, The Annals of Mathematics, 2nd Ser. 35 (1934), 809-835. Schieffelin Claytor, Peanian Continua Not Imbeddable in a Spherical Surface, The Annals of Mathematics, 2nd Ser. 38 (1937), 631-646.
Blackwell, David, Idempotent Markoff chains, The Annals of Mathematics, 2nd Ser. 43, (1942). 560--567.
39
Wilkins, J. Ernest, Jr. Multiple integral problems in parametric form in the calculus of variations. The Annals of Mathematics (2) 45, (1944). 312--334. Blackwell, David, Finite non-homogeneous chains, The Annals of Mathematics, 2nd Ser. 46, (1945). 594--599. Wilkins, J. Ernest, Jr. A note on the general summability of functions. The Annals of Mathematics (2) 49, (1948). 189--199. Bellman, Richard; Blackwell, David On moment spaces. The Annals of Mathematics, 2nd Ser. 54, (1951). 272-274. Kevin Corlette. Archimedean superrigidity and hyperbolic geometry. Annals of Mathematics 2nd Series 135 (1992), no. 1, 165-182 Gangbo, Wilfrid. McCann, Robert J. The geometry of optimal transportation. Acta Mathematica 177 (1996), no. 2, 113--161.
Okikiolu, Katherine. Critical metrics for the determinant of the Laplacian in odd dimensions. The Annals of Mathematics, 2nd Ser. 153 (2001), no. 2, 471--531.
E. A Carlen and W. Gangbo. Constrained steepest descent in the 2-Wassertein metric, Annals of Math. 157, May (2003).
The First Africans
1947: The earliest record of a Mathematics Ph. D. by an African appears to be a Ghanaian African, Dr. A. M. Taylor from Oxford University, U.K., in 1947.
Nigeria: Indigenous mathematics research activities in Nigeria were pioneered by Drs. Chike Obi, Adegoke Olubummo (1955), and James Ezeilo, who obtained their Ph.D.’s in mathematics from British Universities in the 1950's (see, for example, “Mathematics in Nigeria Today,” among others). Dr. Grace Lele Williams became, in 1963, the first Nigerian woman to earn a Ph.D. in mathematics from the University of Chicago.
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6. CONCLUDING REMARKS The purpose of this paper was to present a chronological introduction of AfricanAmericans in the field of Mathematical Sciences. It is evident that these AfricanAmerican Mathematicians remain as a source of inspiration to us to excel in mathematics and other fields of knowledge, and achieve our goals. The achievements of these AfricanAmerican Mathematicians, despite the difficulties they had to overcome, stand as a beacon for us. It is hoped that the materials presented in this article will be useful to the practitioners and researchers in various fields of theoretical and applied sciences who are interested in the knowledge of diverse cultures, including global and historical perspectives, with special reference to the field of mathematical sciences. ACKNOWLEDGMENT The author would like to express his sincere gratitude and acknowledge his indebtedness to the various authors and, specially, to Dr. Scott W. Williams, Professor of Mathematics, The State University of New York at Buffalo, whose works were liberally consulted during the preparation of this article.
REFERENCES Allen, J. E. (1971). Black History, Past and Present. Exposition Press Inc., Jericho, N. Y.
Carwell, H. (1977). Blacks in Science: Astrophysicist to Zoologist, Exposition Press, Hicksville, N.Y. Dudewicz, E. J., and Mishra, S. N. (1988). Modern Mathematical Statistics. John Wiley & Sons, New York. Kapur, J. N., and Saxena, H. C. (1999), Mathematical Statistics. S. Chand & Company Ltd., New Delhi. Kenshaft, P. C. (1987). Black Men and Women in Mathematical Research. Journal of Black Studies, December, 19:2, 170 - 190. Newell, V. K., Gipson, J. H., Rich, L. W., and Stubblefield, B. (1980). Black Mathematicians and their Works, Dorrance & Company. Rohatgi, V. K., and Saleh, A. K. M. E. (2001). An Introduction to Probability and Statistics, John Wiley & Sons, Inc., New York.
Sammons, V. O. (1989). Blacks in Science and Education. Hemisphere Publishers, Washington, D.C.
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Sertima, I. V. (1983). Blacks in Science. Transactions Books.
Taylor, J., editor (1955). The Negro in Science. Morgan State College Press. Williams, S. W. (1999). Black Research Mathematicians, African Americans in Mathematics II. Contemporary Math. 252, 165 - 168.
Williams, S. W. A Modern History of Blacks in Mathematics. www.math.buffalo.edu/mad/madhist.html. Williams, S. W. Mathematicians of the African Diaspora. www.math.buffalo.edu/mad/index.htm.l Zaslavsky, C. (1973). Africa Counts: Number and Pattern in Africa Culture. Prindle, Weber & Schmidt.
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Polygon Spring 2010 Vol. 4, 43-55 SURVEY OF STUDENTS’ FAMILIARITY WITH GRAMMAR AND MECHANICS OF ENGLISH LANGUAGE – AN EXPLORATORY ANALYSIS M. Shakil1, V. Calderin2 and L. Pierre-Philippe3 Department of Mathematics, Miami Dade College, Hialeah Campus, Hialeah, FL 33012, USA. Email: mshakil@mdc.edu 2 Department of English, Miami Dade College, Hialeah Campus, Hialeah, FL 33012, USA. Email: vcalderin@mdc.edu 3 Department of ESL and Foreign Languages, Miami Dade College, Hialeah Campus, Hialeah, FL 33012, USA. Email: lpierrep@mdc.edu 1
ABSTRACT In recent years, there has been a great interest in the problems of grammar and mechanics instruction to the freshman English. In this paper, the students’ familiarity with grammar and mechanics of English language has been studied from an exploratory point of view. By administering a survey on the grammar and mechanics in some classes, the data have been analyzed statistically which shows some interesting results. It is hoped that the findings of the paper will be useful for researchers in various disciplines.
KEYWORDS ANOVA, grammar, hypothesis testing, mechanics, prescriptivist approach, Shannon’s diversity index.
1. INTRODUCTION
As noted by Teorey (2003), although the usage of prescriptivist approach to grammar instruction was rejected by the linguistic community nearly one hundred years ago, its importance in the present day instruction of English language cannot be overlooked. It appears from the literature that not much work has been done on the problem of students’ familiarity with grammar and mechanics of the English language. Certain guessing experiments to measure the predictability (defined in terms of entropy) of ordinary literary English were devised by Shannon (1951). A study to determine the predictability of English whether it is dependent on the number of preceding letters known to the subject was conducted by Burton and Licklider (1955). The variations in the predicting capacities of students learning English as a foreign language were studied by Siromoney (1964). Recently, Joyce (2002) has studied the use of metawriting to learn grammar and mechanics. Using freshman composition, the problems of grammatical errors and skills have been studied by Teorey (2003). In this paper, we propose to study the students’ familiarity with grammar and mechanics of English language from an exploratory point of view. The data have been analyzed statistically. The organization of this paper is as
43
follows. Section 2 discusses the methodology. The results are given in section 3. The discussion and conclusion are provided in Section 4. 2. METHODOLOGY A survey consisting of 20 multiple choice questions (see Appendix I) was constructed to test studentsâ&#x20AC;&#x2122; familiarity with English grammar and mechanics in six different courses in the spring semester of 2009. The courses selected were ENC 0021, ENC 1101, ENC 1102, EAP 1640, MGF 1107 and MAC 2233. The survey was administered by the instructors in each of these courses. A total of 121 students participated in the survey the details of which are provided in the following Tables 1 and 2 below.
Discipline ENC MAT Total
Table 1: Surveyed Courses Courses Respondents ENC 0021, ENC 1101, 71 ENC 1102, EAP 1640 MGF 1107, MAC 2233 50 6 121
Table 2: Survey Respondent Characteristics Gender Native Non-native Total English English Speakers Speakers Male 23 34 57 Female 29 35 64 Total 52 69 121 3. RESULTS 3.1 MASTERY REPORT The total number of questions in the survey was 20. Each question was assigned 1 point. The possible points in the survey were 20. The score unit was assumed to be percent. The minimum % to pass was 60. The mastery report of the survey participants is provided in the Figure 1 below.
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Figure 1: Mastery Report 3.2 ITEM ANALYSIS For the standard item analysis report of the survey questions, the participants were divided into three different groups, that is, Group I: (ENC 0021, EAP 1640); Group II: (ENC 1101, ENC 1102); and Group III: (MGF 1107, MAC 2233). The descriptive statistic of the performance of these groups in the survey is provided in Table 3 below. Table 3: Descriptive Statistic of Group Performance Group
I II III
Respondent
Mean Score
Median Score
S. D.
Reliability Coefficient (KR20)
Highest Score (out of 20)
Lowest Score (out of 20)
32 39 50
13.88 14.03 14.22
13.90 14.64 14.27
2.75 2.13 2.18
0.63 0.44 0.41
20.00 17.00 19.00
5.00 9.00 6.00
Further, the standard item analysis report of the survey questions for the said three groups is provided in the Figure 2 below.
Figure 2: Standard Item Analysis Report
3.3 HYPOTHESIS TESTING: INFERENCES ABOUT TWO MEAN SCORES This section discusses the hypothesis testing and draws inferences about the mean
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scores of two independent samples. Following the procedure on pages 474-475 in Triola (2010) of not equal variances: no pool, the hypothesis testing was conducted for three sets of two independent groups by using the statistical software package STATDISK. The results of these tests of hypotheses are provided below. (I) INFERENCES ABOUT MEAN SCORES OF ENC AND MAT PARTICIPANTS For this analysis, we defined the two groups as follows: ENC/EAP: ENC 0021, ENC 1101, ENC 1102, EAP 1640 MAT: MGF 1107, MAC 2233 The descriptive statistic of ENC/EAP and MAT participants is given in Table 4 below. Table 4: Descriptive Statistic of ENC and MAT Participants Group
Respondent
ENC/EAP MAT
71 50
Mean Score 13.96 14.22
S. D. 2.44 2.18
The results of the hypothesis test to draw the inferences about the mean scores of ENC/EAP and MAT participants are provided in Table 5 and Figure 3 below. Table 5: Hypothesis Testing about Mean Scores of ENC/EAP and MAT Assumption: Not Equal Variances: No Pool Let µ1 = Mean Score of ENC/EAP and µ2 = Mean Score of MAT. Claim: µ1 = µ2 (Null Hypothesis) Test Statistic, t: -0.6147 Critical t: ±1.981298 P-Value: 0.5400 Degrees of freedom: 112.3724 95% Confidence interval: -1.098025 < µ1-µ2 < 0.5780247 Fail to Reject the Null Hypothesis Sample does not provide enough evidence to reject the claim
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Figure 3: Hypothesis Testing about Mean Scores of ENC/EAP and MAT (II) INFERENCES ABOUT MEAN SCORES OF NATIVE ENGLISH SPEAKING AND NON-NATIVE ENGLISH SPEAKING PARTICIPANTS For this analysis, we defined the two groups as follows: ENG: Native English Speaking Participants NON-Eng: Non-native English Speaking Participants The descriptive statistic of ENG and NON-ENG participants is given in Table 6 below. In order to compare the scores of ENG and NON-ENG participants, the respective boxplots are drawn on the same scale in Figure 4 below. Table 6: Descriptive Statistic of ENG and NON-ENG Participants Group
Respondent
ENG NON-ENG
52 69
Mean Score 73.84615 67.68116
Median
S. D.
75 70
10.36658 12.05318
Figure 4: Comparing Scores of ENG (Col. 1) and NON-ENG (Col. 2) Participants
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The results of the hypothesis test inferences to draw about the mean scores of ENG and NON-ENG participants are provided in Table 7 and Figure 5 below. Table 7: Hypothesis Testing about Mean Scores of ENG and NON-ENG Assumption: Not Equal Variances: No Pool Let µ1 = Mean Score of ENG and µ2 = Mean Score of NO-ENG. Claim: µ1 = µ2 (Null Hypothesis) Test Statistic, t: 3.0182 Critical t: ±1.980468 P-Value: 0.0031 Degrees of freedom: 116.8722 95% Confidence interval: 2.119718 < µ1-µ2 < 10.21026 Reject the Null Hypothesis Sample provides evidence to reject the claim
Figure 5: Hypothesis Testing about Mean Scores of ENG and NON-ENG (III) INFERENCES ABOUT MEAN SCORES OF MALE AND FEMALE PARTICIPANTS For this analysis, we defined the two groups as follows: M: Male Participants F: Female Participants The descriptive statistic of the Male and Female participants is given in Table 8 below. In order to compare the scores of Male and Female participants, the respective boxplots are drawn on the same scale in Figure 6 below.
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Table 8: Descriptive Statistic of Male and Female Participants Group M F
Respondent 57 64
Mean Score 69.91228 70.70313
Median
S. D.
70 75
10.79398 12.56308
Figure 6: Comparing Scores of Male (Col. 1) and Female (Col. 2) Participants The results of the hypothesis test to draw the inferences about the mean scores of Male and Female participants are provided in Table 9 and Figure 7 below. Table 9: Hypothesis Testing about Mean Scores of Male and Female Participants Assumption: Not Equal Variances: No Pool Let µ1 = Mean Score of M and µ2 = Mean Score of F. Claim: µ1 = µ2 (Null Hypothesis) Test Statistic, t: -0.3724 Critical t: ±1.980123 P-Value: 0.7103 Degrees of freedom: 118.8560 95% Confidence interval: -4.995995 < µ1-µ2 < 3.414395 Fail to Reject the Null Hypothesis Sample does not provide enough evidence to reject the claim
Figure 7: Hypothesis Testing about Mean Scores of Male and Female Participants
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3.4 ANALYSIS OF VARIANCE (ANOVA) AND DIVERSITY ANALYSIS This section discusses the analysis of variance for testing the hypothesis of equality of the mean scores and diversity analysis for testing the hypothesis of evenness ratio of respondent performance based on gender-language spoken. All these analyses were carried out by using the statistical software packages STATDISK and EXCEL. (I) Respondent Performance Based on Gender-Language Spoken The performance of respondent based on gender-language spoken is provided in Table 10 and Figure 8 below. Table 10: Respondent Performance Based on Gender-Language Spoken Group AA AB BA BB BC
Gender â&#x20AC;&#x201C; Language Spoken Male-English Male-Spanish Female-English Female-Spanish Female-Other
% of Students Scoring 60 or above 18.18181818 24.79338843 23.14049587 23.14049587 0.826446281
% of Students Scoring Below 60 0.826446281 3.305785124 0.826446281 4.958677686 0
Figure 8: Respondent Performance Based on Gender-Language Spoken (II) Analysis of Variance (ANOVA) Following the procedure on pages 628-631 in Triola (2010), this section discusses the ANOVA for testing the hypothesis of equality of the mean scores of four independent groups based on gender-language spoken, that is, AA, AB, BA, and BB. The results of ANOVA are provided in Table 11 and Figure 9 below. (Note: There was only one female who spoke French and so was included in group BB for analysis purposes.)
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Table 11: ANOVA: Hypothesis Testing About Equality of Mean Scores ANOVA OF AA, AB, BA, BB (BC included in BB) Alpha = 0.05 Source: DF: SS: MS: Test Stat, F: Critical F: Treatment: 3 1156.315368 385.438456 2.941614 2.682134 Error: 117 15330.461492 131.029585 Total: 120 16486.77686 Reject the Null Hypothesis Reject equality of means
P-Value: 0.036012
Figure 9: ANOVA: Hypothesis Testing About Equality of Mean Scores (III) Diversity Analysis Applying the Shannonâ&#x20AC;&#x2122;s Measure of Diversity Index (in terms of entropy) (Shannon, 1948), this section discusses the diversity analysis for testing the hypothesis of evenness ratio of respondent performance based on gender-language spoken, that is, AA, AB, BA, BB, and BC. The results of Diversity Analysis are provided in Table 12 below. Table 12: Diversity Analysis Based on Gender-Language Spoken Group
Gender â&#x20AC;&#x201C; Language Spoken
AA AB BA BB BC
Male-English Male-Spanish Female-English Female-Spanish Female-Other
Proportion (p) of Students Scoring 60 or above 0.181818182 0.247933884 0.231404959 0.231404959 0.008264463
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Hypothesis: Does the respondent performance (that is, proportion of students scoring 60 or above based on gender-language spoken, that is, AA, AB, BA, BB, and BC, as provided in Table 12 above) suggest more diversity in the groups’ familiarity with the English grammar and mechanics?
The Shannon’s Measure of Diversity Index H and Evenness Ratio E H , where
0 E H 1 , for the above Table 12, are computed as follows. Note that if E H 1 , there is complete evenness. H 1.372718 E H 0.852918 Since E H 0.852918 1 , there appears to be complete evenness in the respondent performance (that is, proportion of students scoring 60 or above based on genderlanguage spoken, that is, AA, AB, BA, BB, and BC, as provided in Table 12 above). 4. CONCLUSIONS This paper discussed the students’ familiarity with grammar and mechanics of English language from an exploratory point of view. A total of 121 students from six different courses, that is, ENC 0021, ENC 1101, ENC 1102, EAP 1640, MGF 1107 and MAC 2233, participated in the survey. The minimum % to pass was 60. Out of 121 survey participants, 90.10 % scored 60 or above. Based on the hypothesis testing, the following inferences were drawn about the survey participants. 1. There was sufficient evidence to support the claim that the mean scores of Male and Female participants were same. 2. There was sufficient evidence to support the claim that the mean scores of ENC/EAP and MAT participants were same. 3. There was sufficient evidence to reject the claim that the mean scores of Native English speaking and Non-native English speaking participants were same. 4. There was sufficient evidence to reject the claim of the equality of mean scores of four independent groups based on gender-language spoken, that is, AA, AB, BA, and BB. 5. There appears to be complete evenness in the respondent performance (that is, proportion of students scoring 60 or above based on gender-language spoken).
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It is hoped that the findings of the paper will be useful for researchers in various disciplines. ACKNOWLEDGMENT
The authors would like to express their sincere gratitude and acknowledge their indebtedness to the students of the courses, that is, ENC 0021, ENC 1101, ENC 1102, EAP 1640, MGF 1107 and MAC 2233, in the spring semester of 2009, for their cooperation in participating in the survey. Further, the authors are thankful to Professor Francia Torres for allowing us to administer the survey in her ENC0021 course and to Mr. Cesar Ruedas for assisting in test item analysis.
REFERENCES
Burton, N. G., and Licklider, J. C. R. (1955). Long-range constraints in the Statistical Structure of Printed English. American Journal of Psychology, 68, pp. 650 – 653. Joyce, J. (2002). On the Use of Metawriting to Learn Grammar and Mechanics. The Quarterly, Vol. 24, No. 4, pp. 1 - 5. Shannon, C.E. (1948). A Mathematical Theory of Communication. Bell System Technical Journal, 27, pp. 379 - 423; 623 - 656. Shannon, C.E. (1951). Prediction and Entropy of Printed English. Bell System Technical Journal, 30, pp. 50 - 64. Siromoney, G. (1964). An Information-theoretical Test for Familiarity with a Foreign Language. Journal of Psychological Researches, viii, pp. 267 – 272. Teorey, M. (2003). Using Freshman Composition to Analyze What Students Really Know About Grammar. The Quarterly, Vol. 25, No. 4, pp. 1 - 5. Triola, M. F. (2010). Elementary Statistics. Addison-Wesley, N. Y.
APPENDIX A Grammar Research Project
Spring 2009
Sentence Structure – Identify the type of sentence: A. Simple
B. Compound
C. Complex
1. Pat and Rob both work in the industrial complex. 2. While Pat is in the accounting department, Rob is an engineer. 3. Rob works the late shift, so he rarely sees Pat.
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4. Pat needs to leave work by 3PM in order to pick up his son from school.
Verb Tenses and Forms - Which Answer Corrects the Sentence 5. As I began to write my essay, my computer falled off the desk and broke. A. begins
B. fell
C. breaked
6. Before the pitcher threw the ball, the player ran and stealed second base. A. throw
B. runs
C. stole
7. When Kelly saw the dish, he will eat all the food and forget to save some for Saul. A. sees
B. will eats
C. forgot
8. Whenever I study for an exam, I closed my door and turn on my desk lamp. A. studying
B. close C. turned
Commonly Confused Words - Which Answer Corrects the Sentence 9. Drinking too many sodas can effect your health. A. to
B. affect C. you’re
10. A lot of investors loose money through risky investments. A. A lot
B. lose
C. though
11. The buyers should have tried to except their offer. A. should of
B. accept C. they’re
12. Mary would like to take the Design course, but it’s all ready full. A. coarse
B. its
C. already
Punctuation – Identify the correct sentence 13. A. After watching the movie, Sally needed to return the DVD, so she borrowed her father’s car. B. After watching the movie Sally needed to return the DVD, so she borrowed her father’s car. C. After watching the movie, Sally needed to return the DVD so she borrowed her father’s car. 14.
A. Marco can go to the meeting, but not the party because somebody’s going to
his house for
dinner.
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B. Marco can go to the meeting but not the party because somebody’s going to his house for
dinner.
C. Marco can go to the meeting but not the party, because somebody’s going to his house for 15.
dinner.
A. Samuel took a month’s leave of absence in order to be with his Aunt May,
who was very ill. B. Samuel took a month’s leave of absence in order to be with his Aunt May who was very ill. C. Samuel took a month’s leave of absence, in order to be with his father, who was very ill. 16.
A. The new business plan is said to have many advantages, such as maintaining
facilities
increasing profits and allowing for raises and new hires.
B. The new business plan is said to have many advantages, such as maintaining facilities,
increasing profits and, allowing for raises and new hires.
C. The new business plan is said to have many advantages, such as maintaining facilities,
increasing profits, and allowing for raises and new hires.
Spelling - Identify the misspelled word. 17. It was (a.) truley an (b.) honor to have (c.) known Dr. Livingstone. 18. My brother is (a.) pursuing a (b.) career as a (c.) licenced broker. 19. The (a.) committee was able to (b.) accomodate the new members without (c.) noticeable difficulties. 20. Luis had an uneasy (a.) conscience for having (b.) embarassed Samantha with the (c.) surprise party.
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Polygon Spring 2010 Vol. 4, 56-80 EFFECTS OF DEVELOPMENTAL COURSES ON STUDENTSâ&#x20AC;&#x2122; USE OF WRITING STRATEGIES ON THE FLORIDA COLLEGE BASIC SKILLS EXIT TEST
1
M. L. Varela 1 Department of Communication, Arts & Philosophy, Miami Dade College, InterAmerican Campus, Miami, FL 33135, USA. Email: mvarela@mdc.edu ABSTRACT
The writing strategies students use most often in preparing for the subjective and objective tests of writing for College Preparatory Writing 3 were examined. To address this, data was collected using a comprehensive survey that asked students about the strategies they used in four different domains: vocabulary strategies, comprehension strategies, grammar strategies, and strategies to specifically improve writing skills. It was hypothesized that studentsâ&#x20AC;&#x2122; use of writing strategies on the exit exam resulted in a substantial percentage of students retaking the course. The results indicated that the percentage of students using different strategies varied dramatically. Some strategies were used very frequently while others were not.
KEYWORDS Developmental writing, exit tests, writing skills, writing readiness, community college.
1. INTRODUCTION
In the 1970s and 1980s, a high school diploma guaranteed high-paying jobs, however, given today's career markets and job competition, a college education has become essential and necessary. Obtaining a college degree is valued and beneficial to the potential college graduate (National Center for Education Statistics [NCES], 2003). Students entering colleges or universities are expected to bring prior knowledge and experiences learned at the high school level as a foundation for college study. Basic skills in English, mathematics, reading, and writing are the underlying groundwork essentials for a productive college experience and completion (NCES, 2003). These skills are then 56
further developed through a series of courses taken at the college or university level for the purpose of obtaining a certificate or a degree. The harsh reality is that a majority of students entering colleges and universities do not have the basic principles associated with becoming a college student, and as a result require special interventions in the form of developmental or remedial courses (Carter, Roth, Crans, Ariet, & Resnick, 2001). In 1996, NCES revealed that 77% of higher education institutions in the nation with an enrollment of freshmen offered at least one remedial reading, writing, or mathematics course in fall of 1995. Similarly, the same research was conducted in 2000 and reported in 2004. The research revealed that 76% of the higher education institutions still offered at least one remedial reading, writing, or mathematics course in the fall of 2000. The difference in the 1% drop in a four-year period is insignificant in relation to the number of underprepared students currently entering colleges and universities nationwide (NCES, 2004). Further, the Florida Department of Education (2007) reported in 1999 that 59% of high school students entering the community college system require remediation in one or more areas. The need for remediation is prevalent among community colleges and while the exact percentages are not known, slightly 37% of entering college freshmen needed at least one area of remediation. The presence of developmental programs in 94% of public colleges and 82% of private colleges in Florida reflect the present continuing need (Wyatt, 1992). For one particular college in South Florida, 81% of students enrolled are underprepared according to scores analyzed on the Computerized Placement Test (CPT) (Bashford & Mannchen, 2005; Rodriguez, 2006). Since 1985, the State of Florida has
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required entry-level testing for students seeking Associate in Arts and Associate in Science degrees. In 2006 the College Academic Student Support Council stated “The CPT is used for placement at all Florida community colleges for most programs” (p. 4). Therefore, every degree-seeking student at the college must take the CPT. The College Academic Student Support Council also stated the CPT is the test that determines how college-ready the students are since it “assesses students' content knowledge in reading, sentence skills, and mathematics” (p. 4). Since the CPT is an adaptive test, the computer automatically determines which questions are presented to the students based on their responses to prior questions. This technique zeroes-in on just the right questions to ask without being too easy or too difficult. Consequently, Morris (2006) stated “The greater the students demonstrate skill level, the more challenging will be the questions presented” (p. 2). Students who take any of the three levels of remedial writing should be prepared to move to the next level, which is ENC1101 or regular freshman English Composition 1. However, according to the subject college's records, the Research and Testing Committee revealed that the progression of students from college preparatory writing to college level English has declined for the past three years and is now 48% (Morris, 2006). Upon learning this, the researcher set out to discover possible reasons why the decline was consistent for three years. A set of 28 writing strategies where examined with the sampled student population to identify a possible correlation between students’ frequent use of strategies and their passing rate on the exit test.
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2. RESEARCH QUESTIONS AND METHODOLOGY RESEARCH QUESTIONS Based on the concern that students may not be applying the proper strategies to successfully pass the Florida College Basic Skills Exit Test, four research questions were analyzed. Therefore, for the purpose of this study the researcher investigated strategies used by the ENC0021 student population that could be predictors of the decline in enrollment from ENC0021 to ENC1101. The purpose of this study was multifold and the following research questions were addressed: 1. What are the most common writing strategies that students employ? 2. Is there a relationship between the use of different strategies? That is, do students who frequently use one type of strategy (e.g., vocabulary) also use other strategies (e.g., grammar) with high frequency? 3. What are student’s perceptions of the Florida College Basic Skills Exit Test and the content of its essay prompts? 4. Do writing professors think students feel writing has value in high school and college courses, in overall academic performance, and in their future? Research has indicated possible reasons as to why students enter college underprepared. According to Hoyt and Sorensen (2001) the most popular trend in education today is the “chain of blame” game. This “chain of blame” occurs when “universities blame the high schools, the high schools blame the middle schools, and the middle schools blame the elementary schools for poor student preparation” (p. 26). In essence, the lack of preparation at the secondary level has become a hindrance for students who wish to pursue a college education.
59
Furthermore, in a recent study of high school preparation and placement testing, Hoyt and Sorensen found that as part of the standards movement, including their home state of Utah, certain states are “implementing mandatory proficiency tests, releasing report cards on schools,” and “differentiating high school diplomas, giving some students credit for demonstrating competence in college preparatory courses based on proficiency exams” (p. 32). A similar approach has also taken effect in Florida schools in regard to the FCAT. Hoyt and Sorensen also discovered that teachers “may be awarding passing grades to many students who have not adequately learned the material” (p. 32). This scenario jeopardizes those students whose intentions are to attend college. In addition, Hidi and Harackiewicz (2000) stated that another possible reason for the underpreparedness of secondary students is the lack of motivation and effort. Hidi and Harachiewicz affirmed that boring courses, demanding professors, and difficult assignments all contributed to the college students’ lack of effort. However, the research did not indicate as to when the underpreparedness occurred. There is clearly a need for more structured readiness at the secondary level so that students will be well-prepared prior to entering college, but research still indicates that a need for remediation at the college level will continue to be prevalent today and in years to come (Hoyt & Sorensen, 2001; Wyatt, 1992). Colleges and universities have a responsibility to maintain appropriate admission standards. But the admissions process at open institutions, give underprepared students a second chance at a college education, and should be structured to ensure that students are prepared for college level course work (Hoyt & Sorensen, 2001).
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The progression of students from College Preparatory Writing 3 to English Composition 1 (ENC0021-ENC1101) respectively, has declined for the past three years (Morris, 2005). In ENC0021 two state-mandated tests are to be taken and passed before students are allowed to register for ENC1101. This study focused on tracking the number of students who move from ENC0021 to ENC1101. In another study of student preparation, Thot-Johnson and Vanniarajan (2002) focused on students reading and writing strategies and high-stakes performance. Their study indicated that students used writing strategies that they believed were useful strategies. Thot-Johnson and Vanniarajan noted that students “would feel empowered and would be further motivated to use them, which subsequently would result in increased skill execution” (p. 5). The study also specified that students who do not internalized writing strategies experience difficulty in becoming independent thinkers and writers. However, research showed that students of writing who are underprepared worked twice as hard and wrote twice as many drafts as their “prepared” counterparts, and were conscientious about their progress (Community College Survey of Student Engagement, 2005; Crouch, 2000). Writing abilities vary by individuals. Each one has a set of unique life experiences developed, different experiences with strategies, and different ways of communicating. When the final exam writing prompt was given to students, no two writers used the same prewriting techniques in order to develop a cohesive essay, nor did the student writers expressed the same point of view. This was due in part because students were taught to write in different ways.
61
According to Carter, Roth, Crans, Ariet, and Resnick (2001) the explanation most commonly given by community college officials for the high failure rate on the CPT is that “students’ course-taking choices in high school did not equip them with the skills needed to do college-level work” (p. 73). Thus, the possibility of these studies might have attributed to the causes of the educational trends, but one can never be sure. Is the relationship between the chain of blame game and students’ lack of success on the CPT so obvious and so closely related that one influences the outcome of the other? If so, ultimately where does the chain of blame game begin or end? There is a need for a collaborative effort between the local high schools and the local community colleges and universities. Hoyt and Sorensen (2001) suggested that college and university faculty should assist high school instructors in the process of developing English and mathematics curriculum to better prepare students for subsequent college level course work. Perhaps pre college students would benefit from their suggestions since the subject college is a diverse college. And although only 19% of all entering students are college-ready, the college promises to help produce individuals of great success and fortitude. Finally, the implementation for newly designed placement exams at the college level are still unknown at this time, but there is evidence that new proposals are in the work and will be available in the near future (Sanchez, 2006).
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METHODOLOGY This study focused on a population made up of 74 college preparatory students. The 74 students were enrolled in five courses of ENC0021. Students and professors were selected based on a volunteer basis and availability of time. A questionnaire (Appendix B) surveying the 74 students was distributed to collect data addressing the research questions. An additional questionnaire (Appendix C) was distributed to the professors that taught writing for the spring term 2008 with the idea of gaining a greater perspective of the students enrolled in ENC0021 as well as the professors' teaching philosophy. A total of eight full- time professors volunteered for the study. The participants, to include students and professors, were made aware of the significance of the study via a Letter to Professors (Appendix D) and a Letter to Survey Recipients (Appendix E). The data determined students' attitude about writing and about the Florida College Basic Skills Exit test for the sole purpose of aiding the researcher in reporting the findings. In order to have conducted such an investigation, the researcher chose an experimental design approach to determine if there was a correlation between the Florida College Basic Skills Exit test and studentsâ&#x20AC;&#x2122; non-passing status from the developmental level of writing courses to regular level college courses. 3. CONCLUSIONS This study will contribute to the literature as the existing literature has not studied the correlation between studentsâ&#x20AC;&#x2122; use of writing strategies and the Florida College Basic Skills Exit Test. This chapter will highlight the summary of survey results, summarize exit exam results, summarize qualitative teacher surveys, discuss implications for
63
practitioners, integrate findings with the current study with previous studies, discuss limitations, and offer recommendations. One of the primary research questions of this study addressed the use of different writing strategies. To address this, data was collected using a comprehensive survey that asked students about the strategies that they used in four different domains: vocabulary strategies, comprehension strategies, grammar strategies, and strategies to specifically improve writing skills. The subsequent analysis results summarize the use of these four broad writing strategies, each of which was addressed using a series of questionnaire items. For each strategy, students were first asked whether they used the strategy. If they reported using a strategy, a follow-up question asked whether the student used the strategy “Some of the time” or “Most of the time”. The percentage of students using different strategies varied dramatically. Some strategies were used very frequently while others were not. Considering all four categories (vocabulary strategies, comprehension strategies, grammar strategies, and strategies to specifically improve writing skills), the survey addressed 28 unique strategies. Table 13 summarizes the overall results by rank ordering the 28 strategies according to the percentage of students that use each approach. As seen in the table, only 6 of the 28 strategies (21.4%) were used by more than 90% of the students. Among these top strategies, four were vocabulary-related. A larger tier of 10 strategies were used by 80% to 90% of the students. As seen in the table, this set of strategies included a mix from the four categories. Finally, nearly half of the strategies were used by fewer than 70% of the students. Among this set of approaches, two strategies were used with very low frequency: observing classmates’
64
essays (55.6%) and giving up on what to say (46.6%). Giving up is a poor strategy, so it is not a surprise that this approach was ranked last. However, nearly half of the sample reported using this strategy. Obviously, this has an important bearing on studentsâ&#x20AC;&#x2122; ability to improve their reading and writing skills. Table 13 Overall Use of 28 Strategies Survey Question
Percent
Category
Q24.
Reread the paragraph
98.6
C
Q21.
Use a different word with a similar meaning
95.9
V
Q13.
Guess the meaning based on context
94.5
V
Q25.
Distinguish the relevant details
93.2
C
Q19.
Use the spell check function
93.2
V
Q16.
Pay attention to how a word is used
90.5
V
Q30.
Use the grammar check
89.2
G
Q31.
Notice grammar mistakes when proofreading
89.2
G
Q39.
Revise what you have written
87.7
W
Q28.
Summarize the information after reading
86.5
C
Q33.
Decide in advance what to write about
86.3
W
Q12.
Use a dictionary
85.1
V
Q18.
Remember the context in which it occurs
84.9
V
Q34.
Decide in advance what content to put in
84.7
W
Q32.
Make an outline
83.8
W
Q29.
Pay attention to grammatical structure
82.4
G
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Q27.
Make predictions about the contents of essay
76.7
C
Q26.
Make comparisons with your own experiences
76.4
C
Q35.
Focus on learning grammar
75.3
W
Q14.
Ask your instructor for examples
74.0
V
Q20.
Write the word down
68.9
V
Q15.
Look it up if it is important
65.8
V
Q38.
Show your writing to others
65.8
W
Q22.
Consult the thesaurus
62.2
V
Q36.
Read a lot of books
60.8
W
Q17.
Translate the word in your native language
60.3
V
Q37.
Observe how essays are written by classmates
55.6
W
Q23.
Give up what you want to say
46.6
V
Note. V = vocabulary, C = comprehension, G = grammar, and W = writing A separate set of analyses examined the impact of the Florida State Writing Exit Test on course performance. Specifically, students were categorized according to whether they had satisfactory performance in the class prior to taking the exam. Among the students who were performing satisfactorily, 88.5% passed the exit exam. This means that 11.5% of the students who were otherwise performing well had to repeat the course because they failed the exit exam. Looking at these results differently, 29 students failed the exit exam. Among these students, 24% had satisfactory performance prior to taking the exit exam. This suggests that the exit exam does result in a substantial proportion of students retaking the course.
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An analysis of research question 3 revealed that professors believe their students employ the capabilities of being successful at writing. The overall consensus was that one view looks at writing as a process of filling in the blanks of a 5-paragrah formula that doesnâ&#x20AC;&#x2122;t have much meaning beyond preparation for standardized exams. Another view looks at writing as a genuine process of exploration and creative reflection that is part of living their lives. However, the overall opinion was that some studentsâ&#x20AC;&#x2122; view are somewhere in the middle of the two extremes. And while many students understand the more creative model, they do not see it as one that is valued in school, even though they may apply it on their own. Although at diametric extremes in years of experience, the overall philosophies were similar. The instructors interests were on behalf of their studentsâ&#x20AC;&#x2122; successes and capabilities in learning how to writing at the college level and to become life-long learners. In accordance with the outcome of table 13, the top six strategies students used with most frequency are considered weak strategies. These strategies are not consistent with approaches that will improve student performance. With the exception of paying attention to how a word is being used in context, the overall results of the top six strategies are ineffective according to the writing curriculum at the college level. Cleary, practitioners need to be made aware of the types of strategies being used by the writing student population in the classroom, since these same strategies are most likely the same ones being implemented when students take the Florida College Basic Skills Exit Test. The strategies used by 80% to 90% of the students are strategies that could be considered helpful depending on the goals of each individual writing instructor. And although instructor goals may vary, generally the ultimate outcome is for students to feel
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comfortable with writing in a college setting. Therefore, instructors need to emphasize on the strategies that are used by the larger population of students and not necessarily the ones they use most frequently in the classroom. This finding also has important implications for high school educators, counselors, and parents. High school students should be advised as early as the ninth grade of college preparedness. One study revealed that the more students that take the more difficult courses in high school consequently score higher on standardized test, thus eliminating the need for remediation at the college level. (Carter, Roth, Crans, Ariet, & Resnick, 2001) On the whole, the implications of the results on instruction indicate that students use writing strategies with high frequency at least 80% of the time. Students will use what instructors teach them. If that is the case, it is obvious then that effective strategies need to be taught. One reason to teach students these strategies is due in part because writing is process based as opposed to content based. Instructors can only teach students how to learn to write (Thot-Johnson & Vanniarajan, 2001). It is important to integrate the results of this study with previous research studies. Several studies had similar outcomes in regards to students’ frequent use of writing strategies and performance on standardized testing. Thot-Johnson and Vanniarajan's (2002) study revealed that by the time students enter undergraduate studies they realize that they must possess reading and writing abilities in order to become “independent learners of academic material” (p. 4). Another similarity between this study and the researcher’s study was that the majority of the writing student population did not find the writing prompt interesting. Although the researcher’s
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participants did not feel the topic was too American culture, it perhaps did not target the participants’ schema and therefore the topic was found uninteresting. Moreover, the sample size was also closely related (Thot-Johnson’s & Vanniarajan=77, the researcher=74). However, when students were questioned on their self-perceived level of writing ability in English in Thot-Johnson’s and Vanniarajan’s study, “24 students (31.2%) felt that their writing ability was below average, 36 students (46.8%) felt it was average, and 4 students (5.2%) perceived that their ability was good” (p. 8). These results are for a total of 64 students. The study did not report on the writing ability of 13 of the students sampled. And when students were asked the same question on the researcher’s study, 3 students (4.5%) felt their writing ability in English was below average, 23 students (31.08%) felt it was average, 8 students (10.81%) reported it was very good, 2 students (2.70%) felt it was excellent, and 38 students (51.35%) felt their writing ability in English was good. It was interesting to reveal that 79.9% of students whose native language is Spanish felt that their writing ability in English was good. The research suggested that although Spanish is the language most often used by students at the college, it did not affect students writing ability in English. As noted, the study most closely related to the researcher’s study was Thot-Johnson and Vanniarajan (2002). And although the studies had many similarities, they differed in geographical location. Thot-Johnson and Vanniarajan conducted their study in California (West Coast), whereas the researcher conducted her study in Florida (East Coast). Moreover, Hoyt and Sorenson’s (2001) study revealed the importance of validating standardized testing and accurate placement of students. They stressed that standardized tests that asses writing skills are problematic because of the “difficulty in accurately
69
measuring writing abilities” (p. 33). The same was true for this study in regards to the Florida College Basic Skills Exit Test. The ENC0021 exit test cannot be taught in terms of content. Again, what instructors need to focus on is teaching students how to learn to write instead. The researcher did notice however that at least one study had a difference outcome. While Hidi and Harackiewicz’s (2000) study revealed that students’ underpreparedness was a lack of motivation and effort, the researcher’s study indicated that 53.4% of the participants did not give up on what they wanted to say in their final exam essay. Students in this study as compared to Thot-Johnson and Vanniarajan's (2002) study used 16 of the 28 strategies questioned on the survey. They use strategies they felt comfortable with and strategies they knew well. After reading the research studies, the researcher was aware that students’ lack of preparedness at the secondary level was affecting their ability to perform well on the CPT as well as on the ENC0021 exit test. The researcher’s findings were consistent with the literature except in terms of geographical area and age group. The researcher’s study contributes to the literature by studying a sample size that ranged in age from 18 to 54 and where the primary language of 79.7% of the participants is Spanish. A number of limitations should be noted about this study’s results. As a general caveat, the use of a survey design warrants caution when interpreting the study results. Specifically, the survey asked students to retrospectively recall which writing strategies that they used. It is difficult to determine whether these retrospective accounts accurately reflect what students actually use in practice. The accuracy of these survey questions
70
requires that students are cognitively aware of the strategies that they are employing as they write. The level of awareness that allows students to accurately answer these survey questions probably varies considerably across people. Another limitation of this study is that it was not possible to link student reports of strategy use to their actual test performance. Anonymity requirements did not allow the surveys to contain identifying information, so it was not possible to link a survey record to course performance or to test performance. Ideally, it would have been desirable to determine whether the use of certain strategies is associated with better course performance or better exam performance. Unfortunately, this was not possible. Third, generalizability is always something that should be considered when interpreting the results from a study. The student population from which this studyâ&#x20AC;&#x2122;s sample was drawn is quite different from the general college student population. Specifically, the students ranged between 18 and 54, with a mean of M = 25.24 (SD = 8.84). This is a somewhat non-traditional age range for college students. Also, the vast majority of students (79.7%) in the sample reported that Spanish was their native language, and only 10.8% of students reported English as their native language. The high rate of Spanish language speakers is not surprising, given that the study was conducted in a large metropolitan city in South Florida, but it is not representative of the broader college student population. Finally, many of the students reported relatively low levels of reading and writing ability. This may or may not be representative of students at other universities. This investigation was also limited to the writing developmental students enrolled at the college used in this study. An experimental group was selected to represent the entire
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writing student population at the college. In doing so, it was believed that the outcome would be representative of the effectiveness of the Florida College Basic Skills Exit Test administered to developmental writing students at the community college level. This study was limited to the faculty members teaching ENC0021 and ENC1101. Other faculty teaching subsequent sections of writing were not included in the study. Consequently, the faculty will not have access to the data and end results to possibly aid their own developmental students. Furthermore, the shortcoming ingrained in the use of questionnaires to collect the type of data needed for this study might have impacted the validity or reliability of the data. While this study adds to the literature, it is recommended that future researchers should take these findings and conduct additional research on studentsâ&#x20AC;&#x2122; use of effective strategies in the classroom through observation. And, compare if the effective strategies correspond with the ones that this study found were used most frequently. The data also revealed that 44 (59.5%) students felt that there was not enough time to complete the essay part of the exit test. And 38 (51.4%) students felt there was not enough time to complete the grammar portion of the exit test. Given these data, more time allotted on the Florida College Basic Skills Exit Test is recommendation. It is inferred that if more time was given, more students would have done better on the test. It is also recommended for instructors to assess their studentsâ&#x20AC;&#x2122; proficiency in the English language and use of writing strategies. They can do this by administrating a diagnostic assessment in writing at the beginning of each ENC0021 course. Once they have scored the diagnostic assessment, instructors need to examine and determine the
72
studentsâ&#x20AC;&#x2122; level of learning and achieved practices. Instructors should also determine how results will be disseminated. Finally, with proper techniques on how to write effective essays, proper use of writing strategies and cognitive skills in English, instructors can teach ENC0021 students on how to successfully achieve a passing score on the Florida College Basic Skills Exit Test.
REFERENCES
Bashford, J. (2005). What happens to students with all-but-FCAT certificates of completion? Retrieved October 1, 2006 from www.mdc.edu
Carter, R. L., Roth, J., Crans, G., Ariet, M., Resnick, M. B. (2001). Effect of High School Coursetaking and grades on passing a college placement test. The High School Journal, 84(2), 72-87.
Community College Survey of Student Engagement (CCSSE). (2005). Engaging students, challenging the odds. Retrieved November 3, 2006 from http://www.ccsse.org
Crouch, M. (2000). Looking back, looking forward; California grapples with remediation. Journal of basic writing, 19(2), 44-71.
Florida Department of Education. (2007). K-20 Articulation: Policies, Procedures and Challenges. Retrieved November 5, 2007, from http://www.fldoe.org/cc/chancellor/newsletters/clips/articulationchartsynthesis1.asp?style =print
Hidi, S. & Harackiewicz, J. M. (2000). Motivating the academically unmotivated: A critical issue for the 21st century. Review of Educational Research, 70(2), 151-179.
Hoyt, J. E. & Sorensen, C. T. (2001). High School preparation, placement testing, and college remediation. Journal of Developmental Education, 25(2), 26-33.
Morris, C. (2006). Computerized placement test. Retrieved October 1, 2006, from www.mdc.edu
National Center for Education Statistics (NCES). (2003). Remedial Education at Higher Education Institutions in Fall 1995, NCES 97-584, Washington, DC: 2006. Retrieved October 1, 2006, from http://nces.ed.gov/pubs/97584.pdf 73
Rodriguez, S. (2006). Basic skills assessment results fall terms 2001 through 2005. Retrieved October 8, 2006, from www.mdc.edu
Sanchez, C. (2006). Commission mulls standardized testing in colleges. National Public Radio. Heard on February 14, 2006.
Thot-Johnson, I. D. (2002). Students' reading and writing strategies and their WST performance. The CATESOL journal, 14(1), 73-101.
Wyatt, M. (1992). The past, present, and future need for college reading courses in the U.S. Journal of Reading, 36(1), 10-20.
Appendixes Appendix B A Survey on Studentsâ&#x20AC;&#x2122; Writing Strategies and Their Florida State Exit Writing Exam Performance Directions: Please answer all the questions as accurately as possible. This information is being requested for research purposes and will remain confidential. Thank you for your participation. Part A: Background Information 1. Gender: Male_______ Female ________ 2.
Age: ___________
3.
Academic Level: ________________
4.
What is your major? ____________________________________
5.
What is your native language? ________________________________________
6.
How would you describe your current reading ability in English? a. Below average b. Average c. Good d. Very good e. Excellent
7.
How would you describe your current reading ability in your native language? a. Below average b. Average 74
c. Very good d. Excellent 8.
How would you describe your current writing ability in English? a. Below average b. Average c. Good d. Very good e. Excellent
9.
How would you describe your current writing ability in your native language? a. Below average b. Average c. Good d. Very good e. Excellent
10.
Was your elementary school education in English? Yes/No If yes, from which grade? From grade: _______
11.
Was your high school education in English? Yes/NO If yes, from which grade? From grade: _______
Part B: Writing Strategies Vocabulary 12. When you come across an unknown word while reading in English, do you use a dictionary? (either English or bilingual)?
13.
Yes/No If yes: a. Most of the time b. Some of the time When you come across an unknown word while reading in English, do you try to guess the meaning of the unknown word based on the context?
14.
Yes/No if yes: a. Most of the time b. Some of the time When you come across an unknown word while reading in English, do you ask your instructor for examples of how to use the word?
15.
Yes/No if yes: a. Most of the time b. Some of the time When you look up an unknown word in a dictionary while reading in English, do you look it up only if it is important?
16.
Yes/No if yes: a. Most of the time b. Some of the time When reading in English, do you pay attention to how a word is used? Yes/No
if yes: a. Most of the time
b. Some of the time 75
17.
When you are trying to learn a new word in English, do you try to remember its meaning by translating it in your native language?
18.
Yes/No if yes: a. Most of the time b. Some of the time When you are trying to learn a new word in English, do you try to remember its meaning by remembering the context in which it occurs?
19.
Yes/No if yes: a. Most of the time b. Some of the time While writing essays on the computers, do you use the spell check function?
20.
Yes/No if yes: a. Most of the time b. Some of the time When you are trying to learn the spelling of a new word in English, do you try to remember it by writing it down one or more times?
21.
22.
23.
Yes/No if yes: a. Most of the time b. Some of the time When you do not know the exact word you want while writing in English do you attempt to use a different word that has a somewhat similar meaning? Yes/No if yes: a. Most of the time b. Some of the time When you do not know the exact word you want while writing in English do you consult the thesaurus? Yes/No if yes: a. Most of the time b. Some of the time When you do not know the exact word you want while writing in English do you give up what you want to say?
Yes/No if yes: a. Most of the time b. Some of the time Comprehension 24. When you donâ&#x20AC;&#x2122;t understand a paragraph while reading in English, do you reread it?
25.
26.
27.
Yes/No if yes: a. Most of the time b. Some of the time When you read in English, can you distinguish the relevant and important details from the irrelevant and unimportant details? Yes/No if yes: a. Most of the time b. Some of the time When you read a paragraph, a story, or a news item in English, do you make connection or comparisons between your own experiences and those of your characters? Yes/No if yes: a. Most of the time b. Some of the time When you start to read an academic essay in English, can you make predictions about what the essay will contain in the second half? Yes/No
if yes: a. Most of the time
b. Some of the time 76
28.
When you read a chapter in a textbook or a journal article, or an academic essay in English, can you summarize the information after you have read it in order to remember it? Yes/No
Grammar 29.
30.
31.
if yes: a. Most of the time
b. Some of the time
When you read in English, do you pay attention to how sentences are grammatically constructed? Yes/No if yes: a. Most of the time b. Some of the time When writing essays on the computer, do you use the grammar check? Yes/No if yes: a. Most of the time b. Some of the time While proofreading your written essays, do you notice any grammar mistakes? Yes/No
if yes: a. Most of the time
b. Some of the time
Improving Writing Skills 32. Before you start writing an academic essay, do you make an outline?
33.
Yes/No if yes: a. Most of the time b. Some of the time In order to improve your writing skills, do you decide in advance what to write about? Yes/No
34.
35.
36.
if yes: a. Most of the time
b. Some of the time
In order to improve your writing skills, do you decide in advance what content to put in which paragraph? Yes/No if yes: a. Most of the time b. Some of the time In order to improve your writing skills, do you focus on learning grammar (either by enrolling in grammar classes or on your own)? Yes/No if yes: a. Most of the time b. Some of the time In order to improve your writing skills, do you read a lot of books?
37.
Yes/No if yes: a. Most of the time b. Some of the time In order to improve your writing skills, do you observe how essays are written by your classmates?
38.
Yes/No if yes: a. Most of the time b. Some of the time In order to improve your writing sills, do you show your writing to another person aside from your teacher? Yes/No
if yes: a. Most of the time
b. Some of the time 77
39.
In order to improve your writing skills, do you revise what you have written more than once? Yes/No
if yes: a. Most of the time
b. Some of the time
Part C: The Florida State Writing Exit Exam 40. When are you planning to take the Florida State Writing Exit Exam? (Please enter date) ___________________ 41. What do you think of the exit exam as a writing test?
42.
43.
Excellent Good Poor What do you think of the exit exam as a grammar test? Excellent Good Poor Do you think that there is enough time (60 min) to do the essay part of the exit exam? Yes, there is enough time to do the essay part of the exit exam. No, there is not enough time to do the essay part of the exit exam. c. I’m not sure if there is enough time to do the essay part of the exit exam. Do you think there is enough time (45 min) to do the grammar part of the exit exam? a. b.
44.
a. b. c.
45.
Yes, there is enough time to do the grammar part of the exit exam. No, there is not enough time to do the grammar part of the exit exam. I’m not sure if there is enough time to do the grammar part of the exit exam.
Does the essay prompt (content-wise) interest you? a. Yes, the essay prompt interests me. b. No, the essay prompt does not interest me. c. I’m not sure if the essay prompt interests me.
46.
Is the essay prompt (content-wise) too American –culture specific? a. b. c.
47.
Yes, the essay prompt is too American-culture specific. No, the essay prompt is not too American-culture specific. I’m not sure if the essay prompt is too American-culture specific.
Do you have a hard time writing with pen and/or pencil? 78
a. b. c.
Yes, I have a hard time writing with pen and/or pencil. No, I do not have a hard time writing with pen and/or pencil. I’m not sure if I have a hard time writing with pen and/or pencil.
Note. The Students’ Writing Strategies and their Florida State Exit Writing Exam Performance questionnaire is from “Students’ Reading and Writing Strategies and Their WST Performance,” by I. D., Thot-Johnson and S. Vanniarajan, 2002, The CATESOL Journal, 14, pp. 73-101. Copyright 2002 by The CATESOL Journal. Adapted with permission. Appendix C A Survey of Faculty Opinion on Student Writing Directions: Please respond to all the questions as accurately as possible. This information is being requested for research purposes and will remain confidential. Thank you for your participation. 1. How long have you been teaching developmental writing? 2. What is your teaching philosophy? 3. In your professional opinion, do you think students see writing as valuable tool for general college courses? Why or why not? 4. In your professional opinion, do you think students see writing as valuable tool for overall academic performance? Why or why not? 5. In your professional opinion, do you think students see writing as valuable tool in their future? Why or why not? 6. How often do you use the Holistic Scoring Guide for ENC0021 when grading the Florida College Basic Skills Exit Essay Exam? 7. a. All the time b. Most of the time c. Some of the time d. Never 8. How are students’ writing evaluated in your writing class? (Circle all that apply.)
a. b. c. d. e. f. g. h. 9.
Student/teacher conferences Peer conferences Self-evaluation Holistic Scoring Analytic Scoring Teacher generated rubrics Students generated rubrics The college or district rubrics
How often would you say students seek your for help with their writing during office hours? 79
a. All the time b. Most of the time c. Some of the time d. Never Appendix D Letter to Professors
Dear ENC0021 Instructor:
My name is Marisol Varela and I am a doctoral student in the Fischler School of Education and Human Services at Nova Southeastern University. As part of my applied research dissertation, I am conducting a survey of students enrolled in remedial writing courses. The studentsâ&#x20AC;&#x2122; writing strategies, their subsequent performance and attitude towards the Florida State Writing Exit Exam are the primary focus of this study. Clarence Jones EdD is my dissertation advisor. I will be contacting you during your office hours to schedule a time to visit your class(es) and administer the survey. Please do not hesitate to contact me via electronic mail or telephone with concerns or questions on this study. Thank you in advance for your cooperation and extend my deepest appreciation. Sincerely, Marisol Varela Appendix E Letter to Survey Recipient Dear ENC0021 Student: You have been selected to participate in a study on the Florida State Writing Exit Exam. The information will be kept confidential and the data will be analyzed anonymously. Please answer all of the questions as truthfully as you can. The result of this study, which is part of my applied research dissertation at NSU, will enable the writing instructor to better understand how the Florida State Writing Exit Exam impacts students as well as how your writing preferences help you in preparing for the exam. Your participation is greatly appreciated. Good Luck on your Florida State Writing Exit Test! Sincerely, Marisol Varela
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Polygon Spring 2010 Vol. 4, 81-82
COMMENTS ABOUT POLYGON
*********************************************************************** Dr. Norma Martin Goonen President, Hialeah Campus Miami Dade College Thank you, Dr. Shakil, for providing scholars a vehicle for sharing their research and scholarly work. Without opportunities for sharing, so many advances in professional endeavors may have been lost. NMG Dr. Norma Martin Goonen President, Hialeah Campus Miami Dade College *********************************************************************** Dr. Ana María Bradley-Hess Academic and Student Dean, Hialeah Campus Miami Dade College Welcome to the third edition of Polygon, a multi disciplinary peer-reviewed journal of the Arts & Sciences! In support of the Miami Dade College Learning Outcomes, one of the core values of Hialeah Campus is to provide “learning experiences to facilitate the acquisition of fundamental knowledge.” Polygon aims to share the knowledge and attitudes of the complete “scholar" in hopes of better understanding the culturally complex world in which we live. Professors Shakil, Bestard and Calderin are to be commended for their leadership, hard work and collegiality in producing such a valuable resource for the MDC community.
Ana María Bradley-Hess, Ph.D. Academic and Student Dean Miami Dade College – Hialeah Campus 1800 West 49 Street, Hialeah, Florida 33012 Telephone: 305-237-8712 Fax: 305-237-8717
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Comments About â&#x20AC;Ś
*********************************************************************** Dr. Caridad Castro, Chairperson English & Communications, Humanities, Mathematics, Philosophy, Social & Natural Sciences Hialeah Campus Miami Dade College POLYGON continues to grow and to feature our local MDC scholars. Thanks to you and your staff for providing them this opportunity. Cary Caridad Castro, J.D., Chairperson English & Communications, Humanities, Mathematics, Philosophy, Social & Natural Sciences Miami Dade College â&#x20AC;&#x201C; Hialeah Campus 1776 W. 49 Street, Hialeah, FL 33012 Phone: 305-237-8804 Fax: 305-237-8820 E-mail: ccastro@mdc.edu *********************************************************************** Dr. Arturo Rodriguez Associate Professor Chemistry/Physics/Earth Sciences/Department North Campus Miami Dade College I want to congratulate you and the rest of the colleagues who created the POLYGON that is occupying an increasingly important place in the scholarly life of our College. Now, the faculties from MDC have a place to publish their modest contributions. arturo Dr. Arturo Rodriguez Associate Professor Chemistry/Physics/Earth Sciences/Department North Campus Miami Dade College 11380 NW 27th Avenue Miami, Florida 33167-3418 phone: 305 237 8095 fax: 305 237 1445 e-mail: arodri10@mdc.edu
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