ASSESSMENT OF PROJECT-BASED LESSON ON LINEAR EQUATIONS IN DEVELOPING CRITICAL THINKING SKILLS
A THESIS
Presented to the Graduate School of La Salle University Ozamis City
In Partial Fulfillment of the Requirements for the Course EDUCATIONAL STATISTICS
RICHARD S. TUTANES May 2017
Abstract
This study assessed the development of Critical Thinking Skills (CTS) on the Compare and Contrast, Application of Knowledge, Error Analysis, Problem Solving, Analyzing Perspective, Induction and Deduction classifications through a Project-Based Lesson (PBL) which was developed, evaluated, revised and implemented. In this study, results showed that the respondents were highly confident in perceiving themselves to have a strong CTS level, however, in the actual context, many of them were weak in most of the classifications. Furthermore, results revealed that there was a positive increase in the mean scores of the achievement test which indicated a positive significant conceptual gain. It also showed that there was a significant development of CTS level among the respondents, which implied a significant improvement in their ability to think critically.
Introduction The most dominant kind of assessment in schools is Assessment of Learning. Its purpose is summative, intended to certify and report learning to parents about students’ progress in school and to give feedback to students of their progress and performance. In Assessment of Learning, the results are expressed symbolically, generally as marks across several content areas. This is the kind of assessment that still dominates most classroom assessment activities, especially in secondary schools, by teachers who are in charge of both creating and marking the test. Teachers use the tests to assess the quality and accuracy of student output. Typically, the teachers don’t give much indication of mastery of particular ideas or concepts because generally, the test content is too limited. As education becomes an essential ingredient for a successful future, more attention will be allocated to how grades are computed and how well they actually reflect what they are taken to mean (Earl, 2003).
It is every teachers aim for students to develop a variety of skills, including the ability to reflect on their own learning and to improve on any previous unsatisfactory performance. To this, we can consider requiring our students to prepare a Mathematics Portfolio. It was in the context of assessing the variety of thinking skills that a student will develop that this paper was conceptualized. Statement of the Problem The main objective of this study was to determine if the developed Project-Based Lesson (PBL) has the impact on the development of critical thinking skills among the incoming grade 8 junior high school students who took the summer reading camp at Lala National High School (LNHS) during the summer of 2017. More specifically, the study sought to answer the following questions: (1) How is the project-based lesson on linear equations in two variables developed?; (2) What is the self-perception of the respondents on their level of critical thinking skills (CTS) on the seven classifications of CTS?; (3) What are the scores of the respondents in the Critical Thinking Skills Test in the pre-test and in the post-test?; (4) Is there a significant difference between the self-survey result of CTS in the pre-test and in the post-test?; and (6) Is there a significant difference in the critical thinking skills of the respondents in the pre-test and in the post-test?
Conceptual Framework
Prior knowledge
self perception on CTS Level critical thinking Skills
Development Of Project-Based Learning Instruction in Linear Equations
Classroom Utilization
Developed Project-Based Lesson Improved Critical Thinking Skills
Figure 1. Research Paradigm The present investigation sought to find out the development of critical thinking skills among the incoming grade 8 junior high school students who took the summer reading camp at Lala National High School (LNHS) during the summer of 2017 through project-based lesson in linear equations. It was hoped that the project-based lesson would develop critical thinking skills that would eventually help achieve better performance among students. Scope and Limitation This study was conducted at Lala National High School, Maranding, Lala, Lanao del Norte among incoming grade 8 junior high school students who took the summer reading camp during the summer of 2017. In terms of determining whether or not the students developed Critical Thinking Skills the researcher made use of the Critical Thinking Skills Test Result in the pre-test and in the post-test. Review of Related Literature
Buck Institute for Education (2011) stated that a rigorous and in-depth Project Based Learning is organized around an open-ended Driving Question/Challenge. These focus and deepen students’ work and their learning by focusing on significant issues, debates, questions and/or problems. It creates a need to know essential content and skills. Project-Based Learning requires inquiry to learn and/or create something new. It also requires critical thinking, problem solving, collaboration, and various forms of communication. Project-Based Learning allows some degree of student voice and choice. It incorporates feedback and revision. In the students’ conduct of projects they gain a deeper understanding of the concepts and standards at the heart of a project. Projects also build vital workplace skills and lifelong habits of learning. Kernon (2009) said that Project-Based Learning allows for a more learner-centered “teaching” and thus fosters learner autonomy. Because of this and if the task given is real-life relevant, it can enhance student’s motivation and eventually leads to improved learning. In the process, Project-Based Learning allows deep thinking skills. Students also learn interpersonal skills like team work, team leading, project managing and intrapersonal communication. Combined with web 2.0 tools or 3D virtual worlds like Second Life, students also learn the technical skills which they need or will need in the future activities. To conclude, Project-Based Learning is highly collaborative as it ushers interdisciplinary integration and application. Gabennesch (2006) says critical thinking skills are the various higher-order cognitive operations involved in processing information, rather than simply absorbing it: analyzing, synthesizing, interpreting, explaining, evaluating, generalizing, abstracting, illustrating, applying, comparing, recognizing logical fallacies.
Methodology Respondents of the Study The subject of the study were the incoming grade 8 junior high school students who took the summer reading camp at Lala National High School (LNHS) during the summer of 2017, a group of 31 students who will become part of the grade 8 students of Lala National High School.
Research Design This study was a classroom-based research. It made use of pre-test – post-test one group research design with qualitative support. In order to evaluate the effects of project-based lesson on students’ conceptual gain and critical thinking skills, the respondents undertook an on-going assessment during the duration of the study through journal writing. The students were asked to write reflections on every activity. Specifically, this was a nonequivalent dependent variable design (NEDV) wherein there was only one group of subject but there were other dependent variables to consider, namely: (a) conceptual gain on linear equations; and (b) respondents self-perception on their level of critical thinking skills on the seven classifications. The primary independent variable in this study was the project-based unit which was implemented in the class for the whole duration of the research. The dependent variables above were not designed to affect each other.
Research Instruments
The following instruments proved to be very useful in the conduct of this research: (1) Achievement Test; (2) Critical Thinking Skills (CTS) Perception Questionnaire; (3) CTS Test which integrates the seven CTS classifications which are: (a) Compare and Contrast; (b) Application of Knowledge; (c) Error Analysis; (d) Problem Solving; (e) Analyzing Perspectives (f) Induction and (g) Deduction; (4) Mathematics Portfolio that included the following: self introduction, table of contents, three activities on plotting of points on the Cartesian coordinate system, a quiz on the Cartesian coordinate system, an activity on finding the solutions to the linear equations in two variables, the data recorded on the business income template, the ratings of the outputs and their daily and final journals.
Data Gathering Procedure Development of the Project-Based Lesson (PBL) Figure 2 shows the steps which were considered in the development of the Project-Based Lesson (PBL). Determine the objectives from PSSLC
Determine respondents’ output: slide presentation
Design the PBL Mathematics Content Activities/Tasks Items for the achievement test Items for the CTS self-perception questionnaire Rubrics for students outputs: Portfolio and slide presentation
Evaluate PBL thru the research adviser, panel members and panel of experts Rubric for Lesson Plan Development of PBL Revise the PBL Utilize the PBL
Figure 2. Development of the Project-Based Lesson Data Analysis The following tools were used to analyze the result of the study: (1) Mean and Standard Deviation; (2) t-test ; (3) ANOVA and (4) Content Analysis of the Journal Entries.
Results and Discussions It was made sure that the formulated objectives for the Project-Based Lesson (PBL) were aligned with the standards based on the Philippine Secondary Schools Learning Competencies. The standards were identified and mapped with the objectives of the PBL. The first draft of the PBL was evaluated by the panel of experts (a math master teacher, a math coordinator and an administrator) through the use the unit plan rubric. The elements evaluated using the said rubric were: instructional goals and objectives, instructional strategies, assessment, technology used, materials needed and organization and presentation. The comments and suggestion of the panel of experts regarding the developed PBL was carefully noted. Based on the valuable evaluation of the panel of experts, the PBL was revised following their comments and suggestions. With an overall rating of excellent, the PBL was administered to the respondents.
Comparison of Respondents’ Perception on their CTS Level
Results show that most of them perceived themselves as having a strong CTS level in the Compare and Contrast, Application of Knowledge, Problem Solving, Analyzing Perspective, Induction and Deduction classifications; most of them perceived themselves as having a weak CTS level in the Error Analysis classification during the pre-test while most of them said that they had a strong CTS level in this classification during the post-test; It goes to show that the respondents were very confident of their CTS level in all classifications.
Respondents’ Performance on the CTS Test The CTS test result during the pre-test and post-test showed that, in actual context, most of the respondents had a weak CTS level in the following classifications: Compare and Contrast, Application of Knowledge, Analyzing Perspective and Induction. Furthermore, they had the weakest CTS level in the Problem Solving classification during the pre-test which dramatically improved and moved to just having a weak CTS level during the post-test. It is interesting to note that in both test, most of the respondents were having a strong CTS level in the Deduction classification.
Respondents’ Achievement Test Result The achievement test result of the respondents in the pre-test and post-test is presented in figure 3 It shows that there is a general increase of the test results from the pre-test (mean = 9.29) to the post-test (mean = 15.61). The portfolio rating of the respondents, peers, parents and teacher to the quality of portfolio output is presented in figure 4 It shows that most of the portfolios rated by the
respondents (15), peers (16) and the teacher (18) gained satisfactory ratings while most the portfolios rated by the parents (17) obtained a very satisfactory rating.
Critical Thinking Self-Survey Comparison The comparison of the respondents’ CTS self-survey results shows that, with the mean
Figure 3. Respondents’ Achievement Test Result
difference of 0.00, with a 0.02 standard deviation of difference and upon the application of t-test for paired observation, it was found out to be not significant at a 0.05 level of significance with 30 degrees of freedom. This means that there is no significant difference between the CTS selfsurvey result during the pre-test and post-test. It implies further, that the respondents were consistent in rating themselves in terms of their perception on the CTS level in all classifications.
Assessment on Quality of Respondents’ Portfolio
Respondents
Peer
Parent
Teacher
Figure 4. Ratings on the Quality of Portfolio Outputs among the Respondents, Peer, Parent and Teacher
Critical Thinking Test Comparison Comparison of the respondents’ CTS test results is shown in Table 1. With the mean difference of 1.07, with a 0.92 standard deviation of difference and upon the application of t-test for paired observation, it was found out to be significant at a 0.05 level of significance with 30 degrees of freedom. This means that there is a significant difference between the CTS test result during the pre-test and post-test. It implies further, that there is a significant development of the level of thinking among the respondents from the pre-test to the post-test.
Table 1. Comparison of the Respondents’ CTS Test Result CTS Test Result Compared Groups Mean
Pre-test
Post-test
8.35
9.42
Standard Deviation Mean Difference SD Difference Degrees of Freedom t-computed p-value *significant at 0.05 level of significance
2.27
3.19 1.07 0.92 30 2.32* 0.0274
Ho1: There is no significant difference between the CTS test result during the pre-test and post-test.
Comparison of Achievement Tests Comparison of the respondents’ Achievement test results is shown in Table 2. With the mean difference of 6.32 and a 1.53 standard deviation of difference and upon the application of t-test for paired observation, it was found out to be significant at 5% level with 30 degrees of freedom. This means that there is a significant difference between the Achievement test results in the pre-test and post-test. It implies further, that there is a positive significant conceptual gain among the respondents from the pre-test to the post-test.
Table 2. Comparison of the Respondents’ Achievement Test Result CTS Test Result Compared Groups Mean Standard Deviation Mean Difference SD Difference Degrees of Freedom t-computed p-value
Pre-test
Post-test
9.29 4.25
15.61 5.78 6.32 1.53 30 6.58* 0.0000
* significant at 0.05 level of significance Ho2: There is no significant difference between the Achievement test result during the pre-test and posttest.
Comparison of Portfolio Ratings by Respondents, Peers, Parents and Teacher
Table 3 illustrates the ratings of the respondents’ quality of portfolio outputs by the respondents themselves, peers, parents and the teacher. Result shows that upon application of one way analysis of variance (ANOVA), there is no significant difference among the ratings of the respondents, peers, parents and teacher in the quality of the respondents’ portfolio. This implies further, that the ratings of the quality of portfolio output by the respondents, peers, parents and teacher were consistent.
Table 3. Comparison among the Ratings of the Respondents, Peers, Parents and Teacher on the Portfolios’ Quality Source SS df Treatment 310.80 3 Error 5,571.42 120 Total 5,882.22 123 ** not significant at 0.05 level of significance
MS 103.599 46.428
F 2.23**
p-value 0.0881
Ho3: There is no significant difference among the ratings of the respondents, peer, parent and teacher in the quality of the respondents’ portfolio.
Insights from Respondents’ Journal Entries
Based on the content analysis of the respondents’ responses in their journal, the following insights were obtained and well noted: 1. In the first journal where they were asked to state what they have learned in the past lessons, the respondents claimed that they have learned how to plot, connect and graph the coordinates in a graphing paper on a Cartesian coordinate. They also learned how to define linear equations, algebraic expressions, coordinates and quadrants. They gained knowledge about
portfolios. They learned how to apply linear equations in two variables and they found out the importance of listening to get a better score. Finally, they realized the importance of following instructions to get better scores in activities and quizzes. 2. When the respondents were asked to reflect on their score in their first quiz, some said that they were happy with their score because they got more than the passing mark. Most of them, though, were sad with their low scores because of the following reasons: not able to follow instructions; not able to understand the instructions; not able to study their lessons at home and for being late. 3. On the two activities done by the respondents in determining the location of points on the Cartesian plane, they reflected that the activities were fun and challenging. Some were happy because they finally learned how to locate the points into the different quadrants and in the x and y axes. A significant number of them realized that they should follow instructions so that they will have a better score. Few said that their work should be clean. Lastly, they realized that they should study next time so that they will have a better score in the next activity. They should not be late nor absent so that they will learn something. 4. In the fourth activity about finding the solutions to linear equations in two variables, the respondents made the following realization: the activity is colorful and challenging and that they learned how to solve problems. Also, they realized that when they study their lessons they will get a better score in the activities and that when they don’t study their lessons they will not understand the problems. They find these problems hard and confusing which caused them getting low scores. Some said that they were not able to do well in the activities because they were affected by their problems at home.
5. The final journal entry of the respondents was their reflection on the project conducted in the market where they were asked to conduct a survey on how profitable a business is. The respondents found out that having a business is not easy; you have to work hard in order to sell and earn money, you have to be patient and be friendly to customers and must learn marketing skills to sell your product. They realized that having a good business will get you a lot of customers and in turn will yield profit. They realized that, should they decide to have a business in the future, they will pursue that type of business which they found the most profitable. Few said that having a business is fun and enjoyable. Some said it is very important to select a business carefully because other businesses are not profitable. And notably, they learned the use and importance of portfolio in making their project.
Conclusions and Recommendations Conclusions
The developed Project-Based Lesson (PBL) was aligned with the indicated national standards and objectives set by the Bureau of Secondary Education. The PBL was rated excellent by the panel of experts which made it suitable for administration. The respondents confidently perceived themselves to have a strong Critical Thinking Skill (CTS) level in most of the CTS classifications in both pre-test and post-test. In the CTS test result; most of the respondents were weak in most of the classifications both in the pre-test and the post-test.
There was a contradiction between the CTS (perceived) self-survey result and CTS (actual) test result, since, most of them said they have a strong CTS level in almost all of the classifications while, in the actual context, they were weak in almost all of the classifications. There was a significant increase in the achievement test results from the pre-test to the post-test. Most of the portfolios rated by the respondents, peers and the teacher received satisfactory ratings while most of the portfolios rated by the parents obtained a very satisfactory rating. There was no significant difference between the CTS self-survey result during the pretest and post-test. This means that there was no significant change of perception among the respondents in terms of their CTS level in both pre-test and post-test. There was a significant difference between the CTS test result during the pre-test and post-test. This means, that there was a significant development of CTS level among the respondents from the pre-test to the post-test. There was a significant difference between the Achievement test results in the pre-test and post-test. This means, that there was a conceptual gain among the respondents from the pretest to the post-test. There was no significant difference among the ratings of the respondents, peers, parents and teacher in the quality of the respondents’ portfolio. This means, that the ratings of the quality of portfolio output by the respondents, peers, parents and teacher were consistent. This implies further, that with the inclusion of other people in rating the outputs of students would not be bias as evidence by the result of this study.
These were the insights drawn from the responses of the respondents written in their journal: (1) they have learned basic concepts of the Cartesian coordinate system; (2) they gained knowledge about portfolio and its importance; (3) they realized the importance of listening and following instructions in order for them to have better scores in activities and quizzes; (4) they realized that studying at home will help a lot in improving their scores and that some promised to themselves that they will start to study their lessons at home; (5) they said that activities were fun and challenging and they liked doing all the activities, especially the one where they were asked to gather data outside of school; (6) they realized that managing a business is not easy, but they realized that it is one way to earn money; (7) they also found out that there are particular businesses which are more profitable than others so selecting the right business is very important; and, they decided that when they want to pursue having a business in the future, they already have an idea on what to put up.
Recommendations
Implications to Mathematics Education The researcher highly recommends the use of PBL in teaching linear equations in two variables. It is also recommended to include the mathematics portfolio as a tool for ongoing assessment of students’ progress where students, peers and even parents are given the chance to rate their output. Spending time beyond what is expected to slow learners is most recommended. In addition, recorded interviews for one-on-one discussions on journal entries that show psychological connections should be given emphasis to have a better understanding of students’ behavioral patterns in correlation to their learning progress.
The researcher also recommends for educators to have the training on Critical Thinking Skills Development and its Classifications so that they will be able to integrate the CTS in their classroom.
Implication to Research
Project-Based Learning could be applicable to other topics in mathematics. The development of Critical Thinking Skills cannot be achieved overnight. Our minds have the greater abilities waiting to be tapped be and used to its maximum potentials. It is, therefore, our role as educators to harness these skills among our beloved learners. The seven CTS classifications presented and evaluated in this study is by far the first level of the development of Critical Thinking Skills if introduced, used and practiced inside the classrooms. A wide range of critical thinking skills is still to be introduced and developed among our students that include: (1) making inferences; (2) formulating assumptions; (3) interpreting given data; (4) forming and consolidating arguments; (5) making adductions and (6) refuting given arguments. There is much to be done in this generation and with the world going too fast, learners should be trained to become critical thinkers to be able to survive in the so-called high-technologically fastpaced-world. Furthermore, studies should be made on the effects of technology to the level of thinking among students of this generation and to identify if there is a positive or negative effect on the learning processes.
References Buck Institute for Education (2011). PBL Starter Kit: To-the-Point Advice, Tools and Tips for Your First Project. http://www.bie.org/tools/toolkit/starter. Accessed: May 10, 2010
Gabennesch, Howard, April 2006, Critical thinking: What is it good for? (In fact, what is it?)http://www.csicop.org/si/show/critical_thinking_what_is_it_good_for_in_fact_what_i s_it/, Accessed: May 11, 2010 Kernon, Nergiz April 11, 2009, Project-Based Learning in Second Life, http://slexperiments.edublogs.org/2009/04/11/project-based-learning-in-second-life/, Accessed: May 11, 2010