Cooperative learning in college algebra : a team-achievement-challenge (TAG) model

Abstract

College Algebra is one of the most difficult and feared subjects not only in high school but in college as well. The difficulty lies from the fact that Algebra is an abstract subject where symbols are used to represent unknown numbers. In Arithmetic where everything is concrete, all operations involve numbers without any need for interpretation. In contrast, Algebra involves symbols that need interpretations, concepts, rules and mechanics that should be followed in harmony in order to perform the required tasks correctly. One can imagine a child being taught with concrete things and then suddenly is taught something that is abstract. It is like asking someone to appreciate a painting of a portrait and then asking him to appreciate an abstract painting when he has no idea as to what it represents. This paradigm shift from the concrete to the abstract has confused and frustrated many students of Algebra including UC freshman students. The learning of Algebra requires so much interpretation of these symbols and ideas, understanding of many different concepts, following numerous rules, and knowing the mechanics in applying these concepts and rules. The lecture method can provide much of these tasks though it becomes quite incomplete when all of these tasks are not experienced first hand by the learners. Leherer (2008) cites Dewey, a pragmatist, as having said that the basic fact in learning is that the brain learns by doing. Constructivists believe that children learn when their beliefs or presumptions are challenged by new ideas or knowledge foreign to them. They also believe that children learn by experiencing new things. Cooperative learning, more specifically the TAC model, offers to provide all of these. For one, it is preceded by a lecture to provide the concepts, rules and mechanics. Next, it gives the students the opportunity to make their own examples based on what they have learned; then these are disputed by the other teams in the team challenge. The students are motivated by the team challenges and the rewards, and their individual assessments are measured by the teacher challenge. This study aimed to determine the effect of cooperative learning, more particularly the Team-Achievement-Challenge, in the performance of UC freshman students taking up College Algebra. More specifically, this study wanted to resolve the following questions: 1. What is the performance of UC students in factoring polynomials and simplifying rational and radical expressions before and after the treatment? Hypothesis: The performance of UC students in factoring polynomials, simplifying rational and radical expressions before and after the treatment is average. 2. What is the difference in the performance of UC students before and after the treatment? Hypothesis: The difference in the performance ,of UC students before and after the treatment is significant. 3. What is the difference in the performance of UC students in the TAC model and in the Traditional Method of teaching? Hypothesis: The difference in the performance of UC students in the TAC model and in the Traditional Method is significant. 4. What instructional material can be developed using the Team-Achievement-Challenge (TAC) model to enhance the teaching of College Algebra in UC? The researcher used the quasi-experimental design to compare the effects of the TAC model and traditional method of teaching. More particularly, a matching only pre-test-post-test control group design was used to eliminate as many intervening variables as possible. The subjects of the experiment were from the four Algebra classes of the researcher during the lit Trimester of the school year 2010-2011. There were 49 students each from the two criminology classes, 38 from a business administration class, and 32 from another business administration class combined with criminology students. The researcher managed to match 27 pairs from the two criminology classes and 21 pairs from the two business administration classes, or a total of 48 pairs. The data gathered were statistically treated using frequency distribution, mean, weighted mean, Pearson product moment correlation coefficient, Spearman-Brown whole test reliability, Cronbach alpha, and the t-Test for paired sample mean. The following summarized the findings of this experiment: 1. The performance of UC students in factoring polynomials, simplifying rational and radical expressions was low failing. 2. There was a significant difference in the performance of UC students before and after the TAC model was applied. 3. There was significant difference in the performance of UC students in the TAC model and in the traditional method of teaching as applied to factoring polynomials and simplifying rational expressions. For simplifying radical expressions, the difference in their performance was not significant. Based on the findings, the following conclusions are drawn: 1. The over-all performance of UC students in factoring polynomials, simplifying rational and radical expressions was low failing. For each of the three topics, their performances in factoring polynomials and simplifying radical expressions were both low failing, while for simplifying rational expressions, it was fair. 2. The difference in the performance of UC students before and after the treatment was found to be very significant over-all and for each of the individual topics. 3. The difference in the performances of UC students in the TAC model and in the traditional method as applied to factoring polynomials and simplifying rational expressions were both significant. In simplifying radical expressions, their performance was not significantly different from each other. The TAC model and the traditional method were equally effective when applied to simplifying radical expressions. Therefore, the TAC model was prove to be more effective than the traditional method in increasing the performance of students in two out of the three topics included in the experiment. In response to the conclusions arrived at in the study, the researcher recommends the following actions: 1. Adopt the TAC model and the TAC manual as an additional teaching method and learning tool in teaching College Algebra. 2. Conduct further studies as to the reasons for the minimal advancement in performance of UC students in College Algebra. 3. Conduct further studies on different cooperative learning models in order to determine which model is the most effective in improving the performance of UC students in College Algebra. The researcher also recommends the following to increase students' performances in College Algebra: a. Increase the awareness of students on the importance and application of Algebra in their chosen careers to reduce surface learning by the students. b. Familiarize math teachers with the TAC model in order for them to learn how to use it effectively and appropriately, and become aware of its limitations. c. Students must take advantage and make the most of the TAC model to improve not only their intellectual but their social skills as well.