Using Problem-Based Learning to Improve College Students’ Mathematical Argumentation Skills

Problem-based learning are very common in mathematics teaching and learning in college level where students are exposed to problems and required to solve them. However, in general, when students are making efforts to solve the problems, they usually implement direct problem solving strategy without involving argumentation as one of the most important component of the problem solving process. Through argumentation, a reasoning process will take place and will involve thinking about what data gathered, what theorem support the process, how rebuttal is given, and what final claim to confirm. A student is able to comprehend a certain problem meaningfully when he/she is able to state the reasons, to elaborate the data, to express assurance, and even to make a claim of a problem in correct ways. Therefore, in order to see if the students have already acquired the skills to express mathematics problem meaningfully, they can be asked to express ideas orally and rewrite the ideas in mathematical arguments. Thus, this research was intended to find out if the students have improved their mathematical argumentation in Calculus 1 course. A learning process that facilitates the students to develop arguments is needed in order to improve their mathematical argumentation skills. Therefore, this research took students at the Dept. of Mathematics Education in UHAMKA University as the subjects in which four classes of them were taken as the samples using purposive random sampling technique. The four classes were then divided into two groups: two classes as control groups and two other classes as experimental groups. In this research, the teaching and learning process in the experimental groups used Problem-based Learning (PBM); meanwhile, conventional learning process (KS) was implemented in the control groups. There were 141 students involved in this research. And the instrument used in this research was a test intended to measure mathematical argumentation skills. The data was analyzed using t-test and ANOVA through one and two lines. Based on the analysis, this research found that there was significant differences in mathematical argumentation between PAM Groups (upper, middle, and lower) on Problem-based Learning. There was differences in the improvement of PAM for upper and middle groups. Significantly, the improvement of students’ mathematical argumentation skills in PAM groups using Problem-based Learning is better than those using conventional learning. There was also significant improvement on students’ mathematical argumentation skills in each of PAM groups between those using Problem-based Learning and Conventional Learning. Collectively, both factors of PM groups and learning approach have given significant effects on students’ mathematical argumentation skills.