Abstract:

Lachner and Nückles (2016) have pointed out that in mathematics explanations, it is important to include background information such as the rationale for and process for finding the solution. It has also been shown that during learning activities one student teaches another, they should explain and ask questions to build knowledge, not just give the answers (Roscoe & Chi, 2007). Pattern Language is one of the methods for encouraging students to change their behavior. Pattern Language is a set of patterns, which are rules of thumb describing situations, problems, solutions, and results. Users can select patterns according to their situations and concretize and practice the abstract solutions described in the patterns (Iba & Furukawazono, 2013).

In this study, we developed Pattern Cards, a card format of Pattern Language, to promote the implementation of desirable skills in collaborative activities conducted by students in high school mathematics classes. The Pattern Cards consist of the background situations that may arise when incorporating collaboration activities in mathematics classes, the problems that may arise, the skills that provide solutions to those problems, and the ideal situations with problems solved.

This study aimed to examine the effects of using Pattern Cards on students’ activities and beliefs in cooperation in high school mathematics classes. The participants were 126 first-year students in high school. The students engaged in a learning activity; one teaches another in mathematics classes, referring to the Pattern Cards. Before and after the activity, we conducted a questionnaire survey containing 30 items on a 5-point Likert scale: active learning quality (12 items) and beliefs in cooperation (18 items). We included in our analysis 117 students who participated in the activity and answered all the questions.

We conducted a Wilcoxon signed-ranks test to compare the questionnaire results before and after the activity. We found a significant increase in the total mean value of the active learning quality scale, W = 1887.00, p = .009, r = .30. In other words, the results suggest that the quality of the activity was improved by referring to the Pattern Cards during the learning activity one student teaches another in mathematics classes. In particular, the item “Through discussion and presentation, students gain a deeper understanding of the content of the class from multiple perspectives” improved significantly, W = 371.00, p = .002, r = .46. On the other hand, there was no significant difference in the total mean values of the belief in cooperation. This result may be because the students engaged in the activity only once. We analyzed the change in the value of each item in the scales to determine detailed influences on the students’ beliefs in cooperation. The value of the item “Even people who are not good at many things can achieve good results if they cooperate” increased significantly, W = 785.00, p = .033, r = .29. The value of the item “Some people always cut corners when working in a group” decreased significantly, W = 1092.00, p = .027, r = .32. Additionally, no items indicated a significant worsening of beliefs in cooperation. We concluded that referring to the Pattern Cards had positive influences, in part, on the students’ beliefs in cooperation, not negative ones. Further studies should examine the effects of long-term and continuous use of the Pattern Cards.

Keywords:

Collaborative Learning, Cooperative Learning, Mathematics Education, Pattern Language.