CircleBoard-Pro: Concrete manipulative-based learning cycle unit for learning geometry

摘要

Currently, a manipulative is commonly used in mathematics education as a supported tool for teaching and learning. With engaging natural interaction of a concrete manipulative and advantages of a learning cycle approach, we proposed the concrete manipulative-based learning cycle unit to promote mathematics learning. Our main objectives are to observe possibilities on the use of a concrete manipulative in learning geometry, and to assess students' understanding of a specific topic, angle properties in a circle, of secondary level students. To meet the first objective, the concrete manipulative, called CricleBoard-Pro, was designed. CircleBoard-Pro is built for easy to writing on or deleting from, accurate angle measurement, and flexible movement. Besides, learning activities and worksheets were created for helping students to learn angle properties in a circle. Twenty eighth graders on a lower secondary school in Indonesia were voluntarily involved to learn mathematics using CircleBoard-Pro with the designed learning activities and worksheets. We informally observed students' performance by focusing on criteria of using manipulative tools in learning mathematics while the learning activities were also observed in terms of whether they work and which step of activities need to be improved. The results of this part showed that CircleBoard-Pro complied the criteria of the use of the manipulative in learning mathematics. Nevertheless, parts of learning activities and worksheets need to be improved. Based on the results of the observation, CircleBoard-Pro, learning activities, and worksheets were merged together and became the CircleBoardPro embedded on 5E (Engage - Explore - Explain - Elaborate - Evaluate) learning cycle unit. Then, students understanding were assessed to reach the second objective. Six ninth graders from an Indonesian school in Thailand were recruited to participate in this study. Conceptual tests for both pre-and post-test, and semi-structured interview were used. Students' pre-and post-test answers were analyzed not only by descriptive statistics but also in qualitatively discussion. The dialogues between the interviewer and interviewees were transcribed and analyzed to find in-depth understanding. Finally, we can conclude that the participated students had better comprehension of angle properties in a circle even they could not perform proof by themselves. For further study, we will focus on how we can help students to develop their geometric thinking.