No abstract

Mathematical representations are an essential tool in the study of mathematics and problem solving. They are also used in word problems to facilitate the transformation from textual to symbolic information. We proposed a stepwise, blocked, structured state transition graph (STG) based on the principles of instructional message design. In this study, we adopted a posttest-only non-equivalent group design to compare the performance of students who used either STG or matrix-like tables to learn to solve word problems via transition matrices. We also took into account the student's previous learning achievements in mathematics. The participants included four classes of senior students in a vocational high school, with two classes randomly designated as the experiment (STG) group and two designated as the control (Table) group. Highachieving students taught using STG outperformed their counterparts who were taught using matrix-like tables. The performance of low-achieving students appeared to be unaffected by the instructional method. These findings suggest that STG provides a clear representation of the relationships used in matrix calculation, which makes it easier to select and organize information. Nonetheless, alternative methods will be required to improve the performance of low-achieving students.

This study examined the effectiveness of an integrated context approach to the instruction of basic compass-and-straightedge construction. The formulation of a perpendicular bisector of a segment was used as a knowledge module to guide students from the preattention level to the elaboration level of information processing. The students were expected to select and organize information in their working memory for integration with prior knowledge. The knowledge module was presented in a multimedia environment using a pre-training and rehearsal approach. In immediate and delayed test results, integrated context learning proved significantly more effective than the traditional context in preparing students to deal with retention problems and transfer problems, regardless of the students' prior knowledge. These findings demonstrate the effectiveness of integrated context in the instruction of compass-and-straightedge construction; however, the factors that actually facilitate learning have yet to be fully elucidated.