期刊名称：Eurasia Journal of Mathematics, Science & Technology Education
印刷版ISSN：1305-8223
电子版ISSN：1305-8223
出版年度：2018
卷号：14
期号：5
页码：1875-1886
DOI：10.29333/ejmste/85424
出版社：Pamukkale Univ Dept Sci Education
摘要：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.
关键词：instructional message design; representation; state transition graph;
transition matrix
