The Effect on Students' Mathematical Beliefs by Integrating History of Mathematics in the Classroom.

摘要

This study, with an analysis of over 40 empirical researches about the history of mathematics teaching, discovered that only a few studies conducted research about the evolution and development of history of mathematics and they seldom analysed students' mathematical beliefs. In order to fill the gap, this study is aimed to design the topic of function through the perspective of the evolution and development, namely from the Babylonian tables to discontinuous function. It also seeks to explore how that affects students' mathematical beliefs including math fun, math humane scale, mathematical evolution, and students' views of mathematics.;The study was conducted among two classes of F.4 students who have the similar mathematics abilities in a local secondary school. One is the experimental group and another one is the reference group. The teaching materials developed by the researcher were used in the experimental group while the textbooks were used in the reference group.;Through cognitive tests, questionnaires, interviews, concept maps and teacher journals, the way in which the history of mathematics affects students' mathematical beliefs is explored. The subsequent analysis of the data attempts to answer the following questions: How the history of mathematics affects students' mathematical cognitive level? How history of mathematics affects students' mathematics attitudes? What difficulties the teacher suffers when using this teaching material? Are there any differences between the normal teaching and history of mathematics teaching? Are there any changes in teacher's mathematical belief? Is it appropriate to conduct history of mathematics teaching in senior form?;This study discovers that history of mathematics has different effects on students of various mathematical abilities. When selecting the material of history of mathematics, stakeholders need to pay attention to students' mathematics abilities and interests as well as make appropriate adjustments to teaching, so that students of different mathematical ability can obtain different levels of expansion on their mathematical beliefs.