• The Mathematical Education
• /
• v.48 no.1
• /
• pp.47-59
• /
• 2009

Recently our society confronts with the concern over the college students' apparent lack of understanding and interesting of mathematics. In late 1980s the calculus reform movement in US was triggered to increase both passing rates and a general interest in the subject. The purpose of this paper is to investigate teaching of college calculus and its curriculum in order to promote students' interesting and understanding. We deal with 4 questions. Firstly, we research the history and motivation of the calculus reform movement in US. Secondly, we do case study about the debate between reformed and traditional calculus. Then we evaluate the effectiveness of reformed calculus in comparison to traditional calculus. Finally we investigate possible ways to apply reformed calculus in our university mathematics education and suggest some points to improve teaching calculus.

• Research in Mathematical Education
• /
• v.13 no.1
• /
• pp.13-22
• /
• 2009

School children in Brunei Darussalam, as elsewhere, learn how to apply a lot of algorithms and formulas in mathematics. These include methods of finding the lowest common multiple and highest common multiple of numbers and methods of factorizing quadratics. Investigations and experience have shown that both able and less able students learn to do these mechanically and unimaginatively and in a way that is reliable when answering examination questions. Most of them do not, however, learn these algorithms and methods so as to develop a deeper insight of what they learn and thereby perform even more effectively in examinations. Yet it is possible to teach these and other methods for understanding in ways that are enjoyable and enable students to use them effectively and with flair.

• East Asian mathematical journal
• /
• v.26 no.2
• /
• pp.115-140
• /
• 2010

The purpose of this paper was to develop manipulative materials to teach the angle concepts and construct a teaching-learning program by using that. Furthermore, this study analyzed how does the program affect students understanding of the angle concepts. To check the effects of learning activities with manipulative materials on the understanding of an angle concepts, applied observation during class and write a mathematics journal writing, a description of students impressions at the end of the class and analyzed before and after test paper. We find that students approached the subject more friendly and knew well about the mathematical concepts by using materials. Furthermore, this activity helped that way to solve add and subtract of the angle, estimate ability, round angle concept, positive response in mathematics learning.

• The Mathematical Education
• /
• v.47 no.2
• /
• pp.181-195
• /
• 2008

The purpose of this study was to investigate the understanding of basic knowledge of mathematics for $6^{th}$ grade students in elementary school by an essay test and provide instructional suggestions for teachers. A total of 132 students from 6 classes in 3 elementary schools were tested and analyzed in terms of the characteristics of correct answers and types of incorrect answers. The results showed that students had poor understanding of basic conceptual concepts and principles throughout six content areas of school mathematics curriculum, despite their good performance on mathematical skills. This study included implications to teaching and learning for each of the content areas.

• School Mathematics
• /
• v.12 no.1
• /
• pp.61-77
• /
• 2010

Understanding of mathematical terms plays one of the key factors in understanding and utilizing related mathematical contents. In order to understand such terms well, it is necessary to define and use them appropriately. In this study, we first investigate specific instances of inappropriate using or representing mathematical terms in elementary school mathematics textbooks from a mathematical point of view and a consistent point of view. We then suggest implications for using and representing such mathematical terms appropriately.

• East Asian mathematical journal
• /
• v.35 no.4
• /
• pp.451-465
• /
• 2019

Textbooks are official materials so that these are the most frequently used teaching materials in school. The teacher constructs the lesson based on the contents of the textbook to achieve the learning goal. Thus, textbooks play an important role because the quality of the contents in textbooks affects the cognitive level of students. This study investigates the cognitive domain based on Bloom's Taxonomy of Educational Objectives(knowledge, understanding, application, analysis, synthesis and evaluation) of 'Values and Expression' in the mathematics textbook of the first grade of middle school reflecting the 2015 revised mathematics curriculum. We also looked at cognitive levels based on Bloom's Taxonomy of Educational Objectives. As a result, it was found that understanding was dominant in 'Values and Expression'. Also, although the problem of requiring a higher level of cognition is increasing as the unit finishes, there are still a high percentage of low level of problems.

• Research in Mathematical Education
• /
• v.21 no.1
• /
• pp.35-46
• /
• 2018

In this perspective paper, we present seven elements of the appropriate educator mindset for teaching in the constructivist elementary mathematics classroom. The elements include supporting students as they construct their own understanding, eliminating deficit view of slow learners, setting new understanding and growth as the learning objective, providing opportunities to co-construct meaning with peers, using student contributions as the source of curricular material, encouraging all students to participate in learning, and providing instruction not bounded by time. In our struggles to provide authentic, inclusive elementary classrooms, we hope that our discussion of the educator mindset can increase discourse on constructivism from philosophy to practice in the community of mathematics education and policy makers.

• East Asian mathematical journal
• /
• v.35 no.2
• /
• pp.259-275
• /
• 2019

The researches on the didactic transposition in mathematics education have been conducted almost for 35 years in Korea. Those studies have been quite usually interested in the extreme phenomena such as Topaze Effect, Meta-Cognitive Shift, etc. However, the understanding on the meaning and roles of contextualization and decontextualization in the theory of didactic transposition is needed theoretically in mathematics education and also practically in school mathematics. In particular, for the purpose of managing the efficient instruction on the class, the proper and plentiful role and application of the contextualization is very important in the aspect of the teacher as well as the learner respectively. By this reason, this study investigates the meaning and role of reflection based on the concept of contextualization.

• Journal for History of Mathematics
• /
• v.34 no.6
• /
• pp.195-204
• /
• 2021

Mathematical induction is one of the deductive methods used for proving mathematical theorems, and also used as an inductive method for investigating and discovering patterns and mathematical formula. Proper understanding of the mathematical induction provides an understanding of deductive logic and inductive logic and helps the developments of algorithm and data science including artificial intelligence. We look at the origin of mathematical induction and its usage and educational aspects.

• Journal of Educational Research in Mathematics
• /
• v.22 no.2
• /
• pp.117-136
• /
• 2012

The goal of this study is to investigate a didactic transposition method of text books and high school students' understanding for the Normal Distribution. To accomplish this goal, framework descriptors were developed to analyse the didactic transposition method and interpret the students' understanding based on the Historico-Genetic process of the Normal Distribution, the meaning of the Normal Distribution as a scholarly knowledge and the results of previous studies on students' understanding for the Normal Distribution. This study presented several recommendations for instruction of the Normal Distribution according to the results of analysing the didactic transposition method and interpreting the students' understanding in terms of the developed framework.