• The Mathematical Education
• /
• v.45 no.2 s.113
• /
• pp.191-204
• /
• 2006

Computer technology has a potential to change the contents of school mathematics and the way of teaching mathematics. But in our country, the problem whether computer technology should be introduced into mathematics classroom or not was not resolved yet. As a tool, computer technology can be used by teachers who are confident of the effectiveness and who can use it skillfully and can help students to understand mathematics. The purpose of this study was to investigate the effective way to introduce and utilize computer technology based on the status quo of mathematics classroom setting. One possible way to utilize computer technology in mathematics classroom in spite of the lack of computer and the inaccessibility of useful software is using domain specific simulation software like 'Polyhedron'. 'Polyhedron', as we can guess from the name, can be used to explore regular and semi regular polyhedra and the relationship between them. Its functions are limited but it can visualize regular polyhedra, transform regular polyhedra into other polyhedra. So it is easier to operate than other dynamic geometry software like GSP. To investigate the effect of using this software in mathematics class, three classes(one in 6th grade from science education institute for the gifted, two in 7th grade) were chosen. Activities focused on the relationship between regular and semi regular polyhedra. After the class, several conclusions were drawn from the observation. First, 'Polyhedron' can be used effectively to explore the relationship between regular and semi regular polyhedra. Second, 'Polyhedron' can motivate students. Third, Students can understand the duality of polyhedra. Fourth, Students can visualize various polyhedra by reasoning. To help teachers in using technology, web sites like NCTM's illuminations and NLVM of Utah university need to be developed.

• Research in Mathematical Education
• /
• v.14 no.3
• /
• pp.211-218
• /
• 2010

It is a truism that mathematics is about relations (cf. [Halford, G. S. (1999). The properties of representations used in higher cognitive processes: Developmental implications. In: Sigel, I. E. (Ed.), The Development of Mental Representation: Theories and Applications (pp. 147-168). Mahwah, New Jersey: Erlbaum]). In this article we are considering few problems related to the Viviani's and Routh's Theorems. All Problems are connected by the relation which exists between the distances of the point inside the triangle to it sides. We show how reasoning about the relations could lead the student's problem solving process and give easy to understand solutions of the problems. Among the problems being considered are the proof of the Converse to Viviani's Theorem, the formulas for areas of all figures formed by the sides of triangle and its cevians.

• School Mathematics
• /
• v.3 no.2
• /
• pp.373-399
• /
• 2001

The function is a basic and key concept to understand mathematical problems. However, many students have difficulties to expand the knowledge to other related concepts and to transfer the knowledge to real world problems. The reasons for the problem may be that the concept of function is taught by simplified and abstracted formula without fully understanding of the reasoning process. Also, the examples for the concepts are artificial and not related to students' experiences. Situated learning theory provides great implications to solve these problems. So, this study was designed to teach the concept of function more meaningful to students by appling situated learning theory. Thirty-eight middle school students were participated in this study. Students were provided the instruction designed according to the principles of situated learning theory. Then, they were asked to complete attitude survey questionnair and a performance assessment task. The result showed that the instruction based on situated learning theory was useful to Promote students' understanding and motivation for learning. More implications of the study was provided in the paper.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.10 no.1
• /
• pp.83-93
• /
• 2006

This paper introduces rule-based reasoning (RBR) based self-recovery system for network fault in ubiquitous computing. This system is fault management system for fault recovery of rule-based for self-recovery in ubiquitous computing environment. We proposed rules of network fault recovery applied the system as a distinguished reason of network fault. And, in this paper, the network fault self-recovery system proved the rules that applied each situatpion through the simulation.

• School Mathematics
• /
• v.13 no.1
• /
• pp.19-36
• /
• 2011

This study provides middle school students with an opportunity to construct elementary functions with dynamic geometry based on the proportion between lengths of triangle to activate students' intuition in handling elementary algebraic functions and their geometric properties. In addition, this study emphasizes the process of justification about the choice of students' construction method to improve students' deductive reasoning ability. As a result of the pilot lesson study, this paper shows the characteristics of the students' construction process of elementary functions and the roles the teacher plays in the process.

• Research in Mathematical Education
• /
• v.11 no.3
• /
• pp.185-196
• /
• 2007

In order to study the new curriculum, as well as to help teachers understand new textbooks well, the authors make horizontal comparisons between Editions A and B of Experimental Mathematics (2) textbook in ordinary senior high schools (Grades 10-12) of PEP Edition, which focuses on the topic of line slope. The interview was made with 11 selected teachers who are teaching the content in the light of Edition B. It was found that there are obvious differences in the introduction of concepts and the exercises. The interviews showed that teachers were familiar to the contents of Edition A and saw it reasonable, because few differences are found between Edition A and the old Edition. The teachers also viewed that though the contents of Edition B were easy and fit to self-educated, but its reasoning is not clear, and the examples are not enough so that the teachers need to add additional examples.

• Research in Mathematical Education
• /
• v.23 no.1
• /
• pp.47-62
• /
• 2020

Learning through "recreational mathematics" has become a meaningful outlet to children of all ages. The Edumatrix set is a didactic tool for the development of logical and abstract reasoning among students. In this paper, we provide several illustrative exercises involving Edumatrix that teachers can utilize in their classrooms. We formulate students' expected learning outcomes by aligning each exercise to the CCSSM content standards as well as examining which Standards for Mathematical Practices (SMP) our proposed exercises promote.

• School Mathematics
• /
• v.2 no.1
• /
• pp.165-181
• /
• 2000

The teaching-learning methods of figures using computers make loose the difficulties of geometry education from the viewpoint that the abstract figures can be visualized and that by means of this visualization the learning can be accomplished through the direct experience or control. In this thesis, we present a teaching-learning method of figures using Cabri II so that the learners establish their knowledge obtained through their search, investigation, supposition and they accomplish the positive transition to advanced 1earning. So the learners extend their ability of sensuous intuition to their ability of logical reasoning through their logical intuition.

• Research in Mathematical Education
• /
• v.25 no.1
• /
• pp.65-89
• /
• 2022

Despite its recognition in the field of mathematics education and mathematics, students' understanding about proof and performance on proof tasks have been far from promising. Research has documented that teachers tend to accept empirical arguments as proofs. In this study, an online survey was administered to examine how Korean secondary mathematic teachers make judgements on mathematical arguments varied along representations. The results indicate that, when asked to judge how convincing to their students the given arguments would be, the teachers tended to consider how likely students understand the given arguments and this surfaces as a controversial matter with the algebraic argument being both most and least convincing for their students. The teachers' judgements on the algebraic argument were shown to have statistically significant difference with respect to convincingness to them, convincingness to their students, and validity as mathematical proof.

• Journal of Educational Research in Mathematics
• /
• v.19 no.4
• /
• pp.493-511
• /
• 2009

The purpose of this thesis is to discuss the characteristic methods of Mathematics Education. However, it is not simple to find the proper research method of Mathematics Education since Mathematics Education deals with the practice of teaching and learning mathematics, as well as the topics of scholarly research on the practice. Issues on Mathematics Education might vary with the epidemical aspects, which are basic attitudes toward the knowledge and understanding about Mathematics. Thus, this thesis will discuss two questions: First, What are the distinguishing characteristics of Mathematics Education as a field of study, when compared with ones of mathematics? Second, What are the characteristic methods of Mathematics Education, when compared with ones of other academic fields? For solving those questions, this thesis starts from meanings of science and education. And it also classifies Mathematics as formal science whereas Mathematics Education as social science by showing differences between Mathematics and Mathematics Education: research subject of Mathematics targets on mathematics itself and it uses the deductive method. On the other hand, Mathematics Education research handles the practice of mathematics of students and uses plausible reasoning. Also, it will also show why Mathematics Education shares lots of aspects with social science, not with natural science, which has many different characteristics from those of social science. Many researchers have agreed that Education should be categorized into the social science but misplaced Mathematics Education and Science Education into the natural science. It is true that physics and chemistry are natural science. And also it should be said that pure science is formal science. But it should be considered that just like Education, Mathematics Education and Science Education are in the category of social science.