• The Mathematical Education
• /
• v.41 no.1
• /
• pp.35-44
• /
• 2002

The purpose of this study is to estimate teachers'conceptions of mathematics through the conception on compositions of mathematical knowledge, the conception on structure of mathematical knowledge, the conception on status of mathematical knowledge, the conception on mathematical activity, and the conception of mathematics learning. This study reached the following conclusions: Most of teachers has more internal viewpoint than external viewpoint on the compositions, structures and status of mathematical knowledge, mathematical activity and mathematics learning.

• The Mathematical Education
• /
• v.50 no.2
• /
• pp.165-184
• /
• 2011

The purpose of this study is to detect the possibility of the development of conception of a graph and the formula with the absolute value through context questions, and also to investigate the effectiveness of the each step of the mathematical modeling activities in helping students to have the conception. The research was conducted to analyze the process of development of the mathematical conception by applying the mathematical modeling activities two times to subjects of two academic high school students in the first grade. The results of the study are as follows: Firstly, the subjects were able to comprehend the geometric conception of the absolute value and to make the graph and the formula with the sign of the absolute value by utilizing the condition of the question. Secondly, the researcher set five steps of the intentional mathematical model in order to arouse the effective mathematical notion and each step performed a role in guiding the subjects through the mathematical thinking process in consecutive order; consequently, it was efficacious in developing the conception.

• Research in Mathematical Education
• /
• v.12 no.3
• /
• pp.215-233
• /
• 2008

Deep comprehension of basic mathematical notions and concepts is a basic condition of a successful teaching. Some elements of algebraic thinking belong to the elementary school mathematics. The question "What stays the same and what changes?" link arithmetic problems with algebraic conception of variable. We have studied beliefs and comprehensions of future elementary school mathematics teachers on early algebra. Pre-service teachers from three academic pedagogical colleges deal with mathematical problems from the pre-algebra point of view, with the emphasis on changes and invariants. The idea is that the intensive use of non-formal algebra may help learners to construct a better understanding of fundamental ideas of arithmetic on the strong basis of algebraic thinking. In this article the study concerning arithmetic series is described. Considerable number of pre-service teachers moved from formulas to deep comprehension of the subject. Additionally, there are indications of ability to apply the conception of change and invariance in other mathematical and didactical contexts.

• Education of Primary School Mathematics
• /
• v.14 no.2
• /
• pp.147-164
• /
• 2011

The national mathematics curriculum revised in 2007 emphasized students' mathematical communication and the curriculum is currently applied to all grades. In order to promote students' mathematical communication, the teacher needs to understand full implications and apply them to instruction. This study examined how teachers employed mathematical communication in their instruction and how they perceived it. The results showed that teachers had lack of understanding of student-centered instruction and mathematical communication. They also did not use various representation activities and discussion-based activities as expected. The number of students per classroom was reported by teachers as a main barrier to promote mathematical communication, but it did not make substantial differences in practice. Building on the results, this paper included implications for improving teachers' conception of mathematical communication.

• The Mathematical Education
• /
• v.51 no.2
• /
• pp.161-171
• /
• 2012

Generally mathematics is regarded as a subtle subject to grasp their true meaning. And teacher's personal conceptions of mathematics influence greatly on the teaching and learning of mathematics. More over often teachers confess their difficulties in explaining the true nature of mathematics. In this paper, applying the theory of epistemology, we tried to search factors that must be counted important when trying to understand the true nature of mathematics. As results, we identified five characteristics of mathematical knowledge such as logical reasoning, abstractive concept, mathematical representation, systematical structure, and axiomatic validation. Next, we tried to investigate math education major students' conception of mathematics using these items. To proceed this research we asked 51 students from three Universities to answer their opinion on 'What do you think is mathematics?'. Analysing their answers in the light of the above five items, we got the following facts. 1. Only 38% of the students regarded mathematics as one of the five items, which can be considered to reveal students' low concern about the basic nature of mathematics. 2. The status of students' responses to the question were greatly different among the three Universities. This shows that mathematics professors need to lead students to have concern about the true nature of mathematics.

• Journal of Educational Research in Mathematics
• /
• v.27 no.4
• /
• pp.663-678
• /
• 2017

Semiotic studies in mathematical education have been based on Saussure, Peirce, and Frege and many prior researches have explored the concepts in a perspective of semiotics. However, the relationship among semiotical elements and the formation and the evolution of a conception are still ambiguous and veiled in many aspects. This thesis is intended to show how a conception was formed and evolved by expression, which is an element of semiotics. In this process, I sought to partially illuminate the relationship among expressions, concepts, and objects.

• Journal of the Korean School Mathematics Society
• /
• v.6 no.2
• /
• pp.117-126
• /
• 2003

In this article, we described students' conceptions of fraction, based on the mathematical learning theory of Skemp who contributed to the understanding of a mathematical conception in the real world problems. We analyzed students' responses to given three problems in order to examine a degree of the conceptual understanding in their responses. In conclusion, it suggests some instructional methods which facilitate students to understand the conceptions the fraction implies.

• Communications of Mathematical Education
• /
• v.24 no.2
• /
• pp.345-363
• /
• 2010

The purpose of this study is to investigate and analyze informal knowledge of students who do not learn the conception of proportion and to identify how the informal knowledge can be used for teaching the conception of proportion in order to present an effective method of teaching the conception. For doing this, proportion was classified into direct and inverse proportion, and 'What are the informal knowledge of students?' were researched. The subjects of this study were 117 sixth-graders who did not have prior learning on direct and inverse proportion. A total eleven problems including seven for direct proportion and four for inverse proportion, all of them related to daily life. The result are as follows; Even though students didn't learn about proportion, they solve the problems of proportion using informal knowledge such as multiplicative reasoning, proportion reasoning, single-unit strategy etc. This result implies mathematics education emphasizes student's informal knowledge for improving their mathematical ability.

• Research in Mathematical Education
• /
• v.9 no.1 s.21
• /
• pp.25-45
• /
• 2005

Background Phenomenography suggests that more variation is associated with wider ways of experiencing phenomena. In the discipline of mathematics, broadening the 'lived space' of mathematics learning might enhance students' ability to solve mathematics problems Aims The aim of the present study is to: 1. enhance secondary school students' capabilities for dealing with mathematical problems; and 2. examine if students' conception of mathematics can thereby be broadened. Sample 410 Secondary 1 students from ten schools participated in the study and the reference group consisted of 275 Secondary 1 students. Methods The students were provided with non-routine problems in their normal mathematics classes for one academic year. Their attitudes toward mathematics, their conceptions of mathematics, and their problem-solving performance were measured both at the beginning and at the end of the year. Results and conclusions Hierarchical regression analyses revealed that the problem-solving performance of students receiving non-routine problems improved more than that of other students, but the effect depended on the level of use of the non-routine problems and the academic standards of the students. Thus, use of non-routine mathematical problems that appropriately fits students' ability levels can induce changes in their lived space of mathematics learning and broaden their conceptions of mathematics and of mathematics learning.

• The Mathematical Education
• /
• v.50 no.4
• /
• pp.429-440
• /
• 2011

This paper analysed gifted middle students' conception of the definitions of point and line and the uses of definitions in proving. The findings of this paper suggest that the concept of mathematical definitions is very unnatural to students, therefore teachers and textbooks need to explain explicitly the characteristics of mathematical definitions which are different from dictionary definitions using common sense. Also introducing undefined terms in middle school geometry would give students a critical chance to deal with the transition from dictionary definitions to mathematical definitions.