• Journal of Educational Research in Mathematics
• /
• v.26 no.4
• /
• pp.683-700
• /
• 2016

The traditional teaching-learning in mathematics, which pursue only one correct answer, should be reexamined to cope with an age of uncertainty. In this research, Perry's epistemological development scheme was noticed as a theoretical approach to diagnose problems of dualistic mathematics lessons and to search solutions of the problems. And Design-Based Research method was adopted, We developed the epistemological development scheme through considering Perry's theory and related studies, scaffoldings and teaching-learning to enhance students' epistemological positions in mathematics. Based on these discussions we designed teaching experiment about operations with negative numbers, and analyzed its didactic implications.

• Journal of Elementary Mathematics Education in Korea
• /
• v.23 no.4
• /
• pp.365-382
• /
• 2019

This study aimed to analyze the moderated effects of mathematics test-preparation strategies in the relation between elementary school students' epistemological beliefs about mathematics and test anxiety. The moderated effects were tested by using structural equation modeling with the Ping's two-step approach. The subjects were 810 6th graders (411 male, 399 female) from 13 elementary schools situated in G Metropolitan City. Tests for epistemological beliefs about mathematics, test anxiety, and mathematics test-preparation strategies were used as measurement scales. The results of this study were as follows. The moderated effects of mathematics test-preparation strategies in the relation between epistemological beliefs about mathematics and test anxiety were statistically significant. Higher level of epistemological belief about mathematics were linked to lower level of test anxiety, while lower level of epistemological belief about mathematics led to an increased influence of test-preparation strategies levels on test anxiety. Students who had higher levels of epistemological belief about mathematics displayed lower level of test anxiety when using high levels of test-preparation strategies. Students who scored lower in the epistemological belief about mathematics had lower level of test anxiety when employing low levels of test-preparation strategies. Therefore, to lower the level of test anxiety among elementary students, the intervention program need to consider the appropriate levels of test-preparation strategies in accordance with each student's level of epistemological belief about mathematics.

• Journal of the Korean School Mathematics Society
• /
• v.19 no.3
• /
• pp.261-275
• /
• 2016

Many students have dualistic beliefs about mathematics and its learning- for example, there is always just one right answer in mathematics and their role in the classroom is receiving and absorbing knowledge from teacher and textbook. This article investigated some epistemic implications and limitations of common mathematics teaching practices, which often present mathematical facts(or procedures) and treat students' errors in a certain and absolute way. Langer and Piper's (1987) experiment and Oliveira et al.'s (2012) study suggested that presenting knowledge in conditional language which allows uncertainty can foster students' productive epistemological beliefs. Changing the focus and patterns of classroom communication about students' errors could help students to overcome their dualistic beliefs. This discussion will contribute to analyze the implicit epistemic messages conveyed by mathematics instructions and to investigate teaching strategies for stimulating students' epistemic development in mathematics.

• Journal of Gifted/Talented Education
• /
• v.22 no.4
• /
• pp.805-821
• /
• 2012

The purpose of this study was to investigate the relationship between epistemic beliefs and creativity of gifted students. To resolve the above research questions, this study used epistemic beliefs inventory and Torrance's TTCT to 87 1st grade gifted middle school students enrolled in Daegu metropolitan city. The results of this study are as follows. Firstly, sophistical epistemic beliefs of the gifted students were higher than their naive epistemic beliefs. Secondly, Pearson's correlation analysis showed significant relations between fixed ability and verbal creativity, and between provisional knowledge and verbal creativity, and showed significant relations between variables of sophistical epistemic beliefs and figural creativity. Lastly, this study revealed that fixed ability, expert authority and provisional knowledge explain considerable amount verbal creativity of the gifted students. And authority of the acceptance and provisional knowledge affect considerably their figural creativity.

• School Mathematics
• /
• v.19 no.4
• /
• pp.775-793
• /
• 2017

In this study, instruments were developed to measure of mathematics attitudes by conceptualization of epistemological beliefs as a cognitive dimension, mindfulness as a conative dimension, affect as an affective dimension. Perry's epistemological development scheme and Langer's mindfulness theory was noticed as a theoretical approach. Exploratory factor and confirmatory factor analyses, and a reliability test were assessed. This article suggest a new framework for analysing attitudes toward mathematics and changes in attitudes toward mathematics.

• Journal of The Korean Association For Science Education
• /
• v.40 no.4
• /
• pp.359-374
• /
• 2020

This study is a complex type consisting of survey study and self-study. The former investigated elementary teachers' epistemological beliefs on convergence knowledge and teaching. As a representative of the result of survey study I, as a teacher as well as a researcher, was the participant of the self-study, which investigated my epistemological belief on convergence knowledge and teaching and my execution of convergent science teaching based on family resemblance of mathematics, science, and physical education. A set of open-ended written questionnaires was administered to 28 elementary teachers. Participating teachers considered convergent teaching as discipline-using or multi-disciplinary teaching. They also have epistemological beliefs in which they conceived convergence knowledge as aggregation of diverse disciplinary knowledge and students could get it through their own problem solving processes. As a teacher and researcher I have similar epistemological belief as the other teachers. During the self-study, I tried to apply convergence knowledge system based on the family resemblance analysis among math, science, and PE to my teaching. Inter-disciplinary approach to convergence teaching was not easy for me to conduct. Mathematical units, ratio and rate were linked to science concept of velocity so that it was effective to converge two disciplines. Moreover PE offered specific context where the concepts of math and science were connected convergently so that PE facilitated inter-disciplinary convergent teaching. The gaps between my epistemological belief and inter-disciplinary convergence knowledge based on family resemblance and the cases of how to bridge the gap by my experience were discussed.

• Communications of Mathematical Education
• /
• v.18 no.2 s.19
• /
• pp.371-382
• /
• 2004

Kamii는 피아제의 발생론적 인식론이란 이론을 모태로 수학을 지도해야 학습자가 수학을 이해를 바탕으로 학습할 수 있다는 믿음을 지니고 있다. 본고에서는 Kamii가 이런 신념을 갖고 실시한 수업을 녹화한 비디오 자료에 나타나는 특징을 분석하였다. 첫 번째 특징은, 교사가 가르쳐야 할 지식을 직접적으로 지도하지 않는 대신에 학습자가 스스로 지식을 구성할 수 있도록 매개자의 역할을 한다는 점이다. 두번째, 기저지식으로서 학습자의 비형식적 지식을 학습자가 적극적으로 활용할 수 있도록 허용하는 분위기이다. 세 번째, 두 번째와 관련되어서 학습자의 사고과정은 성인이나 학문적 체계에서 운용되고 있는 사고 흐름과는 다르다는 것을 인정해 준다. 네 번째, 교사의 역할이 가르쳐야 할 지식을 가르치는데(전수하는데) 있는 것이 아니라 학습자들이 생성해 낸 여물지 않은 아이디어들을 익힐 수 있도록 환경을 조성하는데 있다. 다섯 번째, 학습자마다 기저지식이 다르기 때문에 동일한 학습주제라 할지라도 이해의 폭과 깊이가 다르다. 따라서, 전체학급을 대상으로 하는 수업 중이라 할지라도 개별적 학습을 염두에 두어야 한다. 학생들의 수학적 이해력이 저하된다는 염려의 목소리가 높아지고 있다. 이는 학생들이 이해를 바탕으로 한 수업을 받아 보지 못하기 때문이며, 이런 원인은 아마도 교사 자신이 이해를 바탕으로 한 수업 경험이 간접적으로든 직접적으로든 없기 때문일 것이다. Kamii가 실시한 수업이 학생 스스로 수학을 학습할 수 있다는 구성주의 원리를 적용한 성공적인 사례이며, 이와 같은 방향으로의 교수법의 변화가 있기를 기대한다.

• Journal of Educational Research in Mathematics
• /
• v.16 no.1
• /
• pp.43-58
• /
• 2006

An objective of this paper is to discuss the didactical contracts which have been conceptualized by Brousseau. He modelled mathematics instruction as a game. In such game, didactical contracts existed as its own hidden rules which teacher and student should obey Brousseau introduced it to reveal certain hidden rules which regulates mathematics instruction. Those rules are implicit and reciprocal. In particular, it is not revealed until students break. He defined didactical contracts as teacher's behaviour and corresponding students 'behaviour in order to define it operationally. He he did not define it in psychological and epistemological dimension. But it is necessary to discuss teacher's belief system and epistemology, since teacher's behaviour in instruction is affected by them. He also did not discuss fully teacher's breaking of didactical contracts.