• Journal of Educational Research in Mathematics
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• v.10 no.1
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• pp.85-102
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• 2000

The concept of variables is central to mathematics teaching and learning in junior and senior high school. Understanding the concept provides the basis for the transition from arithmetic to algebra and necessary for the meaningful use of all advanced mathematics. Despite the importance of the concept, however, much has been written in the last decade concerning students' difficulties with the concept. This Thesis is based on research to investigate the hypothesis that LOGO programming will contribute to 6th grader' learning of variables. The aim of the research were to; .investigate practice on pupils' understanding of variables before the activity with a computer; .identify functions of LOGO programming in pupils' using and understanding of variable symbols, variable domain and the relationship between two variable dependent expressions during the activity using a computer; .investigate the influence of pupils' mathematical belief on understanding and using variables. The research consisted predominantly of a case study of 6 pupils' discourse and activities concerning variable during their abnormal lessons and interviews with researcher. The data collected for this study included video recordings of the pupils'work with their spoken language.

• Research in Mathematical Education
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• v.11 no.2
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• pp.127-141
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• 2007

This paper compares and analyzes mathematics teachers' understanding of students' mathematical comprehension after experiences with the Cognitively Guided Instruction (CGI) or the Development of Mathematical Ideas (DMI) teaching strategies. This report sheds light on current issues confronted by the educational system in the context of mathematics teaching and learning. In particular, the declining rate of mathematical literacy among adolescents is discussed. Moreover, examples of CGI and DMI teaching strategies are presented to focus on the impact of these teaching styles on student-centered instruction, teachers' belief, and students' mathematical achievement, conceptual understanding and word problem solving skills. Hence, with a gradual enhancement of reformed ways of teaching mathematics in schools and the reported increase in student achievement as a result of professional development with new teaching strategies, teacher professional development programs that emphasize teachers' understanding of students' mathematical comprehension is needed rather than the currently dominant traditional pedagogy of direct instruction with a focus on teaching problem solving strategies.

• Education of Primary School Mathematics
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• v.25 no.1
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• pp.43-55
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• 2022

It is critical to examine changes in teachers' beliefs on how to teach and learn mathematics through teacher education programs. This study aims to develop an instrument measuring elementary pre-service teachers' beliefs on student- and teacher-centered instruction. After developing questionnaires with mathematics education experts, the structural validity of the instrument was evaluated by collecting and analyzing data from 166 pre-service teachers. Parallel analysis and exploratory factor analysis were applied sequentially to collect validity and reliability evidence. The results showed that this instrument can be used to examine changes in pre-service teachers' two different types of belief: student- and teacher-centered instruction. We also suggested how to interpret scores appropriately.

• Human Ecology Research
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• v.58 no.1
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• pp.105-120
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• 2020

This study helps infant teachers practice a constructivism-based teacher education program that supports infant mathematical inquiry activities and examines improvements in mathematical teaching knowledge, mathematical teaching initiatives, mathematical interaction, constructivism belief and mathematical teaching efficacy. Twenty two experiment group infant teachers and twenty two comparison group infant teachers were chosen at two workforce educare centers. The experiment group infant teachers participated in 18 sessions of a constructivism teacher training program for 8 weeks, but the comparison group infant teachers did not take part in the program. Pretest and post-tests were implemented for the mathematical teaching knowledge, mathematical teaching initiatives, mathematical interactions, constructivism belief and mathematical teaching efficacy in the experiment group. Independent sample t-test and ANCOVA were tested using Windows SPSS statistics 21.0. The homogeneity test for the experiment and comparison group revealed significant differences. ANCOVA was carried out after the pretest score was controlled as a co-variance. Significant differences were indicated in mathematical teaching knowledge, mathematical teaching initiative, mathematical interaction, constructivism belief and mathematical teaching efficacy. The results indicated that a constructivism-based teacher education program to support infant mathematical inquiry activities influenced improvements in mathematical teaching knowledge, mathematical teaching initiative, mathematical interaction, constructivism belief and mathematical teaching efficacy. This study proved the effects of the program based on constructivism theory content for the knowledge, skills and attitude about infant teaching of mathematical initiatives and practiced a program of exploration, investigation, application and assessment for infant teachers. The results can help infant teachers teach mathematical exploration activities and help activate infant mathematical exploration activities.

• Educational Technology International
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• v.17 no.2
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• pp.229-251
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• 2016

This study was designed to investigate the relationship between middle school students' smart media competency and online learning outcomes. The context of this study was on online inquiry-based mathematics and science learning environment, and four-hundred and fifty-five (455) 7^th to 9^th grade students in Korea participated in this research. To assess students' smart device competency, Smart Media Literacy Quotient (SMLQ) which consisted of 18 items regarding the operation ability of smart media and its application (14 items) and positive beliefs of smart media (4 items) was administered to each student. The findings of this study first showed that students' smart media literacy varied according to their characteristics such as gender, grade, class (subject), and socio-economic status. Female students' scores were higher in overall smart media literacy operation and learning ability of smart media than male students. 7^th grade middle school students represented lower smart media literacy scores, compared to 8^th and 9^th graders. Also, minority students were significantly lower in smart media literacy, operation and learning ability of smart media, and positive belief of smart media than the non-minority students. Second, overall smart media literacy and operation and learning ability of smart media varied among high, medium, and low score achievers in inquiry tasks. Low scored students in inquiry tasks were significantly lower in overall smart media literacy and operation and learning ability of smart media than medium scored students. Lastly, smart media literacy also varied by students' dropout/completion. Students who dropped out reported significantly lower scores in overall smart media literacy, operation and learning ability of smart media, and positive belief of smart media.

• Journal of the Korean School Mathematics Society
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• v.19 no.3
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• pp.261-275
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• 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 Educational Research in Mathematics
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• v.16 no.4
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• pp.345-366
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• 2006

In this study, we investigated the methods of using the Cabri3D program for education of problem solving in school mathematics. Cabri3D is the program that can represent 3-dimensional figures and explore these in dynamic method. By using this program, we can see mathematical relations in space or mathematical properties in 3-dimensional figures vidually. We conducted classroom activity exploring Cabri3D with 15 pre-service leachers in 2006. In this process, we collected practical examples that can assist four stages of problem solving. Through the analysis of these examples, we concluded that Cabri3D is useful instrument to enhance problem solving ability and suggested it's educational usage as follows. In the stage of understanding the problem, it can be used to serve visual understanding and intuitive belief on the meaning of the problem, mathematical relations or properties in 3-dimensional figures. In the stage of devising a plan, it can be used to extend students's 2-dimensional thinking to 3-dimensional thinking by analogy. In the stage of carrying out the plan, it can be used to help the process to lead deductive thinking. In the stage of looking back at the work, it can be used to assist the process applying present work's result or method to another problem, checking the work, new problem posing.

• The Mathematical Education
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• v.54 no.2
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• pp.99-117
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• 2015

The purpose of this study was qualitatively conducted for getting the answer of this problem by searching the beliefs of mathematics teachers with experience in technology and the factors that influences these beliefs. The participants in this study consist of eight teachers and one university professor having technological experiences from three years to ten years with a higher degree than M.A. The data was collected through focused group interviews for twice and individual interview as well. Data analysis was completed through several readings of transcripts and then main themes were derived by classifying, comparing, and contrasting codings. The result of this study showed that teachers with the experiences of technological tools have the concrete belief that technology helps both students and teachers understand mathematical concepts and enhance various representational activities and motivations. The result also identified the impeding factors of three beliefs of mathematics teachers. From these beliefs and factors, this study would suggest how to help teachers hold their beliefs about using technologies to improve their teachings and students' learning.

• School Mathematics
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• v.16 no.2
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• pp.387-407
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• 2014

Gender differences have been given major attention in mathematics education in the context of pursuing gender equity in instructional and learning environment. It had been traditional belief that male students would outperform female students in mathematics, especially in the areas as geometry. This belief has been given doubts by cumulated empirical evidences that gender differences are gradually diminishing or even reversing its direction as time goes on. In this study, gender differences in geometry were explored using TIMSS 8th grade mathematics data administered in TIMSS 2003, 2007, and 2011, based on a cognitive diagnostic modeling(CDM) approach. Among various CDM models, the Fusion model was employed. The Fusion model has advantages over other CDM models in that it provides more detailed information about gender differences at the attribute level as well as item level and more mathematically tractable. The findings of this study show that Attribute 3(Three-dimensional Geometric Shapes) revealed statistically significant gender differences favoring male students in TIMSS 2003 and 2007, but did not show significant differences in TIMSS 2011, which provides an additional empirical evidence supporting the recent observation that gender gap is narrowing. In addition to the general trends in gender differences in geometry, this study also provided affluent information such as gender differences in attribute mastery profiles and gender differences in relative contributions of each attribute in solving a particular item. Based on the findings of the CDM approach exploring gender differences, instructional implications in geometry education are discussed.

• The Mathematical Education
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• v.60 no.4
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• pp.529-542
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• 2021

The purpose of this research is to compare the mathematical beliefs that directly or indirectly affect the mathematics learning of Korean languge learners with those of non-Korean languge learners and identify the characteristics. To this end, an analytical comparative research was conducted through a questionnaire survey on perceptions of mathematics learning for 6th grade students of elementary school with different cultural and linguistic backgrounds in the same mathematics classroom. As a result of the analysis, Korean languge learners and non-Korean languge learners gave different meanings to learning mathematics, and they recognized various meanings of success in mathematics. In addition, the math learning ability of non-Korean learners was evaluated higher than that of Korean learners. Based on their positive beliefs, they decided how to resolve conflict situations with different problem-solving results. It will be necessary to prepare a teaching/learning plan that can fully implement multicultural mathematics education in the mathematics classroom where Korean language learners with different cultural and linguistic backgrounds belong. The results of this research can contribute to raising awareness of the need for follow-up researches to find ways to reduce the learning gap between Korean languge learners and non-Korean languge learners. It is expected that this research will contribute to understanding the perceptive characteristics of Korean language learners about learning mathematics and to prepare a plan to utilize them in mathematics lessons.