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Research Design: Qualitative, Quantitative, and Mixed Methods Approaches

미국의 “전국 수학 교사 협의회”(National Council of Teachers of Mathematics, NCTM)는 1989년부터 〈학교 수학의 교육과정과 평가 규준〉(1989), 〈수학 가르침(교수)의 전문성 규준〉(1991), 〈학교 수학의 평가(시험) 규준〉(NCTM, 1995), 〈학교 수학의 원리와 규준〉(2000)을 출판하여 미국의 수학 교육 의 전망(목표, 나아갈 길)과 규준(실행 지침)을 제시하였다. 수학 교사들로 구성된 미국의 NCTM은 학생, 학부모, 학교 행정가 등 많은 사람들과 힘을 합하여 모든 학생들에게 수준 높은 수학 교육을 받을 수 있는 여건(환경, 기회)을 조성하는 데 구심점의 역할을 하였다. 한편 많은 관련 단체들은 여러 배경과 능력을 가진 학생들이 전문성을 지닌 교사(특수 교사를 일컫는 밀이 아니다. 수학 교과를 이해하고 수학의 전문성과 특수성을 가르칠 수 있는 일반 교사를 일컫는 말이다.)로부터 미래를 대비해 평등하고, 진취적이며, 지원이 잘 이루어지고, 공학 도구(IT)가 잘 갖춰진 환경에서 중요한 수학적 아이디어를 이해하면서 학습할 수 있는 수학 교실(미국에서는 우리나라처럼 수학 교사가 수학 시간에 학생의 방(교실: Homeroom)에 찾아가지 않고 학생들이 선생의 방(수학 교실: Classroom)을 찾아온다. 전형적인 수학 교실의 사진은 2쪽에 나와 있다.)을 만들기 위해 함께 힘썼다. NCTM에서 출간한 여러 규준들은 우리나라의 제6차와 제7차 교육과정에도 큰 영향을 미쳤다. 이 글에서는 NCTM(2000)에서 제시한 학습 원리를 간단히 살펴본 다음 이를 중심으로 현재 미국 수학 교육의 교수ㆍ학습 이론의 동향을 살펴본다.

미국 NCTM의 Principles and Standards for School Mathematics에 나타난 수학과 교수,학습의 이론

Meta-analytic procedures for social research

Intuition in Science and Mathematics: an educational approach

Contents: Conceptual and Procedural Knowledge in Mathematics: An Introductory Analysis. The Notion of Principle: The Case of Counting. Children's Mastery of Written Numerals and the Construction of Basic Number Concepts. The Relationship Between Initial Meaningful and Mechanical Knowledge of Arithmetic. Conceptual Knowledge as a Foundation for Procedural Knowledge: Implications from Research on the Initial Learning or Arithmetic. Arithmetic Procedures are Induced from Examples. Using Conceptual and Procedural Knowledge: A Focus on Relationships. Procedures Over Concepts: The Acquisition of Decimal Number Knowledge. On Having and Using Geometric Knowledge. Conceptual and Procedural Knowledge in Mathematics: A Summary Analysis.

Missing Links@@@Conceptual and Procedural Knowledge: The Case of Mathematics

As a result of rapid development in technology, utilizing materials in education has become important. To date, researchers have often explored the effects of using educational materials in mathematics instruction on academic achievement. The purpose of this study was to combine the empirical evidence regarding the effectiveness of educational materials in mathematics. For this aim, a meta-analysis method was used in the current research. In line with the aim of the research, 54 experimental studies published between years of 2005 and 2016 were included in the meta-analysis and 58 effect sizes were calculated from these studies. The results of the meta-analysis showed that using materials in mathematics has a positive and high influence on achievement. According to analysis of mediator variables that are related to instructional characteristics, significant differences are found in the variables of mathematics topic, type of material, and application time. However, teaching with materials in mathematics did not seem to differ in effectiveness from teaching without materials, in terms of methodological characteristics of the studies.

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The Impact of Educational Material Use on Mathematics Achievement: A Meta-Analysis.

Bu calismanin amaci, Turkiye ve Kanada’da kullanimda olan ortaokul matematik ders kitaplarindaki sorulari bilissel ogrenme duzeylerine ve soru turlerine gore inceleyip karsilastirmaktir. Bu baglamda Turkiye’de kullanimda olan ortaokul matematik ders kitaplari ile Kanada’da kullanimda olan “Math Makes Sense” adli ders kitaplari icerik analizine tabi tutularak karsilastirilmistir. Arastirmanin amacina uygun olarak veriler toplanip dokuman analizi yapilmistir. Her iki ulke ders kitaplarinda yer alan matematik sorulari, Sentezlenmis Bloom Taksonomisi uzerinden bilissel surec ve bilgi boyutlarina gore kodlanmis ve sorularin bilissel ogrenme duzeylerine gore benzerlik ve farkliliklari karsilastirmali olarak incelenmistir. Turkiye ve Kanada ders kitaplarinda yer alan sorularin bilissel surec ve bilgi boyutu acisindan benzer ozellikler gosterdigi tespit edilmistir. Ancak Kanada ders kitabinda bilissel beceri gerektiren acik uclu soru turlerine daha cok yer verildigi belirlenmistir. Ders kitaplarinin icerigi olusturulurken uluslararasi sinavlarla uyumlu ust bilissel beceri gerektiren sorulara daha fazla yer verilmesi onerilmektedir.

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A comparison of mathematics questions in Turkish and Canadian school textbooks in terms of synthesized taxonomy

This study aims to analyze the relationship between secondary school seventh grade students’ perception of mathematical self-efficacy, mistake-handling learning awareness, and mathematical anxiety; and to define the power of mistake-handling learning and self-efficacy in predicting mathematical anxiety. In this study, relational model was used and the research group consisted of 323 seventh grade students whose ages range from 12 to 14. According to the findings of the study, when the relationship between mathematical anxiety, self-efficacy, and mistake-handling learning is analyzed, it is observed that there are significant relationships between mathematical anxieties, self-efficacy, and mistake-handling learning. Furthermore, mathematical self-efficacy and mistake-handling learning explain 51% of the total variance of the mathematical anxiety.

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Mathematics Self-efficacy and Mistake-handling Learning as Predictors of Mathematics Anxiety

Available online 10.01.2019 The aim of the present study was to investigate the development of technological pedagogical content knowledge (TPACK) and Web 2.0 self-efficacy beliefs (W2SEB) and to determine the relationship between them for middle school pre-service mathematics teachers through their involvement in a course designed using a Web 2.0 tools. To achieve this aim, thirty pre-service teachers participated in forty two hours of the course in which they could interact with Web-based applications. In the course, pre-service mathematics teachers were requested to develop and present e-content related to the use of these applications for learning outcomes determined in 5-8th grade mathematics curriculum. In order to collect the required data, the TPACK and W2SEB scale were applied to pre-service teachers at the beginning and end of the course. The data obtained from these scales were quantitatively analyzed. Within this scope, while there were positive developments in terms of the technological pedagogical knowledge levels and self-efficacy beliefs, there was a significant relationship identified between them. Additionally, when the regression results related to the post-test are investigated, the TPACK sub-factors of technological and mathematical knowledge were shown to be significant predictors of Web 2.0 rapid content development self-efficacy beliefs. © 2019 IOJES. All rights reserved

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The Relationship between Technological Pedagogical Content Knowledge and Web 2.0 Self-Efficacy Beliefs.

Visualization is mostly despised although it complements and – sometimes – guides the analytical process. This study mainly investigates teachers’ preferences concerning the use of the visualization method and determines the extent to which they encourage their students to make use of it within the problem-solving process. This study was conducted for the ninth-grade students and their mathematics teacher in a social science intensive public school in the city of Erzurum, Turkey. Utilizing case study as the preferred method, data were collected through observations, interviews and student evaluations. This study revealed that visualization has a positive effect at the preliminary phases of teaching the absolute value concept but generates a lack of stimulation during problem solving in further phases of the instruction. This could be explained as a result of current examination system which requires a habituation of the analytical process in solving mathematical questions.

Zeki Aksu

Papers

The Impact of Educational Material Use on Mathematics Achievement: A Meta-Analysis.

A comparison of mathematics questions in Turkish and Canadian school textbooks in terms of synthesized taxonomy

Mathematics Self-efficacy and Mistake-handling Learning as Predictors of Mathematics Anxiety

The Relationship between Technological Pedagogical Content Knowledge and Web 2.0 Self-Efficacy Beliefs.

The preference of visualization in teaching and learning absolute value