#### Editor-in-Chief

Masakazu Okazaki (Okayama University, Japan)

#### Editorial Board

David Burghes (Plymouth University, UK)

Keiko Hino (Utsunomiya University, Japan)

Berinderjeet Kaur (National Institute of Education, Singapore)

Masataka Koyama (Hiroshima University, Japan)

Hee-chan Lew (Korea National University of Education, Korea)

Luis Radford (Laurentian University, Canada)

Heinz Steinbring (Universität Duisburg-Essen, Germany)

Tad Watanabe (Kennesaw State University, USA)

Gaye Williams (Deakin University, Australia)

## Vol.12 February 2019

*Research Articles*

**Hiroki Otani**

Comparing structures of statistical hypothesis testing with proof by contradiction: In terms of argument

*Special Feature Articles: Foundations of Mathematics Education for the Future*

**Erich Ch. Wittmann**

Understanding and organizing mathematics education as a design science - Origins and new developments

**Masataka Koyama **

Framework of a dynamic cycle for promoting the professional development of mathematics teachers and educators in the lesson study of school mathematics

**Masakazu Okazaki, Koji Okamoto and Tatsuo Morozumi**

Characterizing the quality of mathematics lessons in Japan from the narrative structure of the classroom: "Mathematics lessons incorporating students''questions' as a main axis" as a leading case

*Lecture Notes*

**Yves Chevallard**

Introducing the anthropological theory of the didactic: An attempt at a principled approach

## Vol.11 March 2005

...

## Vol.10 December 2002

**Yiu-Kwong MAN and Yin-Kue LO**

On Computing the Volume of Sphere in the East and West: A Comparative Study from the Educational Perspectives

**Aurelia NODA, J. HERNANDEZ and M. M. SOCAS**

Study of Proof and Arguments Used by Students in the Resolution of Well Defined and Ill Defined Problems

**Ngai-Ying WONG, Chi-Chung LAM and Chui-See CHAN**

The Current State of the "Lived Space" of Mathematics Lerning

**Der-Ching YANG and Robert E. REYS**

Fractional Number Sense Strategies Possessed by Sixth Grade Students in Taiwan

## Vol.9 March 2001

**Masataka KOYAMA**

A Research on the Validity and Effectiveness of "Two-Axes Process Model" of Understanding Mathemaics at Elementary School Level

**Taro FUJITA**

The Study of Elementary Geometry (1903) by Godfrey and Siddons (1): Roles of Experimental Tasks in the Teaching of Geometry

**Pessia TSAMIR**

Students' Reactions to Different Representations of Points

**Jane M. WATSON and Helen L. CHICK**

Does Help Help?: Collaboration during Mathematical Problem Solving

## Vol.8 March 2000

**Tadao NAKAHARA, Tetsuro SASAKI, Masataka KOYAMA and Takeshi YAMAGUCHI**

Multi-World Paradigm in Mathematical Learning(1): An Analysis of Mathematics Classes

**Hideki IWASAKI and Takeshi YAMAGUCHI**

The Analysis of Cognitive Process in Generalization: The Expanded Theoretical Framework for Metacognition in Learning and Teaching Mathematics

**Anno van STREUN, Egbert HARSKAMP and Cor SUHRE**

The Effect of the Graphic Calculator on Students' Solution Approaches: A Secondary Analysis

**Mitsuo KANEMITSU, Kentaro HATANO and Mamoru FURUHATA**

On the Ideals of Polynomial Semigroups

## Vol.7 March 1999

**Constance KAMII and Kyoko OZAKI**

Abstraction and Representation in Arithmetic: A Piagetian View

**Antonio ESTEPA, Carmen BATANERO, and F. T. SANCHEZ**

Student's Intuitive Strategies in Judging Association When Comparing Two Samples

**Keith E. HIRST**

Procedural Extrapolation as a Source of Structural Errors in Calculus

**Ikuo NISHITANI**

Match-stick Geometry in Space

**Mitsunori IMAOKA**

Counting the Number of Bounded Domains Separated by Hyperplanes

## Vol.6 March 1998

**Masataka KOYAMA**

Students' Representations of Fractions in a Regular Elementary School Mathematics Classroom

**Egbert G. Harskamp, Cor J. M. Suhre, and Anne van Streun**

The Graphics Calculator in Mathematics Education: An Experiment in the Netherlands

**Saraswathi Kota and Michael O. J. Thomas**

Students' Arithmetic Preferences: Effect on Problem Solving Ability

**Kaye Stacey and Vicki Steinle**

Refining the Classification of Students' Interpretations of Decimal Notation

**Chun-Ip Fung and Ngai-Ying Wong**

Connections Through the Development of Mathematical Ideas: The Case of Solution to High Degree Polynomial Equations in Medieval Chinese Mathematics

## Vol.5 March 1997

**Tadao Nakahara**

Study of the Constructive Approach in Mathematical Education (II): Types of Constructive Interactions and Requirements for the Realization of Effective Interactions

**Constance Kamii and Mary Ann Warrington**

Multiplication with Fractions: A Constructive Approach

**Masataka Koyama**

Research on the Complementarity of Intuition and Logical Thinking in the Process of Understanding Mathematics: An Examination of the Two-Axes Process Model by Analyzing an Elementary School Mathematics Class

**Swapna Mukhopadhyay**

Story Telling as Sense-Making: Children's Ideas about Negative Numbers

**Masanobu Honda**

On Maximal Subalgebras and the Hypercentre of Lie Algebras

## Vol.4 March 1996

**Mohan Chinnappan and Michael Lawson**

Knowledge Extension and Geometry Problem Solving Performance

**Antonio Estepa and Carmen Batanero**

Judgments of Correlation in Scatter Plots: Students' Intuitive Strategies and Preconceptions

**Angustias Vallecillos Jimenez**

Students' Conceptions of the Logic of Hypothesis Testing

**Anthony Ralston, Barbara J. Reys, and Robert E. Reys**

Calculators and the Changing Role of Computation in Elementary School Mathematics

**Tad Watanabe**

Coordination of Units: A Theoretical Model

**Ngai-Ying Wong**

Students' Perceptions of the Mathematics Classroom in Hong Kong

**Yoshimi Kashiwagi, Iasao Kikumasa, Osamu Miyagawa, and Akira Obuchi**

A Note on Equivalence and Weight Enumerators of Codes

## Vol.3 March 1995

**Keith Hirst and Christine Shiu**

Investigations in Pure Mathematics: A Constructivist Perspective

**Ho-Kheong Fong**

Schematic Model for Categorising Children's Errors in Solving a Ratio and Proportion Problem

**Guershon Harel and Merlyn Behr**

Teachers' Solutions for Multiplicative Problems Constance Kami and Mary Ann Warrington Division with Fractions: A Piagetial, Constructivist Aprroach

**Robert E. Orton, Thomas R. Post, Merlyn J. Behr, Kathleen Cramer, Guerson Harel and Richard Lesh**

Logical and Psychological Aspects of Rational Number Pedagogical Reasoning

## Vol.2 March 1994

**Paul Ernest**

Varieties of Constructivism: Their Metaphors,Epistemologies and Pedagogical Implications

**M. C. Batanero and J. D. Godino**

A Methodology to Study the Students' Interaction with the Computer

**Toshihiko and Tohru Tomitake**

The Relationships between Achievement Motivation in Mathematics Learning, Intelligence, and School Mathematics Achievement for Secondary School Students of Japan: A Study of Achievement Motivation in Mathematics Learning (XII)

**Masataka Koyama**

Research into Relationship between the Computation Estimation Ability and Strategy and the Mental Computation Ability: Analysis of a Survey of the Fourth, Fifth, and Sixth Graders in Japan

**Michael Mitchelmore**

Abstraction, Generalisation and Conceptual Change in Mathematics

**Tadao Nakahara**

Study of the Representation System in Mathematics

**Takeshi Yamaguchi**

A Study of Metacognition in Mathematical Problem Solving: The Roles of Metacognition on Solving a Construction Problem

## Vol.1 March 1993

**Walther L. Fischer**

Formal Concept Analysis as a Research Tool in Mathematics Education

**Jerry P. Becker**

Current Trends in Mathematics Education in the United States, With Reference to Computers and Calculators

**Geoffrey Howson**

Some Comments on Mathematics Education in Japan

**Masataka Koyama**

Building a Two Axes Process Model of Understanding Mathematics

**Tadao Nakahara**

Study of the Constructive Approach in Mathematical Education

**Barbara J. Reys, Robert E. Reys and Wendell J. Wyatt**

Calculator Use in Mathematics Teaching in One State in the USA: A 1990 Status Report

**Robert E. Reys**

Research on Computational Estimation: What It Tells Us and Some Questions that Need to be Addressed

Keiichi Shigematsu

Metacognition: The Role of the Inner Teacher (4):

Contrasts between Japan and the United States

Osamu Maruo

On Almost Subideals of Lie Algebras

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