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

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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

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

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

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

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

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

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

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

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

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