### Editors

Mutsumi Amasaki (Algebra)

Ryo Ikehata (Analysis)

Hideki Iwasaki (Mathematics Education)

Sanpei Kageyama (Statistics)

Masataka Koyama (Mathematics Education)

Osamu Maruo (Algebra)

Tadao Nakahara (Mathematics Education)

Tetsu Shimomura (Analysis)

Masakazu Teragaito (Geometry)

## 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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