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Gallardo, Aurora – International Group for the Psychology of Mathematics Education, 2003

A Case Study is presented in this article, where there is a contradiction between pre-algebraic language semantic and syntax used to solve word problems through a negative integers subtraction. Appendix includes answer key. (Contains 1 figure.) [For complete proceedings, see ED500859.]

Descriptors: Semantics, Syntax, Word Problems (Mathematics), Subtraction

Davis, Sarah – International Group for the Psychology of Mathematics Education, 2003

This paper explores the benefits of the design elements of public anonymity and private accountability in classroom Knowledge Sharing Systems (KSS). The major findings of this study indicate that classroom KSS have the potential to allow for greater equity of input, reduce academic anxiety, increase teachers knowledge of student understanding …

Descriptors: Student Participation, Accountability, Internet, Learning Strategies

Cortes, Anibal – International Group for the Psychology of Mathematics Education, 2003

We studied experts' solving methods and analyzed the nature of mathematical knowledge as well as their efficiency in algebraic calculations. We constructed a model of the experts cognitive functioning (notably teachers) in which the observed automatisms were modeled in terms of schemes and instruments. Mathematical justification of transformation…

Descriptors: Mathematics Education, Mathematics Instruction, Algebra, Problem Solving

Cerulli, Michele; Mariotti, Maria Alessandra – International Group for the Psychology of Mathematics Education, 2003

In the framework of a long term teaching experiment we present an Educational approach based on the use of a dynamic geometry software and a symbolic manipulator. Here we present the general ideas of the followed approach focusing on how meanings can originate from phenomenological experience and evolve under the guidance of the teacher. In…

Descriptors: Geometry, Teaching Methods, Experiments, Grade 9

Ferrara, Francesca – International Group for the Psychology of Mathematics Education, 2003

The paper considers a teaching experiment carried out with secondary school students (9th grade), who face modelling tasks to approach some basic concepts of algebra and early calculus. The focus is on an embodied analysis of students' cognitive processes. The analysis highlights the use of metaphors as a means of sharing knowledge. (Contains 2…

Descriptors: Grade 9, Cognitive Processes, Calculus, Discovery Processes

Douek, Nadia; Pichat, Michel – International Group for the Psychology of Mathematics Education, 2003

The aim of this paper is to elaborate on (and provide some experimental evidence for) the following hypothesis: during the first grade students' approach to writing texts, an appropriate educational setting (based on both social interaction managed by the teacher and students' involvement in well chosen concrete experiences) can give them the…

Descriptors: Persuasive Discourse, Interpersonal Relationship, Interaction, Grade 1

Giraldo, Victor; Carvalho, Luiz Mariano; Tall, David – International Group for the Psychology of Mathematics Education, 2003

In this paper, we discuss the (potentially positive) pedagogical role of intrinsic limitations of computational descriptions for mathematical concepts, with special focus on the concept of derivative. Our claim is that, in a suitable approach, those limitations can act for the enrichment of learners' concept images. We report a case study with a…

Descriptors: Undergraduate Students, Foreign Countries, Educational Technology, Mathematical Concepts

Ainley Janet; Wilson, Kirsty; Bills, Liz – International Group for the Psychology of Mathematics Education, 2003

The Purposeful Algebraic Activity Project is concerned with the development of algebraic activity in pupils in the early years of secondary schooling. Here we report on the different ways in which we have observed children articulating generalisations during semi-structured interviews which are being used to gain snap-shots of this development. We…

Descriptors: Computation, Algebra, Secondary School Mathematics, Secondary School Students

Ambrose, Rebecca; Philipp, Randolph; Chauvot, Jennifer; Clement, Lisa – International Group for the Psychology of Mathematics Education, 2003

Because of the importance of beliefs, mathematics educators need to consider ways to assess beliefs and belief change. Beliefs, because they must be inferred, can be difficult to measure, particularly with a common metric that enables one to compare individuals. Some limitations of Likert scales are identified and overcome in a newly developed…

Descriptors: Mathematics Education, Likert Scales, Elementary School Teachers, Student Teacher Attitudes

Antonini, Samuele – International Group for the Psychology of Mathematics Education, 2003

Researches in Mathematics Education about proof by contradiction revealed some difficulties of the students but also that this kind of argumentation comes spontaneously in certain situations. In this paper we shall show some processes that might lead the student to produce a proof by contradiction. In particular, we shall point out a deep link…

Descriptors: Mathematics Education, Persuasive Discourse, Mathematical Concepts, Mathematical Logic

Battista, Michael T. – International Group for the Psychology of Mathematics Education, 2003

Because cognition is the core substance of understanding and sense making, cognition-based assessment is essential for understanding and monitoring students' development of powerful mathematical thinking. The Cognition-Based Assessment System (CBAS) project is applying the results, theories, and methods of modern research in mathematics education…

Descriptors: Elementary School Mathematics, Mathematics Education, Mathematical Logic, Elementary School Students

Bills, Liz; Ainley, Janet; Wilson, Kirsty – International Group for the Psychology of Mathematics Education, 2003

The teaching and learning of early algebra draw heavily on arithmetic and the relationship between these two forms of activity is much debated. Drawing on interviews with 12 year old pupils we consider the ways in which some pupils used substitution of numbers for letters to extend their ability to manipulate algebraic expressions. We argue that…

Descriptors: Teaching Methods, Secondary School Students, Algebra, Symbols (Mathematics)

Berenson, Sarah B.; Nason, Rod – International Group for the Psychology of Mathematics Education, 2003

This study posits that instructional representations are viable assessment tools of subject matter knowledge within the context of lesson study. Evidence is provided and validated, suggesting that representations provide valuable insights into the depth and accuracy of the knowledge prospective teachers bring to instructional settings. It is…

Descriptors: Mathematics Instruction, Preservice Teacher Education, Mathematical Concepts, Evaluation Methods

Blanton, Maria L.; Stylianou, Despina A.; David, Maria Manuela – International Group for the Psychology of Mathematics Education, 2003

This paper explores the role of instructional scaffolding in the development of undergraduate students' understanding of mathematical proof during a one-year discrete mathematics course. We describe here the framework adapted for the analysis of whole-class discussion and examine how the teacher scaffolded students' thinking. Results suggest that…

Descriptors: Undergraduate Students, Mathematics Education, Mathematical Logic, Discussion (Teaching Technique)

Brown, Catherine A.; Koc, Yusuf – International Group for the Psychology of Mathematics Education, 2003

The purpose of this study is to examine how the diverse members of the mathematics education community (in-service secondary mathematics teachers, in-service secondary mathematics teachers, university mathematicians and university mathematics educators) talk about a multimedia case study on mathematics teaching and learning when they interact both…

Descriptors: Mathematics Education, Mathematics Teachers, Computer Mediated Communication, Case Studies