The subject of the paper presents establishing basic characteristics, forms and levels of knowledge interconnectedness in teaching, especially in mathematics and biology teaching. The analysis was realized by considering basic theoretical views in this field, as well as by establishing features and levels of knowledge interconnectedness in the…

Equivalence of algebraic expressions is at the heart of transformational work in algebra. However, we know very little about students' understanding of equivalence. This study is part of a larger project that explores the use of CAS as a didactical tool for promoting both technical and conceptual growth in high school algebra with tasks specially…

Two-year longitudinal case studies of 16 Sydney children extended a study of 103 first graders' use of structure across a range of mathematical tasks. We describe how individual's representations change through five stages of structural development. Children at the pre-structural stage showed inconsistent development presenting disorganised…

This paper describes prospective secondary school mathematics teachers' images and definitions of inflection points. The data indicate that prospective teachers tended to regard f[prime](x)=0 and/or the location "where the graph bends" as necessary/sufficient conditions for inflection points. The solutions were based on previous…

In contrast to the traditional top-down approach, a bottom-up approach is proposed by current reform in mathematics education. According to this alternative proposal, algorithmizing is the activity in which students should be involved. What can we do when we want to enact such an algorithmizing approach in a classroom and our students have already…

Promoting ACademic Excellence in Mathematics and Science for Workers of the 21st Century (PACE) was a consortium project made up of Indiana University Northwest, the Gary Community Schools, and the Merrillville Community Schools. The focus of this project was to prepare teachers and curricula for Tech Prep mathematics and science courses for the…

In this study, we examined 139 prospective elementary teachers' solution processes to additive word problems for which the solution is 1 more or 1 less than the answer produced by the straightforward application of the addition or subtraction of the two given numbers. For each problem, five aspects of their solution processes were examined: (a)…

The research described in this paper was undertaken to determine student-teachers' understanding of infinity in a geometrical context. The methods of analysis of students' responses is presented and these were found to be universally applicable. The findings show that school mathematics does not generally develop the students' ideas of infinity…

In this paper, we discuss issues in planning and conducting research into mathematics learning. We emphasize two central themes: (1) the learners' mathematics (especially the issues and ideas, in given problem situations, that learners choose to think about and to present; and (2) the kinds of knowledge that learners may be building (including…

The Purposeful Algebraic Activity Project is a longitudinal study of the development of pupils' algebraic activity in the early years of their secondary schooling. Here, we report on our empirical findings from the initial semi-structured interviews. We analyse the responses of three pairs of 12-year-old pupils to a range of algebra questions. In…

Astro Algebra is one of six titles in the Mighty Math Series from Edmark, a comprehensive line of math software for students from kindergarten through ninth grade. Many of the activities in Astro Algebra contain a unique technology that uses the computer to help students make the connection between concrete and abstract mathematics. This software…

The National Council of Teachers of Mathematics (NCTM) has published three documents that propose standards related to mathematics education called "The Curriculum and Evaluation Standards for School Mathematics" (1989), "The Professional Standards for Teaching Mathematics" (1991), and "The Assessment Standards for School Mathematics" (1995). The…

The "call for change" issued by the Board of Governors of the Mathematical Association of America (MAA) in "A Call For Change: Recommendations for the Mathematical Preparation of Teachers of Mathematics, 1991" may appear at first glance to concern only the mathematical preparation of teachers. However, two ingredients combine…

The first volume of the proceedings of the 21st annual meeting of the International Group for the Psychology of Mathematics Education contains the following 13 full papers: (1) "Some Psychological Issues in the Assessment of Mathematical Performance" (O. Bjorkqvist); (2) "Neuromagnetic Approach in Cognitive Neuroscience" (S.…

The second volume of the proceedings of 21st annual meeting of the International Group for the Psychology of Mathematics Education contains the following papers: (1) "The Dilemma of Transparency: Seeing and Seeing through Talk in the Mathematics Classroom" (J. Adler); (2) "Abstraction is Hard in Computer-Science Too" (D.…