The author outlines seven types of learning and teaching, and briefly discusses related literature on learning theories. He provides examples, and discusses teaching hierarchies. (SD)

Tasks in which students were asked to write sentences concerning the relationships between pairs of probability concepts are presented and discussed. Methods for using writing tasks in the mathematics classroom are suggested. (DT)

Four measurement activities concerned with mass and one activity dealing with the relation between mass and weight are presented in worksheet form for students. A self-check module is included. (DT)

Advantages of using flow charts are listed. Flow charts for adding and subtracting fractions and for polynomial division are provided. Rules for constructing flow charts are given. (DT)

Drawing floor plans for an apartment is used as the basis for giving students practice in applying the concepts of ratio, fractions, and scale. (DT)

The paper reports on a case study from a teaching experiment on the construction of meaning of integral at secondary school level, starting from the cognitive root of area. In the considered activity, students are faced with some graphs of functions and are asked to work in group to trace the corresponding integral functions. The analysis…

The Purposeful Algebraic Activity project aims to explore the potential of spreadsheets in the introduction to algebra and algebraic thinking. We discuss two sub-themes within the project: tracing the development of pupils' construction of meaning for variable from arithmetic-based activity, through use of spreadsheets, and into formal algebra,…

The Purposeful Algebraic Activity Project is a longitudinal study of the development of pupils' algebraic activity in the early years of their secondary schooling. Analysis of data from a spreadsheet-based teaching programme and from semi-structured interviews leads us to identify three features of the spreadsheet environment that appear to shape…

This paper reports on one aspect of a larger study and comprises an analysis of the beliefs concerning mathematics, its teaching and its learning, and the classroom practice of one secondary mathematics teacher. It focuses on the question, "What specific teacher beliefs about students are relevant to teachers' classroom practice in various…

The strengths and weaknesses of using ethnographic research to investigate equity in a study of a grade 9 class that used a dynamic geometry program with laptop computers will be presented. It will be argued that research approaches that involve "windows on practice" provide understanding of not only who is advantaged and disadvantaged in…

This paper will discuss some findings from a study investigating the development of the proving process in a dynamic geometry environment. Through a detailed analysis of students' processes when working with open geometry problems involving conjecturing and proving in Cabri, an analytical and explanatory framework has been developed. This paper…

Handheld devices, most familiar to educators today in the form of graphing calculators, are rapidly improving their interface, computational, and communication capabilities. Communication capabilities allow participants to rapidly share mathematical objects among their handhelds, potentially contributing to improved classroom discourse. We have…

We present results from a study which investigated the influence of dynamic geometry-based activities in the development of proving skills (in geometry) in high-school students (15-16 years of age). After a 12-week course on Cabri and the writing of conjectures and proofs, students were asked to write and prove conjectures based on their…

Results of a study involving pre-constructed, web-based, dynamic geometry sketches in activities at the secondary school level revealed that the provision of accurate images is an issue. Many students do not automatically understand that an on-screen image is accurate. Others inadvertently create a special case by dragging, then generalise from…

This publication compares first-generation students (i.e., those whose parents have no more than a high school education) with their peers whose parent or parents attended college. It focuses on mathematics course taking--the effectiveness of taking algebra in 8th grade and advanced math courses in high school for subsequent college…