Large lecture classes can often be quite impersonal. Creating a teaching team, consisting of the instructor, graduate assistants, and a few undergraduates, is one of the ways the University of Arizona has adopted in order to make the large lecture class more personal. As members of the Department of Mathematics we train the undergraduates, who are…

Generalizing or making claims that extend beyond particular situations is a central mathematical practice and a focus of classroom mathematics instruction. This study examines how aspects of generality are produced through the situated activities of a group of middle school mathematics students working on an 8-week population-modeling project. The…

Mentoring is proposed as an effective strategy for helping novice teachers develop professional knowledge. However, a recent analysis of mentor-novice conversations in the United States about teaching reveals that they may not be important to the development of teachers' reform-minded practice. While this might be the case involving student…

The recent development of powerful new technologies such as dynamic geometry software (DGS) with drag capability has made possible the continuous variation of geometric configurations and allows one to quickly and easily investigate whether particular conjectures are true or not. Because of the inductive nature of the DGS, the…

Two public schools (A and B) from two cities in southern Taiwan were selected to participate in this study. In each school, two sixth grade classes (an experimental and a control class) were studied. Number sense activities were conducted in the experimental classes through process-oriented teaching model to help children develop number sense,…

This study compared how selected mathematics textbooks from Mainland China and the United States at the lower secondary grade level represent various types of problems for classroom teaching and learning. The examination of problems was carried out based on the classifications of problem types established in the study, including routine problems…

This article advances a view of Computer Algebra Systems (CAS) as powerful inquiry-based learning tools. Through an in-depth exploration of the "Emptying the Bowl" activity, upper level mathematics students test their own mathematical hypotheses, thoughtfully analyse and manipulate computer-generated output, and answer questions…

In a previous paper, we showed the importance of using low-level commands of a CAS in order to enhance the students' conceptual insight into mathematics. In this paper, we wish to emphasise a different use of a CAS, which makes possible the exploration of new topics, when the necessary theoretical results have still not been acquired, and avoids…

As part of a module on mathematical problem solving in an Initial Teacher Education programme, the student teachers are encouraged to produce alternative solutions to the problems they tackle and, in particular, to consider whether ICT can help. In this paper we discuss a number of unusual solutions produced for some of the problems, specifically…

The purpose of this descriptive study was to investigate middle school general education mathematics teachers' beliefs and self-perceived knowledge regarding teaching students with learning disabilities (LD) in inclusive classrooms. Teacher beliefs regarding administrative support and higher education teacher preparation were also examined. The…

This study focuses on the nature of preservice elementary school teachers' understandings of several concepts in elementary number theory that are evoked by a computer-based microworld called "Number Worlds". In particular, the focus is on the concepts of factor, multiple and prime number. The notion of "thickness" is examined with respect to…

Three assumptions frame this study (a) preservice teachers who enjoy reading foster positive attitudes towards reading, (b) life-long reading habits are developed during formative years, and (c) these preservice teachers convey reading strategies that encourage success across content strands. This study examines the relationship between literacy…

The Third International Mathematics and Science Study (TIMSS) reports that the mathematics teaching in Japan is distinctly different from that found in the United States. They attribute part of that difference to the professional development practice of Lesson Study. However, is the pre-service preparation of Japanese mathematics teachers also…

The purpose of this paper is to contribute to the debate about how to tackle the issue of "the teacher in the teaching/learning process", and to propose a methodology for analysing the teacher's activity in the classroom, based on concepts used in the fields of the didactics of mathematics as well as in cognitive ergonomics. This…

Students' mastery of and achievement in high school mathematics is considered pivotal to their opportunities for and within postsecondary education. For this reason, many educators have attempted to implement equity-geared reforms, including detracking, that affect the organization and instruction of high school mathematics. This article describes…