Abstract algebra courses tend to take one of two pedagogical routes: from examples of mathematics structures through definitions to general theorems, or directly from definitions to general theorems. The former route seems to be based on the implicit pedagogical intention that students will use their understanding of particular examples of an…

Recent research suggests that the examination of students' work may lead to changes in teaching practice that are more effective in terms of students' mathematical learning. However, the link between the examination of students' work and the teachers' actions in the classroom is largely unexamined, particularly at the secondary level. In this…

In recent years, the mathematics achievement of Peruvian students has been evaluated in three national and two international studies. The results in all cases suggest very poor learning. A similar situation is found in many developing countries. In this study, we analyzed the opportunities to learn (OTL) mathematics of sixth grade students from…

In this article we analyze the dialogic learning of one pair of students in order to investigate how these students cope with a collaborative learning situation in the classroom. Our aim is to substantiate the claims that not only are young students (8 year olds) capable of solving mathematical problems collaboratively, but that they also take an…

A perceived lack of engagement of many students in middle years mathematics classes provides a challenge for educators. In this article we report a project that investigated students' perceptions of the extent to which their own efforts influence their achievement at mathematics and their life opportunities. We conducted 2 hour interviews with…

Research in mathematics education usually attempts to look into students' learning and other mental processes. It could therefore be expected to build on knowledge acquired within the academic discipline of cognitive psychology. Our aim in this paper is to show how some recent developments in cognitive psychology can help interpret empirical…

This study reports on how students can be led to make meaningful connections between such structures on a set as a partition, the set of equivalence classes determined by an equivalence relation and the fiber structure of a function on that set (i.e., the set of preimages of all sets {b} for b in the range of the function). In this paper, I first…

Using Freudenthal's method of historical phenomenology, the history of statistics was investigated as a source of inspiration for instructional design. Based on systematically selected historical examples, hypotheses were formulated about how students could be supported in learning to reason with particular statistical concepts and graphs. Such a…

This paper examines the change in young children's understanding of "equal", "more", "less", and "between", words commonly used in equivalent and non-equivalent situations, over a 3-year period. Seventy-six children participated in the longitudinal study. Each year they were asked to share their understanding of these four words. Past research has…

Sfard and Kieran [Kieran, C., Educational Studies in Mathematics 46, 2001, 187-228; Sfard, A., Educational Studies in Mathematics 46, 2001, 13-57; Sfard, A. and Kieran, C., Mind, Culture, and Activity 8, 2001, 42-76] have developed a methodological framework, which aims at characterizing the students' mathematical discourses while they are working…

How do teachers conceptualize and deal with context of mathematics word problems in their teaching? This question is discussed based on a study of 14 experienced teachers at the elementary, junior high and senior high school levels. Bruner's notions of paradigmatic and narrative modes of knowing formed the basis of analysis of data from sources…

The framework for this paper is a recently developed theory of abstraction in context. The paper reports on data collected from one student working on tasks concerned with absolute value functions. It examines the relationship between mathematical constructions and abstractions. It argues that an abstraction is a consolidated construction that can…

The main focus of this paper is on the study of students' conceptual understanding of two major concepts of Set Theory--the concepts of inclusion and belonging. To do so, we analyze two experimental classroom episodes. Our analysis rests on the theoretical idea that, from an ontogenetic viewpoint, the cognitive activity of representation of…

This paper focuses on the kinds of notations young children make for fractional numbers. The extant literature in the area of fractional numbers acknowledges children's difficulties in conceptualizing fractional numbers. Some of the research suggests possibly delaying an introduction to conventional notations for algorithms and fractions until…

This study investigates how four prospective teachers interpret and use textbooks while learning to teach mathematics during university coursework and practicum teaching. Results indicate that prospective teachers had varied approaches to using textbooks ranging from adherence, elaboration, and creation. Factors influencing how they engaged with…