Motivated by the observation that formal logic answers questions students have not yet asked, we conducted exploratory teaching experiments with undergraduate students intended to guide their reinvention of truth-functional definitions for basic logical connectives. We intend to reframe the relationship between reasoning and logic by showing how…

How does classroom interaction support students' apprenticeship into the ways of speaking, writing, and diagramming that constitute the practice of mathematics? We address this problem through an interpretative analysis of a whole-group conversation about alternative ways of solving a problem involving percent discounts that occurred in a sixth…

The purpose of this study was to examine the sources that pre-service teachers (PSTs) use when they construct their self-efficacy beliefs and learning goals, which compose their motivational profiles. Pre-service elementary teachers (n = 22) with different motivational profiles participated in narrative interviews designed to examine…

We study in this article mathematics teachers' "documentation work": looking for resources, selecting/designing mathematical tasks, planning their succession, managing available artifacts, etc. We consider that this documentation work is at the core of teachers' professional activity and professional development. We introduce a distinction between…

This empirical paper considers the different purposes for which teachers use examples in elementary mathematics teaching, and how well the actual examples used fit these intended purposes. For this study, 24 mathematics lessons taught by prospective elementary school teachers were videotaped. In the spirit of grounded theory, the purpose of the…

This paper discusses variation in reasoning strategies among expert mathematicians, with a particular focus on the degree to which they use examples to reason about general conjectures. We first discuss literature on the use of examples in understanding and reasoning about abstract mathematics, relating this to a conceptualisation of syntactic and…

The main goal of the study reported in our paper is to characterize teachers' choice of examples in and for the mathematics classroom. Our data is based on 54 lesson observations of five different teachers. Altogether 15 groups of students were observed, three seventh grade, six eighth grade, and six ninth grade classes. The classes varied…

From preliminary analysis of teacher-nominated examples of successful technology-supported practice in secondary-school mathematics, the use of graphing software to teach about algebraic forms was identified as being an important archetype. Employing evidence from lesson observation and teacher interview, such practice was investigated in greater…

Technology is available and accessible in many mathematics classrooms. Adopting technology to support teaching and learning requires teachers to change their teaching practices. This paper reports the responses of a diverse cohort of 92 secondary mathematics teachers who chose to respond to an Australian state-wide survey (Mathematics with…

This paper reviews the present state, recent trends, and prospective lines of development concerning applied problem solving, modeling, and their respective applications. Four major trends are scrutinized with respect to curriculum inclusion: a widened spectrum of arguments, an increased universality, an increased consolidation, and an extended…

Provided is an overview and analysis of recent progress in applying electronic information technology to creation of new environments for intellectual work in mathematics. Describes the impact of numerical computation, graphic computation, symbolic computation, multiple representation of information, programing and information, and artificial…

Described is an article that describes an adaptive computer tutor for arithmetic entitled "Shopping on Mars." The purpose of the tutor is to help children develop an extensive repertoire of information techniques for performing arithmetic in everyday situations and to learn to formulate shortcuts in problem solving. Results of…

Presents computer approach formulated within a framework of versatile thinking designed to overcome obstacles to understanding algebra. Results from related studies comparing the computer and traditional approaches taught to 11, 12, and 13 year olds showed that the computer approach significantly improved the understanding of higher order concepts…

This paper is an attempt at clarifying the concept of "problem," in order to improve the teaching of problem solving. Four categories are employed in the analysis: formulation, context, solutions, and methods of approach. Examples are included. (MNS)

Results obtained when a procedure for assessing the questions on uniersity mathematics examinations to see what skills were needed for their solution are given for a sample of 1400 questions set during 1976 in 10 British universities. The method is a way of focusing rational argument. (MNS)