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…

This paper (1) presents a conceptual framework for analyzing the mathematics addressed in probability lessons and (2) uses the framework to compare the mathematics that two teachers with contrasting teaching approaches addressed in class when teaching the topic of probability. One teaching approach aimed to develop understanding; the other…

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 study brings together two lines of research on teachers' affective responses toward mathematics curriculum reforms: their concerns and their efficacy beliefs. Using structural equation modeling to analyze data on 151 elementary mathematics teachers' concerns and efficacy beliefs 5 years into a mandated curriculum reform on problem solving,…

This study investigated mathematics teachers' professional knowledge among elementary school teachers exposed to a professional training program that either supported self-regulated learning (SRL) or offered no SRL support (no-SRL). The SRL support was based on the IMPROVE metacognitive self-questioning method that directs students' attention to…

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…

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…

There is an increasing awareness of the social dimension in mathematics teacher education. Collaboration and co-operation are regarded as key factors in professional development. In this paper I will analyse some tensions that might arise when the professional development of mathematics teachers is considered a collective enterprise. I will…

Identifies key questions concerning children's intuitions and conceptions of probabilistic notions. Research on the theoretical framework for probability studies, misconceptions and strategies, and pupil attainment is reviewed, and the methodology is evaluated. Finally, implications for classroom practice are discussed. (MNS)

Two teaching studies were conducted, based on a descriptive framework and diagnostic interviews described previously. In the pilot study, low-achieving students were taught individually; in the main study, they were taught in a group. Performance improved in both cases. (MNS)

Ideas on a teaching-learning theory of ratio are presented. Views of children and of members of an international panel are presented, and five questions and their responses are compared with real classroom experience. (MNS)

Discusses the educational value of engaging mathematics students in writing a journal. Provides a table showing the relationship between writing topics and the potential benefits. (Author/YP)

Developed is a working definition of the concept of preformal proof through the analyses of an action proof, a geometric-intuitive proof, and a reality-oriented proof of a differential equation. Instructional problems for teachers and learners in connection with preformal proofs are pointed out. (MDH)