The purpose of this study was to better understand teacher tensions in professional development. The population under study was practicing mathematics teachers engaged in a week-long professional development institute. Data sources included observations, interviews, and teacher products (such as registration forms, surveys, journals, and…

Most countries in Africa have introduced the use of local languages as the language of learning and teaching for the first few years of schooling. Meaning that for the first few years of learning, learners learn mathematics in their local languages. In response to this, most research has focused on the challenges of using local languages in…

A professional learning program for teachers of junior secondary mathematics regarding the content and pedagogy of senior secondary mathematics is the context for this study of teachers' mathematical and pedagogical knowledge. The analysis of teachers' reflections on their learning explored teachers' understanding of mathematical connections and…

The purpose of this study was to investigate prospective mathematics teachers' knowledge of common conceptions and misconceptions that sixth and seventh grade students had about multiplication of fractions. In addition, prospective teachers' knowledge of the sources of these misconceptions and strategies they knew to overcome these misconceptions…

In this paper, we describe a one-day professional development activity for mathematics teachers that promoted the use of comparison as an instructional tool to develop students' flexibility in algebra. Effective use of comparison in mathematics instruction involves using side-by-side presentation of problems and solution methods and subsequent…

Teacher learning through professional development is a complex process and is not yet well understood. Some features of professional development programs are known to be important, such as a focus on learner needs, design of and reflection on classroom artefacts, and the creation and sustaining of communities of support for teacher professional…

In light of recent reform recommendations, teachers are expected to turn proofs and proving into an ongoing component of their classroom practice. Two questions emerging from this requirement are: Is the mathematical knowledge of high school teachers sufficient to prove various kinds of statements? Does teachers' knowledge allow them to determine…

Several studies have documented prospective teachers' (PSTs) difficulties in offering instructional explanations. However, less is known about PSTs' learning to provide explanations. To address this gap, we trace changes in the explanations offered by a purposeful sample of PSTs before and after a mathematics content/methods course sequence.…

In this article, we report on a study of beliefs about mathematics, teaching, and proof conducted with six prospective secondary mathematics teachers as they completed a two-semester sequence of a content course and a methods course. The initial beliefs of the participants were identified using interview and survey data, and potential shifts in…

In this article, I discuss a case of pre-primary and primary school teacher education concerning place value in number representation. In primary school (in Italy, in grades 1 and 2), the topic is usually introduced by means of manipulatives (for instance, abaci and base ten blocks). But it is well known that no artefact is transparent for…

Recently, there have been increased calls for enhancing preschool children's mathematics knowledge along with increasing calls for preparing preschool teachers to meet the demands of new preschool mathematics curricula. This article describes the professional development program Starting Right: Mathematics in Preschools. Focusing on four episodes…

Lamon ("Teaching fractions and ratios for understanding. Essential content knowledge and instructional strategies for teachers," 2nd edn. Lawrence Erlbaum Associates, Mahwah, 2005) claimed that the development of proportional reasoning relies on various kinds of understanding and thinking processes. The critical components suggested were…

This study investigated the effects of a classroom intervention on prospective elementary teachers' ability to evaluate evidence of student achievement of mathematical learning goals. The intervention was informed by a framework for teacher education which aims to provide prospective teachers (PTs) with the skills needed to systematically learn…

In this article, we describe a framework and instrument for measuring the mathematical quality of mathematics instruction. In describing this framework, we argue for the separation of the "mathematical quality of instruction" (MQI), such as the absence of mathematical errors and the presence of sound mathematical reasoning, from pedagogical…

There is a documented need for more opportunities for teachers to learn about students' mathematical reasoning. This article reports on the experiences of a group of elementary and middle school mathematics teachers who participated as interns in an after-school, classroom-based research project on the development of mathematical ideas involving…