It is a challenge for mathematics teachers to provide activities for their students at a high level of cognitive demand. In this article, we explore the possibilities that history of mathematics has to offer to meet this challenge. History of mathematics can be applied in mathematics education in different ways. We offer a framework for describing…

Affective and cognitive processes may be jointly researched to better understand mathematics learning, paying special interest to emotions related to knowledge acquisition. However, it remains necessary to explore these processes in studies linked to the education of pre-service mathematics teachers. This study aims to characterize epistemic…

In this qualitative study, we investigated teachers' use of proportional knowledge resources while being asked to appropriately identify if a given situation was proportional or not using clinical interview data from a large grant funded project. We found that knowledge resources related to the mathematical structure of the situation were most…

Due to the nature of the teaching environment, students may often develop perceptions of their lecturers' ability as mathematicians, based on the pre-prepared and well-rehearsed content they present. In reality, performing mathematical calculations and solving problems is a difficult skill, and students may compare their own experiences…

The purpose of this study was to determine if the MathTwitterBlogosphere (MTBoS), an online community of practice, provides opportunities for mathematics educators to learn about the knowledge and conceptions that support the effective use of cognitively demanding tasks, including mathematical knowledge for teaching, visions of high-quality…

The study investigated preschool teachers' pedagogical content knowledge (PCK) in mathematics. The construct of PCK for teaching mathematics in preschool involves three components: (1) noticing mathematical situations in which children engage; (2) interpreting the nature of children's math activity; and (3) enhancing children's mathematical…

This study explores the relationship between participating in a graduate course aimed at enhancing teachers' theoretical and practical knowledge of mathematical creativity and one teacher's changing perspectives regarding mathematical creativity and tasks that may occasion mathematical creativity. Results indicated that perceptions of…

The purpose of this study was to determine if and how engagement with an online community supports the development of three attributes identified by Wilhelm (2014) that teachers need to have in order to consistently select and implement cognitively demanding tasks, including mathematical knowledge for teaching, visions of high quality mathematics…

This article presents a form of teacher reasoning that we call "proclivities for teaching mathematics." We define proclivities for teaching mathematics as the beliefs, knowledge, and dispositions that are actionable in the flow of instruction, and we argue that growth in this area contributes to positive change in mathematics…

This study is based on a Task Design and Analysis activity from a year-long professional development program. The activity was designed to increase teacher growth in several areas, including knowledge of mathematics, understanding of students' cognitive activity, knowledge of good questions, and ability to develop and improve high quality tasks.…

In this paper, we present an emerging set of learning conjectures and design principles to be used in the development of professional learning tasks that support elementary teachers' learning of mathematics learning trajectories. We outline our theoretical perspective on teacher knowledge of learning trajectories, review the literature concerning…

The development of statistical literacy is fast becoming the focus of a large part of mathematics instruction at primary, secondary and tertiary levels. This broadening of the mathematics curriculum to encompass a focus on statistics makes considerable demands on teachers. Most mathematics teachers acknowledge the practical importance of…

This study of six teachers focuses on the ways they organized the classroom discourse, attended to student thinking, and adapted complex tasks from a Standard-based middle school curriculum. The study explores Cohen's (2011) premise that the knowledge teachers develop is related to their attentiveness to student teaching. This study explores the…

Although teachers' knowledge is thought to contribute to the selection and implementation of mathematical tasks, empirical evidence supporting this claim is scarce. To investigate this relationship and understand its nature, this exploratory study examines the unfolding of tasks in a series of lessons led by 2 elementary school teachers who…

The plethora of data that confronts teachers on a daily basis requires that they know more than simply being able to calculate. It demands that they understand the context in which the mathematical ideas are embedded and what those ideas are telling them in relation to that context. Also, it necessitates that they are prepared to question how…