Examining critical incidents in the mathematics classroom is a useful way for pre-service teachers to understand the experience of teaching. This paper examines the development and trialling of variations of a novel affect-based critical moment protocol that enables preservice mathematics teachers to reflect on their teaching performance. The…

Mathematics in Australia specifies spatial reasoning as a general capability within the curriculum. However, psychological research to date limits spatial assessment to psychometric tests leaving little room for a well-defined spatial curriculum. Although there are clear relationships between mathematics and spatial thinking, the independence in…

In this paper we introduce the term "task science" to encompass the range of activities involved in designing tasks for school mathematics. We argue that task science is enriched by the participation of teachers, but more particularly that participating in task science is a powerful form of professional learning. We describe the role and…

The purpose of the study was to investigate "what students' work and explanation of their work would show about their development of structure sense and their algebraic proficiency after receiving structure-sense teaching for eight weeks in a community college precalculus algebra course." Structure sense is a group of abilities formally…

Research Findings: We evaluated the score stability of the Mathematical Quality of Instruction (MQI), an observational measure of mathematics instruction. Three raters each scored, independently, 100 video-recorded lessons taught by 20 kindergarten teachers in the spring. Using generalizability theory analyses, we decomposed the MQI's score…

Students often express frustrations and negative feelings about math (Ruffins, 2007). The purpose of this chapter was to describe several writing activities that can be used during math instruction to help students gain a greater understanding of mathematical concepts. By doing so, students will recognize how math is all around them, and they will…

This paper presents an example of how paper folding can be used in a geometry class to support conceptual understanding. Specifically, it explains an activity that constructs a rhombus and explores its attributes by using paper folding. The steps of constructing a rhombus are described and some discussion questions are given to consolidate…

A number of probabilistic experiments are described to estimate e, p and v2, with results from computer simulations being used to investigate convergence. A number of possible classroom exercises and extensions are presented.

Mathematics is often positioned as being difficult for Ghanaian teachers to teach and pupils to learn. Although literature point to the educational and scientific relevance of many of the socio-cultural practices in the Ghanaian society, many mathematical concepts are taught out of context in schools. In this paper I will draw on Bishop's (1988)…

This article describes how Charles Lovitt found a classroom activity in a resource book and by peering through a pedagogy lens, enhanced, tweaked, adapted, and extended the idea into a richer, healthier, well balanced classroom lesson. The task described in the article is often presented to students as a flash card for a limited time with the…

For over 50 years, the learning of teaching of "a priori" bounds on solutions to linear differential equations has involved a Euclidean approach to measuring the size of a solution. While the Euclidean approach to "a priori" bounds on solutions is somewhat manageable in the learning and teaching of the proofs involving…

Early experiences of reasoning while playing games of strategy are foundational for future proofs that students will be expected to build using conventionally structured arguments. But how did game playing in school occur? How can educators be sure that mathematical reasoning is going on? The authors investigated these questions to understand how…

This article provides examples of teachable moments that are based on mathematical teaching episodes that the authors have either taught or observed, followed by discussions on how teachers might respond to these moments. It is hoped that this article may act as a stimulus for collaborative professional conversations as to whether or not teachable…

The Harry Potter series is a favorite for out-of-school reading and has been used in school, largely as an object of study in language arts. Using a content analysis to highlight the ways in which J.K. Rowling's work could be used to teach higher dimensionality in math, the authors argues that the content is sufficient in such books to engage the…

This story is a playful retelling of ideas related to infinity. Presented as a historical fiction, the story reflects the thinking of research participants who addressed the ping pong ball conundrum, and where indicated, the individuals who contributed to modern formal understandings of infinity. This story offers a way of engaging with questions,…