The goal of this paper is twofold. First, the paper clarifies and elaborates on an important theoretical construct called orientation with respect to understanding in mathematics, which denotes the degree to which students exhibit an inclination towards and demonstrate an earnest concern for understanding in mathematical learning. Second, the…

This paper presents a research framework for investigating the role of language use in mathematics learning. The paper draws on the wider M[superscript 2]EID study, which explores whether differences in languages (English and Irish) and their use by bilingual mathematical students have a differential impact on their mathematics meta-level…

This paper reports on the novel use of classroom videos by 71 pre-service teachers enrolled in a one-year graduate diploma pre-service teacher education program across three Australian universities. The classroom videos were of an experienced teacher delivering a Year-6 mathematics lesson. Students observed, discussed and debated practices that…

In this study, we considered how middle school teachers understood the relationship between fractions and ratios. We used two instruments to collect data from 11 teachers and relied on Knowledge in Pieces as a lens for considering understandings teachers have and how coherent those understandings are. From our analysis, we developed three main…

This article is a report on the findings of three case studies that focused on elementary teachers' in-the-moment noticing across a month of instruction. Extending Jacobs and her colleagues' framework (Jacobs, Lamb, and Philipp, 2010), this articles categorizes the mediums (i.e., written accounts, verbal interactions, physical strategies) by which…

The authors present an analysis of facilitation across three cohorts of a phase-two professional development project. Four types of discourse are introduced and defined (correcting, eliciting, probing, and responsive). The analysis attends to implementation fidelity and facilitator moves in light of these four types of discourse. Conjectures about…

Existing research from Western countries has consistently shown that the learning environment is an important factor for academic motivation. Self-determination theory, which serves as a theoretical foundation of the present study, suggests that teachers' involvement is an important element of students' learning, regardless of the cultural…

The article reports and discusses a long-term qualitative study of forty 8-10-year-old students who regularly played a math game during math lessons for 9 weeks. The goal was to explore the relations between (i) some of the "pedagogical principles" that underlie the game and (ii) the "playing practice" in terms of what actually takes place when…

The World Bank 2007 TIMSS Video Study provided a distinctive insight into the practices of the Indonesian classroom and identified key strengths and weaknesses of current teaching. This investigation considered this evidence in the development of a structured lesson design that specifically addressed the instructional practices of the teaching and…

This study compared interaction with a computer vs. observation as learning situations for low and high ability student's learning of spatial visualization and geometric transformations. Thirty-two fifth grade boys took the Differential Aptitude Test, Space Relations Subset (DAT), and then participated in the experiment. Pre-test and post-test…