A gulf exists between prior work testing metacognitive instructional interventions and teacher practices that may support metacognition in the classroom. To help bridge this gulf, we designed an observational protocol to capture whether and how teachers provide metacognitive support in their talk and examined whether these supports were related to…

Although reasoning and proof in learning and teaching mathematics is crucial and have gained more presence in school mathematics, both students and their teachers face great difficulties when engaging in proving activities. One potential cause for such difficulties might be due to teachers' conception of proof. However, to date, there are few, if…

Mathematics Teacher Preparation Programs increasingly include a focus on the use of technology for teaching school mathematics. A key feature in this approach to prepare teachers to teach mathematics with technology is to integrally develop teachers' TPSM. Teachers need to understand that critical instructional decisions they make are grounded in…

This study, firstly, aimed at investigating the various types of the multiple math representations and transitions among them in the 8th grade math textbook, and secondly, teachers' use of these representations in teaching. The current study employed the content analysis approach to investigate the multiple mathematical representations and…

U.S. mathematics teachers face considerable pressures to keep up with pacing guides and to prepare students for standardized tests. At the same time, they are called upon to engage students in innovative exploratory activities and to incorporate new technologies into their lessons. These competing priorities pose considerable challenges. Against…

The aim of this research was to explore 11 to 12-year-old children's understanding of the mass of objects made from different materials, and the measurement of this attribute. In depth task-based interviews were conducted with six children attending six different schools; five were in Year 6 and one in Year 7. The children were found to hold…

This paper introduces the Affording Understanding Conceptual Framework as a way for mathematics teacher educators to analyze student 's perceptions of a digital math tool 's helpfulness (e.g., GeoGebra) versus the instructor's perceptions when seeking insights into how a lesson design could be improved. An example of this action research process…

The study was carried out with prospective teachers (PTs) in Primary School Teaching Program in a private university (n=43) and Middle School Mathematics Teaching program in a public university (n=46). In this paper, multiple-case study was adopted to explore PTs' opinions and to reveal the differences between two universities in terms of taking a…

The extent to which the targeted outcomes in education are achieved can be determined by the educational assessment process. Although various alternative ways of assessment have arisen in recent decades, written examinations are still widely used by teachers. This study aims to determine the quality of the questions used by middle school…

How should schools assign students to more rigorous math courses so as best to help their academic outcomes? We identify several hundred California middle schools that used 7th-grade test scores to place students into 8th-grade algebra courses and use a regression discontinuity design to estimate average impacts and heterogeneity across schools.…

To address the problem of low achieving math students, a cross-age math tutoring intervention paired middle school tutors with kindergarten and first grade students with low math skills. This instrumental group case study explored the effects of the intervention on the math skills of the students through teacher interviews and the testing program…

This paper reports on the characterization of the inductive reasoning used by middle school mathematics teachers to solve a task of generalization of a quadratic pattern. The data was collected from individual interviews and the written answers to the generalization task. The analysis was based on the representations and justifications used to…

Middle school is a critical time when students begin formal study of functional relationships in algebra. However, many students struggle in understanding functions as relationships between quantities that change according to a dependency relationship. We report on the influence of Scaling Continuous Covariation in fostering productive ideas about…

This study aimed to explore how prospective middle school mathematics teachers think critically about a newspaper article that reported the findings of a statistical research. Participants of the study were four fourth-year students enrolled at the mathematics teacher education program of a public university. To investigate the research question…

Problem solving is an important aspect of the mathematics classroom and teachers should work to promote problem solving in their classrooms. The purpose of this explanatory mixed-methods study was to examine mathematics preservice teachers' (PSTs) problem-solving performance and connect it with their K-12 and tertiary education problem-solving…