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…

Communicating mathematical ideas through writing, listening, and verbalizing allows students to think about how they "think" about mathematics. By focusing this communication on a reflection of how one thinks about mathematics, metacognitive writing engages students as mathematicians and learners. In this article we describe a…

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…

There is a large body of research that suggests a sound understanding of rational number is vital for success in all areas of mathematics, at school and beyond. In the Australian Curriculum, fractions are formally introduced from Year 1, yet there is evidence to suggest that current approaches are not leading to deep understanding in later years.…

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…

The aim of this article is to inspire more teachers to explore the use of codable robots for teaching mathematics. The authors begin by discussing four benefits experienced by incorporating robots into middle school mathematics classes: (1) reasonable time frames; (2) authentic purposes for mathematics; (3) visual and nonevaluative feedback; and…

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…

Teachers put a great deal of energy into searching for ways to engage each and every student. Some of these efforts fail. Others look promising one day, only to become less effective as the novelty wears off. Teachers want their students to feel ownership of their learning. They also believes that students engage more when learning mathematics…

This article explores facilitating meaningful mathematics discourse, one of the research-based practices described in "Principles to Actions: Ensuring Mathematical Success for All." Two tools that can support teachers in strengthening their classroom discourse are discussed in this, another installment in the series.