Many teachers labor to distinguish between productive and unproductive struggle; they believe that struggle is productive when it engages students in thinking and communicating metacognitively, which is when students think and communicate about their problem-solving processes, strategies, challenges, and successes. One method that helps ensure…

Students in the elementary grades often experience difficulty setting up and solving word problems. Using an equation to represent the structure of the problem serves as an effective tool for solving word problems, but students may require specific pre-algebraic reasoning instruction about the equal sign as a relational symbol to set up and solve…

This article details the adaptation of the FOCUS (Fundamentals of Conceptual Understanding and Success) model (Mireles, Acee, & Gerber, 2014) implemented to improve student success in general education and developmental mathematics at a four-year rural university. The model has been demonstrated successful when implemented at a four-year large…

We present the results of a research project on arithmetic-algebraic thinking that was carried out jointly by a team in Mexico and another in Quebec. The project deals with the concepts of variable and covariation between variables in the sixth grade at the elementary level and the first, second, and third years of secondary school--namely,…

This paper reports on a study designed to investigate preservice teachers' understanding of factorisation, a topic not explicitly taught within their teacher education programme, but one they will be required to teach when they graduate. We query if the knowledge they bring from secondary school, prepares them sufficiently to teach their future…

This article examines how student learning is affected by the use of team-based inquiry learning, a novel pedagogy in mathematics that uses team-based learning to implement inquiry-based learning. We conducted quasi-experimental and observational studies in intermediate level mathematics courses, finding that team-based inquiry learning led to…

Enacting equitable teaching practices and sustaining those practices continue to be challenges in most high schools (National Council of Teachers of Mathematics, 2018), particularly in an era of high-stakes testing. Just one year after Boaler and Staples (2008) reported on the successes of "Railside High," where equitable teaching…

The literature shows that the integration of technological tools, like "GeoGebra," has the potential to improve the teaching and learning of mathematics. The aim of this study was to see whether "GeoGebra" could be used to address identified, systematic misconceptions that National Certificate Vocational (NCV) students hold…

In the study reported on here, we investigated the effects of the use of dynamic geometry software (DGS) (i.e., GeoGebra) on learners' learning and a teacher's beliefs. The learners and teacher involved in the study were from a high-poverty, rural high school in South Africa. We compared grade 11 learners (N = 56) who used GeoGebra in the context…

Using a cluster-randomized controlled trial research design, this study investigates the effect of the first year of a three-year teacher professional development program on grades 1 and 2 student achievement in mathematics. Although the findings reported in the present report do not meet the standard cutoff for statistical significance (e.g., 95%…

The reversal error is a prevalent phenomenon that consists of reversing the relationship between two variables when writing equations from comparison in verbal language. A study with 169 Basque/Spanish bilingual pre-service teachers examined whether this error is mainly due to the students' tendency to employ a direct-translation strategy based on…

In the first chaotic days of the crisis, schools across the United States organized to assemble and distribute instructional materials and to make a rapid transformation from school-based to home-based learning. the impact of this crisis on all students is significant. As districts resume instruction in the upcoming school year, they will not only…