A number of post-colonial countries in Africa have introduced home language instruction for the initial years of schooling. This policy is particularly challenging in mathematics, as there is a paucity of research on how the linguistic features of African languages might be leveraged for the teaching and learning of mathematics. This paper…

Two experiments examined whether concrete models support place value learning. In Experiment 1 (N = 149), 7-year-olds were trained with either a) symbols alone or b) symbols and base-10 blocks. Children in both groups showed significant growth overall, but there were specific effects favoring one training type over another. Symbols-only training…

The notion of flow of a proof encapsulates mathematical, didactical, and contextual aspects of proof presentation. A proof may have different flows, depending on the lecturer's choices regarding its presentation. Adopting Perelman's New Rhetoric (PNR) as a theoretical framework, we designed methods to assess aspects of the flow of a proof. We…

In this commentary, I examine some of the distinctive, foundational difficulties in learning fractions and other types of rational numbers encountered by students with a mathematical learning disability and how these differ from the struggles experienced by students classified as low achieving in math. I discuss evidence indicating that students…

Implementation of evidence-based practices (EBPs) is paramount to students' development of mathematics proficiency. This study investigated "practice-based evidence" of interventionists' actual use of explicit mathematics instruction, a well-established EBP. Specifically, this study analyzed direct observation data collected in a…

During a time when students are accessing instruction virtually because of COVID-19, reflecting on the sixth of the Standards for Mathematical Practice (SMP 6) is a vital step for educators to take. Although the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010) identifies SMP 6 as Attend to precision, associated expertise…

Implementation of evidence-based practices (EBPs) is paramount to students' development of mathematics proficiency. This study investigated "practice-based evidence" (Green, 2008) of interventionists' actual use of explicit mathematics instruction, a well-established EBP. Specifically, this study analyzed direct observation data…

Writing and evaluating contextual problems is an important task in the work of teaching, and thus is part of the knowledge that prospective teachers must develop. In dealing with word problems posed both by children and themselves, prospective teachers will need to attend to the realism of the context and the consistency between the operation and…

Numbers are represented as ordered magnitudes along a spatially oriented number line. While culture and formal education modulate the direction of this number-space mapping, it is a matter of debate whether its emergence is entirely driven by cultural experience. By registering 8-9-month-old infants' eye movements, this study shows that numerical…

In this article, which was first published in 1991, the late Sandy Dawson, discusses aspects of a Lakatosian approach to mathematics teaching. The ideas are illustrated with examples from three teaching situations: making conjectures about the next number in a sequence; making conjectures about the internal angles in a triangle using Logo; and…

The history of the number zero is an interesting one. In early times, zero was not used as a number at all, but instead was used as a place holder to indicate the position of hundreds and tens. This article briefly discusses the history of zero and challenges the thinking where divisions using zero are used.

Despite adequate facilities and several education reforms, most Cambodian teacher trainers fail to provide sufficient content knowledge and student-centered pedagogy. Many also lack the skills to diagnose preservice teachers' misconceptions and to propose adequate solutions. Dictating lessons with little feedback or applied activities or having…

A formative pilot study of a fractions intervention was conducted to address the intervention's potential for improving fifth-grade struggling students' knowledge of fractions, and to identify any logistical or instructional design issues, before scaling up for a randomized control trial. In the first section, we provide details of the formative…

Curricular analysis indicates that the U.S. students are introduced to multiplication in additive terms (as the replication of equal groups and repeated addition). But the virtue of this introduction for supporting students' understanding of the full range of multiplicative relationships is unclear. This paper reports an analysis of all grade 4…

Transitioning from teaching whole number operations to teaching fraction operations can prove difficult, even for the seasoned mathematics teacher. However, with effective literacy practices, teachers can seamlessly shift their students to learning the rules for fractions. The implications can be a mastery of mathematical language used to describe…