Building students' confidence and conceptual understanding early sets a solid foundation for reasoning and exploration. "Nurturing Math Curiosity With Learners in Grades K-2" offers educational tools and strategies teachers can use to integrate mathematical argumentation in early elementary classrooms, allowing space for students'…

In 2 experiments, I studied the effects of an Equivalence Based Instruction (EBI) math intervention on the emergence of untaught selection responses and abstraction to production responses. In Experiment I, using a multiple baseline design, I implemented the EBI intervention among a group of 17 first grade participants with varying levels of math…

The current quantitative study, a naturalistic field experiment, was conducted in a public primary school in Soweto, Johannesburg, with the objective to examine how children's achievement on four assessments at the beginning of Grade R, namely their numeracy, their mathematics-specific vocabulary, their executive functions, and their logical…

This article describes sixth-grade students' engagement in two model-eliciting activities offering students the opportunity to construct mathematical models. The findings show that students utilized their knowledge of fractions including conceptual and procedural knowledge in constructing mathematical models for the given situations. Some students…

We analyze the results of a study conducted for the purpose of assessing the viability of an alternative starting point for teaching fractions. The alternative is based on Freudenthal's insights about fraction as comparison. It involves portraying the entities that unit fractions quantify as always being apart from the reference unit, instead of…

Documenting how students with learning disabilities (LD) initially conceive of fractional quantities, and how their understandings may align with or differ from students with mathematics difficulties, is necessary to guide development of assessments and interventions that attach to unique ways of thinking or inherent difficulties these students…

An emerging consensus suggests that guided discovery, which combines discovery and instruction, is a more effective educational approach than either one in isolation. The goal of this study was to examine two specific forms of guided discovery, testing whether conceptual instruction should precede or follow exploratory problem solving. In both…

The author recently read a research paper by Padberg (2002), in which the development of understanding associated with decimal fractions was studied. Padberg (2002) outlined the situation that existed in Germany, where students were introduced to decimal fractions in the sixth year of school. He claimed that it was assumed students would have a…