Different types of reasoning, such as intuitive, inductive, and deductive, are used in the generalization of figural patterns, as an important part of patterns in school mathematics. It is difficult to demarcate the constructive patterns where the regularity observed in the first few sentences is generalizable to the other sentences and each…

Virtual reality (VR) is a promising avenue to enhance the independence and daily living skills of high school students with intellectual disability. This study investigated the efficacy of a non-immersive VR focused on teaching food preparation skills to secondary students with intellectual disability. Three high school students with intellectual…

Quadratics provide a foundational context for making sense of many important algebraic concepts, such as variables and parameters, nonlinear rates of change, and views of function. Yet researchers have highlighted students' difficulties in connecting such concepts. This in-depth qualitative study with two pairs of Year 10 (15 or 16-year-old)…

Given the importance of mathematics identity for students continued participation and engagement with mathematics, it is important for educators and researchers to be able to explore students' mathematics identity development. However, an instrument with validity evidence that can be used to explore mathematics identity efficiently and with groups…

It's often useful extending students beyond the limiting geometry of triangles and quadrilaterals to regularly consider generalizations of results for triangles and quadrilaterals to higher order polygons. A brief heuristic description is given here of the author applying this strategy, and which led to an interesting result related to the…

Generalizing is a critical aspect of mathematics learning, with researchers and policy documents highlighting generalizing as a core mathematical practice. It can also be challenging to foster in class settings, and teachers need access to better resources to teach generalizing, including an understanding of effective forms of instruction. This…

Researchers established virtual manipulatives as an evidence-based practice for students with intellectual and developmental disabilities (IDD). However, much of the existing research for this population targets middle school students with IDD. This study examined a virtual number line paired with teacher modeling and the system of least prompts…

Self-monitoring of attention (SMA) promotes increased learning opportunities and greater independence for students but has been sparsely researched with high-school students. This study evaluated the effects of a self-monitoring strategy that included the use of a smartphone with a vibrating app to signal high-school students with high-incidence…

Mole, molar mass and the Avogadro number are used constantly to measure the amount of substance in chemical changes. However, students have difficulty in understanding these concepts because they are not familiar with measuring very small amounts of matter that cannot be seen and weighed in daily life, like atoms. The mole concept was developed to…

Understanding fraction as a quantity has been identified as a key developmental understanding. In this study, students in Grades 5, 8, and 11 were asked to compare the areas of two halves of the same square--a rectangle and a right triangle. Findings from this study suggest that students who understand fraction as a quantity use reasoning related…

The National Assessment of Educational Progress (NAEP) program only reports state-level subgroup results if it samples at least 62 students identifying with the subgroup. Since some subgroups constitute small proportions of many states' general student populations, these minority subgroups are seldom sufficiently sampled to meet this sample size…

The purpose of these notes is to generalize and extend a challenging geometry problem from a mathematics competition. The notes also contain solution sketches pertaining to the problems discussed.

In this study, we explored enacted task characteristics (ETCs) that supported students' quantitative reasoning (QR). We employed a design-based methodology; we conducted a teaching experiment with eight secondary school students. Through ongoing and retrospective analyses, we identified ETCs which supported students' quantitative reasoning. The…

Reading research in the United States has mainly focused on early or, less frequently, middle grades and on monolingual (MN or English-only) rather than on multilingual (ML) students. To address these gaps, we focused on factors contributing to high school ML students' reading achievement. In particular, we first used machine learning to identify…

Mathematically gifted students have a high potential for understanding and thinking through mathematical relations and connections between mathematical concepts. Currently, it is thought that generalizing patterns algebraically can serve to provide challenges and opportunities that match their potential. This article focuses on a mathematically…