Mathematics courses should prepare students to use mathematics in a range of contexts, including science. However, students often struggle in applying mathematics in physics courses, even when they understand the mathematical content (Rebello et al., 2007). Often the root of this struggle is attributed to the "student" or the…

In mathematics, there are countless connections between apparently unrelated topics. Students often find these relationships interesting, and they contribute to expanding their mathematical repertoires. This article describes one of these unusual connections, between the sum of periodic functions and the commensurable and incommensurable numbers.…

Inequities in student access to trigonometry and calculus are often associated with racial and socioeconomic privilege, and often influence introductory physics course performance. To mitigate these disparities in student preparedness, we developed a two-pronged intervention consisting of (1) incentivized supplemental math assignments and (2)…

In this paper, we introduce a technology-enhanced pedagogical sequence for supporting lower secondary school students' sense-making of the concept of volume in a non-procedural and non-formula-driven way. Specifically, we illustrate a novel approach of using dynamic geometric environment (DGE) to introduce the meaning of volume and then deriving…

The purpose of this paper is to follow the reasoning of high school students when asked to explain the standard trigonometric limit lim/[theta][right arrow] sin[theta]/[theta]. An observational study was conducted in four different phases in order to investigate if visualization, by means of an interactive technology environment (Geogebra), can…

This case study offers a recounting and analysis of the experiences of one urban educator, in a public high school mathematics classroom setting, working to integrate critical mathematics curricula and pedagogy with youth and in collaboration with a community organization. This project helps to unveil complexities that teachers may experience when…

This article proposes that the reader be nourished by avant-garde elements for new educational practices in the teaching and learning of mathematics. The writing is based on an investigation that was carried out with high school students from Puerto Rico. From a qualitative paradigm with a research design in action, it was explored how students in…

Purpose: Analogical reasoning has been studied using a variety of tasks that generally required consideration of the relationship between the object and its integration to conclude an analog schema. The aim of this study was to describe the model of analogical reasoning schema based on some analogical problems. Research Method: In this study used…

Meaning and understanding are didactic notions appropriate to work on concept comprehension, curricular design, and knowledge assessment. This document aims to delve into the meaning of school mathematical concepts through their semantic analysis. This analysis is used to identify and establish the basic meaning of a mathematical concept and to…

The difficulty in the process of trigonometry teaching, served as a stimulus for the present research, in which the objective consisted of designing and proposing the use of a Trigonometric Cicular Geoplane for the construction of meaningful learning in the area of Mathematics at Israel Technological University. For Its development, a field…

Although social studies or language arts classes may offer more natural settings for "global studies," the author's students have engaged in projects demonstrating that mathematical topics can work well at furthering the goal of increasing students' cultural literacy. The author describes one project here, where students working in…

The purpose of this note is to discuss how paper folding can be used to find the exact trigonometric ratios of the following four angles: 22.5°, 67.5°, 27°, and 63°.

In his beautiful paper, Hasan Fakhruddin reported observations of mirror-like reflections in the rough surface of a ground glass plate. Similar effects have been recently employed for metrology of the roughness of optical diffusers used in modern light emitting device illumination systems. We report the observations of specular reflection in…

We examined asynchronous online discussion boards, specifically those that are unmediated by teacher figures, to identify characteristics of these spaces that support or constrain students as they seek help in mathematics. We analyzed 86 questions and 114 associated responses posted to two Khan Academy discussion boards centered around two related…

If students are asked, "What is the world water crisis?" how would they respond? In the authors precalculus classes, this question is often met with blank stares and students avoiding eye contact. Many students are unaware of the world water crisis--what it is, why it is, or who it affects. Even fewer realize the utility of trigonometry…