Using calculus only, we find the angles you can rotate the graph of a differentiable function about the origin and still obtain a function graph. We then apply the solution to odd and even degree polynomials.

We show that inside every triangle the locus of points satisfying a natural proportionality relationship is a parabola and go on to describe how this triangle-parabola relationship was used by Archimedes to find the area between a line and a parabola.

The effects of a mathematical problem-solving intervention on students' problem-solving performance and math achievement were measured in a randomized control trial with 1,059 7th-grade students. The intervention, "Solve It!," is a research-based cognitive strategy instructional intervention that was shown to improve the problem-solving…

In this article, associate professor Chrystal Dean describes how teachers can challenge their upper elementary students' understanding of area beyond a memorized formula. Herein she describes an activity that will show students the "why" behind using A = l × w to solve rectangular area problems. The activity will help deepen…

The purpose of this study was to deconstruct the relationship between visual static models and students' written solutions to fraction problems using a large sample of students' solutions. Participants in the study included 162 third-grade and 209 fourth-grade students from 17 different classrooms. Students' written responses to open-ended tasks…

We provide a preliminary exploration into the use of note taking when combined with video examples. Student volunteers were divided into three groups and asked to perform two problems. The first problem was explored in a classroom setting and the other problem was a novel problem. The students were asked to complete the two questions. Furthermore,…

Over the last decade, the pedagogical approach known as mathematical modeling has received increased interest in college algebra classes in the United States. Math modeling assignments ask students to develop their own problem-solving tools to address non-routine, realistic scenarios. The open-ended quality of modeling activities creates dilemmas…

From a fallibilist perspective, mathematics gradually develops with problems, conjectures, proofs, and refutations. To attain such authentic mathematical learning, it is important to intentionally treat refutation in mathematics classrooms, such as facing or proposing counterexamples and coping with them. In particular, analysing students'…

We describe the calculation of the distribution of the sum of signed ranks and develop an exact recursive algorithm for the distribution as well as an approximation of the distribution using the normal. The results have applications to the non-parametric Wilcoxon signed-rank test.

This report describes the pilot conducted in the final phase of a project, Expanding Audio Access to Mathematics Expressions by Students With Visual Impairments via MathML, to provide easy-to-use tools for authoring and rendering secondary-school algebra-level math expressions in synthesized speech that is useful for students with blindness or low…

This article introduces an optimization task with a ready-made motivating question that may be paraphrased as follows: "Are you smarter than a Welsh corgi?" The authors present the task along with descriptions of the ways in which two groups of students approached it. These group vignettes reveal as much about the nature of calculus students'…

Educators, policymakers, and parents alike are focused on ensuring the academic success of the nation's students. These efforts interact with the expanding use of technology, which affects the lives of students both inside and outside of the classroom. Thus, the role that technology plays in education is an evolving area of research that continues…

Research in science, technology, engineering, mathematics (STEM) education suggests development of STEM competency requires effective learning environments, including the use of varied representations (e.g., visual, symbolic) and opportunities for students to make connections among them. Although such practices have been advocated in the teaching…

The demands on mathematical problem-solving have increased in almost all school systems internationally and may constitute a barrier for children with special educational needs (SEN). This study explored the role of fluid reasoning (FR), working memory (WM) and complex executive function of planning (EF) in children (N = 62) referred for…

Developing students' strengths while teaching the content required by national and state standards in science, technology, engineering, and mathematics (STEM) is challenging for classroom teachers. In the Cultivating Diverse Talent in STEM (CDTIS) project, the assessment results found in strength-based reports gave teachers the tools needed to…