This observation study documents the amount and quality of mathematics instruction provided to students with intellectual and developmental disabilities in kindergarten through second grade in self-contained special education settings. We observed six special education teachers and their students (N = 12) during a total of 967 min allotted to…

Teaching techniques of integration can be tedious and often uninspired. We present an obvious but underutilized approach for finding antiderivatives of various trigonometric functions using the complex exponential representation of the sine and cosine. The purpose goes beyond providing students an alternative approach to trigonometric integrals.…

The paper explores and clarifies the similarities and differences that exist between proof by contradiction and proof by contraposition. The paper also focuses on the concept of contradiction, and a general model for this method of proof is offered. The introduction of mathematical proof in the classroom remains a formidable challenge to students…

Mathematics learning within the context of videogames is an increasingly important area of study that has not yet fulfilled its promise of powerfully contextualized and transformative learning. This research served to begin pushing the boundaries of the field by relying upon cutting edge mathematics education research on fractions and the best…

This article reports the outcomes of a study that seeks to investigate the role of feedback, by way of an intelligent support system in natural language, in parametrized modelling activities carried out by a group of tertiary education students. With such a system, it is possible to simultaneously display on a computer screen a dialogue window and…

Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem…

Past studies have documented students' and teachers' persistent difficulties in determining whether 2 quantities covary in a direct proportion, especially when presented missing-value word problems. In the current study, we combine a mathematical analysis with a psychological perspective to offer a new explanation for such difficulties. The…

We present a method for finding partial fraction decompositions of rational functions with linear or quadratic factors in the denominators by means of repeated polynomial divisions. This method does not involve differentiation or solving linear equations for obtaining the unknown partial fraction coefficients, which is very suitable for either…

The study reported in this paper concerns the tensions and conflicts that teachers experience while they enact a new set of reform-oriented curricular materials into their classrooms. Our focus is ?n the interactions developed in two groups of teachers in two schools for a period of a school year. We use Activity Theory to study emerging…

Mathematics teachers strive to prepare their students to use mathematics in powerful ways both in and out of school. However, students' ability to use certain mathematical ideas, objects, and processes depends largely on the meanings they develop for the topics they study. Some meanings are simply more beneficial and useful than others. For…

By combining linguistic analysis with metaphors for mediating between a body of knowledge and teaching practice, we exemplify curriculum developers' voices in teacher guides. We discuss two types of voices, that of the Expert, who talks through the teacher and restricts the pedagogical agency of the teacher, and that of the Philosopher, who speaks…

Based on the theoretical elements of the instrumental approach to tool use known as Task-Technique-Theory (Artigue, 2002), this paper analyses and discusses the performance of graduate students enrolled in a Teacher Training program. The latter performance relates to tracing tangent lines to the curve of a quadratic function in Dynamic Geometry…

After being introduced to the distributive law in meaningful contexts, students need to extend its scope of application to unfamiliar expressions. In this article, a process model for the development of structure sense is developed. Building on this model, this article reports on a design research project in which exercise tasks support students…

The "Collaborative Research Project" ("CRP")--a mathematics research experience for undergraduates--offers a large-scale collaborative experience in research for undergraduate students. CRP seeks to widen the audience of students who participate in undergraduate research in mathematics. In 2015, the inaugural CRP had 100…

In this paper I will outline the process I have developed for conducting applied mathematics research with undergraduates and give some examples of the projects we have worked on. Several of these projects have led to refereed publications that could be used to illustrate topics taught in the undergraduate curriculum.