This paper uses the lens of a calculus student to examine different solutions to a weekly puzzler from the radio show "Car Talk," hosted by Tom and Ray Magliozzi. The puzzler describes an automobile that is traveling 75 miles per hour and is 75 miles from its destination. The trip is completed by traveling 1 mile at 75 miles per hour, 1…

Research reported in this article has been conducted from the theoretical perspective of the Anthropological Theory of the Didactic developed by Y. Chevallard and his collaborators, and from the institutional perspective of university mathematics education in France. It focuses on the teaching and learning of algebraic structures. The article…

In this study, we use Mathematical Quality of Instruction (MQI), a content-specific observation framework, to examine the mathematical quality of instruction of three focal lessons in order to examine the instructional aspects illuminated by this framework as well as discuss those aspects not captured by MQI. While prior work provides evidence on…

In more and more countries, the goal of mathematics education is to develop students' mathematical competence beyond procedural and conceptual knowledge. Thus, students need to engage in a rich variety of tasks comprising competencies such as communication, reasoning and problem-solving. In addition, assessment tasks should be constructed to…

In this exploratory case study, the researchers conducted a descriptive, qualitative microanalysis of the tutoring of two eighth grade students with learning disabilities while solving algebra problems. The researchers analyzed the participants' problem solving tendencies and interventions that helped the students succeed. One of the students,…

In understanding upper secondary school students' interpretations of information in graphical representations of a distance--time graph and an ECG graph, little attention has been paid to the analysis of the condition of the conceptual development related to their utterances. Understanding this better can help improve the teaching of…

This paper describes two myths that circulate widely about the potential of students with Learning Disabilities to learn mathematics: (1) that students with Learning Disabilities cannot benefit from inquiry-based instruction in mathematics, and only from explicit instruction; and (2) that students with Learning Disabilities cannot construct their…

This article explores teaching practices described in NCTM's Principles to Actions: Ensuring Mathematical Success for All. Student thinking, a learning cycle, and procedural fluency are discussed in this article, which is the second installment in the series. [For the first installment in this series see "Promoting a Conceptual Understanding…

In this discussion paper we look at questions that adults have about numbers. Many of their questions are not about pure mathematics, but about personal, cultural or societal issues. We discuss how to connect mathematical topics with things people are interested in, based on theoretic knowledge from the field of science communication. We focus on…

Some students may be diagnosed with a learning disability in mathematics or dyscalculia, whereas other students may demonstrate below-grade-level mathematics performance without a disability diagnosis. In the literature, researchers often identify students in both groups as experiencing math difficulty. To understand the performance of students…

We make a case for including difference equations, in particular the discrete logistic equation, in basic differential equations courses. Contrasting the behavior of discrete and continuous models enriches students' understanding of both modeling and differential equations. To facilitate sharing discrete population models with students, some…

The author, a mathematics teacher, describes a seventh grade class where students use scientific notation to calculate how long it takes light to travel a variety of astronomical distances and then interpret the significance of their findings. Ultimately, the goal is to have students see how calculations can help answer large, almost philosophical…

Mathematics assessment is integral in enabling teachers to implement specially designed instruction for students with disabilities. This article presents an overview of an underutilized form of assessment, the clinical interview. A type of diagnostic assessment, clinical interviews are critically important when designing individualized instruction…

This article focuses on one common type of many different classroom discussions, open-strategy sharing (OSS), because it offers a starting point for teachers new to mathematical discussions. The goal of an OSS discussion is to explore multiple possible ways to solve a single mathematical task. Students share strategies, listen to others'…

For 500 years, dream catchers have been cultural symbols of intrigue worldwide. The most common folkloric design is a 12-point dream catcher. According to Native American legend, the first dream catcher was woven by a "spider woman" to catch the bad dreams of a chief's sick child. Once the bad dreams were caught, the chief's child was…