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…

It is critical for mathematics tasks to provide students with the opportunity to engage actively in reasoning, sense making, and problem solving so that they develop a deep understanding of mathematics. Learning mathematics while solving a problem can be like entering a dark room with a single small light. The objects are in the shadows, difficult…

Exemplification is significant for the teaching of mathematics and revealing mathematical structure to learners. Structured exercises and learner generated examples (LGEs) are pedagogical tools intended to provide opportunities for learners to discern and generalize mathematical structure. The aim of this study was to understand how middle school…

Mathematics education researchers have sought to understand the knowledge that teachers need to teach mathematics effectively. Teachers need to know more than merely knowing how to "do the math" at a particular grade level. However, the research community differs on the nature of that knowledge. The construct of "horizon content…

This study aims to determine the opinions of teacher candidates about using history of mathematics (HoM) in the instruction of mathematics. Research data was collected from elementary mathematics education 4th grade students through semi-structured interviews conducted for the purpose of collecting their opinions about using HoM in the instruction…

We draw on our work with designed instructional sequence on Fractions as Measures across three international contexts and explore the functions of the design features related to the stories embedded within the sequence. We discuss functions that relate to how stories support students' meaningful engagement in classroom mathematical activities,…

As part of a much larger study where spatial reasoning is the focus, this paper draws on the language aspects of this strand of the curriculum. The quarantined part of the project discussed in this presentation is based in remote Indigenous schools. We draw on the challenges of the concept of symmetry and where the language of instruction (and…

We describe the mathematical content knowledge a teacher needs in order to achieve a basic level of competence in mathematics teaching. We also explain why content knowledge is essential for this purpose, how Textbook School Mathematics (TSM) stands in the way of providing teachers with this knowledge, and the relationship of this concept of…

To better understand how to support high school students' engagement, advancements in research methods that provide greater understandings of malleable factors of engagement and conditions that affect students' engagement are needed. In this conceptual paper, we introduce four dilemmas that researchers need to navigate to study secondary students'…