Problem-based learning puts students in situations that suggest problems without providing instructions and available knowledge. Therefore, when using problem-based learning, students need to be flexible, self-disciplined, active and self-occupied with knowledge and turn the knowledge the teacher intends to impart into their knowledge. For locus…

Learning the concept of fractions is among the most challenging topics in school mathematics. One of the main sources of difficulties in learning fractions is related to "natural number bias" (Van Hoof, Verschaffel & Van Dooren, 2015). Applying properties of the natural numbers incorrectly in situations involving rational numbers can…

Research in psychology and in mathematics education has documented the ubiquity of "intuition traps" -- tasks that elicit non-normative responses from most people. Researchers in cognitive psychology often view these responses negatively, as a sign of irrational behaviour. Others, notably mathematics educators, view them as necessary…

Approximations of practice provide opportunities for teacher candidates (TCs) to engage in the work of teaching in situations of reduced complexity. A problem of practice for teacher educators relates to how to represent student voice in approximations to engage TCs with interactive practices in meaningful ways. In this article, we share an…

As algebra teachers, the authors explore the following question in this article: "How can algebra 1, algebra 2, and precalculus teachers support students to develop algebraic reasoning and understanding of structure that can serve them in day-to-day algebraic computation?" The article shows how the algebraic identity "(a +…

This article presents a checklist of 10 evidence-based practices for educators to apply in mathematics instruction for students with learning disabilities. The checklist is "actionable," meaning the items on the checklist can be put into action immediately. It provides practical strategies teachers can adopt to fit their lessons…

Concern about children's mathematics performance in Ireland and elsewhere has prompted a range of responses from researchers, policymakers, educators and the media. While policy-level responses in Ireland include revising curricula and implementing a numeracy strategy that calls for increased tuition hours, teachers have also drawn on a wide array…

Tasks that ask students to label rational number points on a number line are common not only in curricula in the upper elementary school grades but also on state assessments. Such tasks target foundational rational number concepts: A fraction (or a decimal) is more than a shaded part of an area, a part of a pizza, or a representation using…

The basic rules of elementary algebra can often appear beyond the grasp of many students. Even though most subjects, including calculus, prove to be more difficult, it is the simple rules of algebra that continue to be the "thorn in the side" of many mathematics students. In this paper we present a result intended to help students achieve a…

Teachers need to address global climate change with students in their classrooms as evidence for consequences from these environmental changes mounts. One way to approach global climate change is through examination of authentic data. Mathematics and science may be integrated by interpreting graphs from the professional literature. This study…

This article describes pedagogic issues in setting objective tests in mechanics using Question Mark Perception, coupled with MathML mathematics mark-up and the Scalable Vector Graphics (SVG) syntax for producing diagrams. The content of the questions (for a range of question types such as multi-choice, numerical input and variants such as…

The treatment of errors in mathematics classrooms has gained attention in recent years, with many researchers suggesting that errors should be used as starting points for student inquiry into mathematics. In the study reported in this article, we examined how teachers used discourse around errors to generate inquiry by looking at the treatment of…

Mathematics departments rarely require students to study very much logic before working with proofs. Normally, the most they will offer is contained in a small portion of a "bridge" course designed to help students move from more procedurally-based lower-division courses (e.g., abstract algebra and real analysis). What accounts for this seeming…

Following a pretest, 11 participants who were naive with regard to various algebraic and trigonometric transformations received an introductory lecture regarding the fundamentals of the rectangular coordinate system. Following the lecture, they took part in a computer-interactive matching-to-sample procedure in which they received training on…

The author has discovered that errors in grades often occur when scores are combined for final marks. These errors are not related to the grading individual assignments. Rather, they occur when teachers at all grade levels bring individual test and assignment scores together for the students' final grades. Unfortunately, professors of mathematics…