In this article, the authors first present the Hands Together! task. The mathematics in this problem concerns the relationship of hour and minute durations as reflected in the oft-overlooked proportional movements of the two hands of an analog clock. The authors go on to discuss the importance of problem solving in general. They then consider…

This paper is about the development of a task sequence to help overcome the fragmented understanding of the "function" concept that students often bring with them into the initial stage of upper secondary school level. Our aim is to make the students' use of functions more flexible in certain respects, for example when functions are…

The task of constructing a square is used to argue that looking for and pursuing several solution routes is a powerful principle to identify and analyse properties of mathematical objects, to understand problem statements and to engage in mathematical thinking activities. Developing mathematical understanding requires that students delve into…

As part of a larger study of student understanding of concepts in linear algebra, we interviewed 10 university linear algebra students as to their conceptions of functions from high school algebra and linear transformation from their study of linear algebra. An overarching goal of this study was to examine how linear algebra students see linear…

The Merriam-Webster dictionary defines "transition" as: (a) the passage from one state, stage, subject, or place to another: change; or (b) a movement, development, or evolution from one form, stage, or style to another. The word transition can refer to an active shift of the person in space and time or status, for example; it can also…

Southern Cross University (SCU) educators and local teachers have developed a five-lesson instructional sequence built around fluke identification as a way of resolving the question: How fast do humpback whales travel up the east coast of Australia?

Textbook content has the ability to influence mathematical learning. This study compares how linear functions are presented in two textbooks, one of South African and the other of German origin. These two textbooks are used in different language-based streams in a school in Gauteng, South Africa. A qualitative content analysis on how the topic of…

In support of efforts to foreground functions as central objects of study in algebra, this study provides evidence of how secondary students use trigonometric functions in contextual tasks. I examined secondary students' work on a problem involving modeling the periodic motion of a Ferris wheel through the use of a visual programming environment.…

This report presents results of teacher and student surveys on how powerful Mathematics Design Collaborative practices are shifting how teachers teach. It also summarizes student achievement data from schools using the strategies in four states. In vignettes and testimonials, teachers who completed Southern Regional Education Board (SREB)…

A literature review establishes a working definition of recreational mathematics: a type of play which is enjoyable and requires mathematical thinking or skills to engage with. Typically, it is accessible to a wide range of people and can be effectively used to motivate engagement with and develop understanding of mathematical ideas or concepts.…

Inquiry-based instruction is a student-centered approach to teaching that focuses on active learning (Barron and Darling-Hammond 2008) in which students engage with "tasks that promote reasoning and problem solving" (NCTM 2014). Specifically, such tasks encourage a variety of solution strategies and stimulate use of the NCTM Process…

The editors of Mathematics Teacher appreciate the interest of readers and value the views of those who write in with comments. The editors ask that name and affiliation including email address be provided at the end of their letters. This September 2016 Reader Reflections, provides reader comments on the following articles: (1) "Innocent…

A central understanding in mathematics is knowledge of "math equivalence," the relation indicating that 2 quantities are equal and interchangeable. Decades of research have documented elementary-school (ages 7 to 11) children's (mis)understanding of math equivalence, and recent work has developed a construct map and comprehensive…

Studies in mathematics education often point to the necessity for students to engage in more cognitively demanding activities than just solving tasks by applying given solution methods. Previous studies have shown that students that engage in creative mathematically founded reasoning to construct a solution method, perform significantly better in…

Previous studies have repeatedly shown that children often incorrectly use an additive model for multiplicative word problems, and a multiplicative model for additive word problems. The present study aimed to investigate which model upper primary school children tend to choose in word problems that are open to "both" ways of reasoning.…