This fourth book in the Mathematics Recovery series equips teachers with detailed pedagogical knowledge and resources for teaching number to 7 to 11-year olds. Drawing on extensive programs of research, curriculum development, and teacher development, the book offers a coherent, up-to-date approach emphasizing computational fluency and the…

This paper presents an investigation by pre-service secondary school teachers in a geometry class of the relationship between the perpendicular distance from the eyeball to the wall (x) and the viewable vertical distance on the wall (y) using a view tube of constant length and diameter. In undertaking the investigation, students used tabular and…

We present three cases showing families' competence in mathematical problem solving as a practical aspect of daily life. At home, parents and children engaged creatively in solving math-relevant problems. They used a combination of everyday practices and school forms, but generally did not recognize mathematics in their problem solving. The…

With teachers and students in Government and Catholic schools in three geographical clusters in Victoria, the Task Type and Mathematics Learning (TTML) project is investigating the best ways to use different types of mathematics tasks, particularly in Grades 5 to 8. This article describes Type 1 tasks and discusses how they contribute to…

This article reports an alternative approach, called the combinatorial model, to learning multiplicative identities, and investigates the effects of implementing results for this alternative approach. Based on realistic mathematics education theory, the new instructional materials or modules of the new approach were developed by the authors. From…

Comparisons made between art and mathematics so often centre on the beauty of mathematics and how its forms might be seen as aesthetically pleasing. Yet the prominence of beauty as an attribute is less prevalent in contemporary art. Rather, art has a much broader scope of concern, perhaps with a greater emphasis on providing apparatus through…

This exploratory study compared a computer-based mathematics education intervention with two more traditional approaches with the purpose of improving instruction in perimeter and area. Kidspiration software, tile/stick manipulatives and pencil/paper-based copying/drawing of shapes were implemented in a 3rd Grade New York City public school…

In this paper, we discuss our experiences with an after-school program in which we engaged middle-school students with low socioeconomic status from an urban community in mathematical problem solving. We document that these students participated in many aspects of problem solving, including the posing of problems, constructing justifications,…

Getting high school students to enjoy mathematics and to connect concepts to their daily lives is a challenge for many educators. The Mathematics of Skateboarding demonstrated innovative and creative ways to engage students in content and skills mapped to state requirements for high school students in Algebra and Geometry.

Proof is a foundational mathematical activity that has been underrepresented in school mathematics. The recently adopted Common Core State Standards in Mathematics includes eight process standards, several of which promote the inclusion of reasoning and proof across all grades, courses, and students. If students are to reach the expectations…

One of the best known numbers in mathematics is the number denoted by the symbol [pi]. This column describes activities that teachers can utilize to encourage students to explore the use of [pi] in one of the simplest of geometric figures: the circle.

One challenge that middle school teachers commonly face is finding insightful, hands-on applications when teaching basic mathematical concepts. One concept that is a foundation of middle school mathematics is the notion of "linear functions." Although a variety of models can be used for linear equations, such as temperature conversions,…

Kalchman describes and discusses preservice teachers' changing views of what it means to know and do mathematics both inside and outside the classroom walls. The context for change is a weekly assignment for methods students to describe and solve mathematical problems in situations that they confront in day-to-day life. The assignment supports…

Interactive visual learning tools (IVLTs) are software environments that encode and display information visually and allow learners to interact with the visual information. This article examines the application and utility of frameworks in the analysis and design of IVLTs at the micro level. Frameworks play an important role in any design. They…

There is a great potential opportunity to use portable physical activity monitoring devices as data collection tools for educational purposes. Using one such device, we designed and implemented a weeklong workshop with high school students to test the utility of such technology. During that intervention, students performed data investigations of…