Looks at the connection between soccer fields and mathematics to help students understand middle school geometry topics. Presents an activity in which students explore relationships among polygons to discover which combinations tessellate and which combinations form polyhedra. (ASK)

Discusses the results of the 1996 National Assessment of Educational Progress (NAEP) of secondary school students on probability and statistics. The most recent results indicate that more attention is being given to data analysis, statistics, and probability, and that student performance on these items is gradually improving compared to the 1990…

The National Council of Teachers of Mathematics (1989) proposes using everyday objects, such as paper, to enable students to explore geometric relationships and vocabulary. Paper-folding and other types of hands-on activities have been found to increase students' ability to communicate mathematically and foster their understanding of mathematical…

This study describes a conceptual teaching approach that helps students make connections between their everyday activities and mathematical word problems. It includes a brief review of the importance of teaching for understanding and describes four principles of conceptual teaching: (1) use cooperative groups; (2) allow students enough time to act…

This article describes an activity that, on the surface, engages the students in basic skill review. Its ultimate goal is to cause students to make conjectures, seek to justify those conjectures, and to think mathematically. (Contains 3 figures.)

This Brief Report describes a secondary analysis of the solutions written by 306 second-year algebra students to four constructed-response items representative of content at this level. The type of solution (symbolic, graphical, or numerical) used most frequently varied by item. Curriculum effects were observed. Students studying from the second…

This article focuses on the dynamics of language in the context of mathematics. The interaction of everyday words and specialized mathematics vocabulary impacts students' development of mathematical understanding. (Contains 4 tables and 1 figure.)

This article provides a picture of the learning environment that is created for the preservice mathematics teacher and how development of spatial abilities can be incorporated into courses for these students. (Contains 3 figures.)

This article explores the algebra that can be uncovered in many middle-grades mathematics tasks that, on first inspection, do not appear to be algebraic. It shows connections to the other four Standards that occur in traditional algebra problems, and it offers strategies for modifying activities so that they can be used to foster algebraic…

Three pieces of literature are used to launch mathematical investigations. The tasks provide opportunities for students to apply proportional reasoning skills, explore linear relationships, calculate a unit rate, and find the relationship between the volume of a cylinder and a cone. A poem, a short story, and a young adult novel are discussed.…

Spatial visualization is an important skill that deserves instructional attention. Strong evidence supports the claim that "measures of mathematical ability tend to be strongly correlated with spatial ability" (Anderson 2000). Thus, there is every reason to believe that time spent helping students develop their spatial visualization skills will…

This article describes using area and ratio concepts to examine why some animals, or people wearing different types of shoes, sink into the surface on which they are standing. Students compute "sinking values" to explain these differences. (Contains 2 figures.)

Traditionally, students learn arithmetic throughout their primary schooling, and this is seen as the ideal preparation for the learning of algebra in the junior secondary school. The four operations are taught and rehearsed in the early years and from this, it is assumed, "children will induce the fundamental structure of arithmetic" (Warren &…

It seems self-evident that there is a significant gap between secondary school and university mathematics, even though the gap may take different forms, which vary with different education systems in different places and at different times. This paper attempts to capture some common forms of this gap, and in particular, it discusses some core…

Mathematical optimization problems are not typical in the classical curriculum of mathematics. In this paper we show how several generalizations of an easy problem on optimal transportation were solved by gifted secondary school pupils in a correspondence mathematical seminar, how they can be used in university courses of linear programming and…