This paper describes the use of quantities in video games by young people as part of a broader effort to understand thinking and learning across naturally occurring contexts of activity. Our approach to investigating the use of quantities in game play is ethnographic; we have followed eight children over a six-month period as they play their own…

This article allows students to apply their knowledge and experience of area and volume to find the volume of Norris Lake, a large reservoir lake in Tennessee. Students have the opportunity to demonstrate their skills in using maps and scales as well as to incorporate the use of technology in developing the solution. This project satisfied the…

Do typical arithmetic problems hinder learning of mathematical equivalence? Second and third graders (7-9 years old; N= 80) received lessons on mathematical equivalence either with or without typical arithmetic problems (e.g., 15 + 13 = 28 vs. 28 = 28, respectively). Children then solved math equivalence problems (e.g., 3 + 9 + 5 = 6 + __),…

Solving indeterminate algebraic equations in integers is a classic topic in the mathematics curricula across grades. At the undergraduate level, the study of solutions of non-linear equations of this kind can be motivated by the use of technology. This article shows how the unity of geometric contextualization and spreadsheet-based amplification…

Poor math performance is a major concern leading the current educational reform agenda. Many educational math critics are claiming a math crisis. Researchers and school personnel are trying to resolve this crisis. Some are looking at curriculum-based evaluation (CBE) as a process for solving this problem. CBE and curriculum-based measurement (CBM)…

This article describes one seventh-grade teacher's classroom efforts to integrate traditional exercises from different content areas to form more robust questions that provide genuine problem-solving opportunities for students. These exercises are illustrated by connecting the Pythagorean theorem with a variety of prealgebra topics. Since the…

This article addresses the issues of coaching and assessing. A preservice middle school teacher's unique solution to the Pizza problem was not what the professor expected. The student's solution strategy, based on sequences and a reinvention of Pascal's triangle, is explained in detail. (Contains 8 figures.)

The purpose of this study was to explore patterns of difficulty in 2 domains of mathematical cognition: computation and problem solving. Third graders (n = 924; 47.3% male) were representatively sampled from 89 classrooms; assessed on computation and problem solving; classified as having difficulty with computation, problem solving, both domains,…

Uniformity, that is, equiprobability of all available options is central as a theoretical presupposition and as a computational tool in probability theory. It is justified only when applied to an appropriate sample space. In five studies, we posed diversified problems that called for "unequal" probabilities or weights to be assigned to the given…

This article proposes four strategies for posing mathematics problems that raise the cognitive demands of the tasks given to students. Each strategy is illustrated with three common middle school mathematics examples: finding the greatest common factor, finding area or perimeter, and finding the equation of a line. Posing these types of problems…

Finding real-world examples for middle school algebra classes can be difficult but not impossible. As we strive to accomplish teaching our students how to solve and graph equations, we neglect to teach the big ideas of algebra. One of those big ideas is functions. This article gives three examples of functions that are found in Arches National…

Inequalities are considered among the most useful tools of investigation in pure and applied mathematics; yet their didactical aspects have not received much attention in mathematics education research until recently. An important aspect of teaching problem solving at the secondary level deals with the notion of equivalence of algebraic…

The present study explores pupils' constructed definitions of the concept of function in relation to their abilities in dealing with tasks of functions involving different forms of representations and problem solving tasks. A major concern is also to examine the interrelations between these three ways of thinking about or dealing with the concept…

A cross-curricular structured-probe task-based clinical interview study with 44 pairs of third-year high-school mathematics students, most of whom were high achieving, was conducted to investigate their approaches to a variety of algebra problems. This paper presents results from one problem that involved solving a set of three linear equations of…

In this article, the author relates how he found "MT202" full of interest and how he was fascinated by the number of threads he found running through it. He then describes how he weaved together these threads. (Contains 1 table.)