Explores the development of understanding of the concept of average with students from grades 3 to 9 through interviews. Observed six levels of response based on an hierarchical model of cognitive functioning. Documents usage of ideas associated with the three standard measures of central tendency and representation as strategies for problem…

Explores the mathematical problem posing and problem solving of U.S. (N=181) and Chinese (N=223) sixth-grade students. Reports that while Chinese students outperform U.S. students on computational tasks, there are many similarities and differences between U.S. and Chinese students in performing relatively novel tasks. Discusses the direct link…

Presents problems from the Mathematics in Context (MiC) project with a central theme concerning the construction of a variety of formulas by students. (AIM)

Suggests six characteristics of mathematical play. Analyzes the problem-solving process for the Six Circles and observations of students solving calculator and integration problems in relation to theories of play and cognitive gain. Discusses some difficulties of implementing a 'play' approach in the classroom and proposes further research…

Describes three open-ended response types that could broaden the conception of mathematical problem solving used in computerized admissions tests: (1) mathematical expression (ME); (2) generating examples (GE); and (3) and graphical modeling (GM). Illustrates how combining ME, GE, and GM can form extended constructed response problems. (SLD)

Introduces an activity in which students prove that milliliters and cubic centimeters are equal. Assigns students in groups for the activity and starts with a realistic story to increase student interest. (YDS)

Reports on (n=11) student attempts at 3 combinatorial questions focusing mainly on 3 aspects of strategy: (1) listing; (2) subdivision into cases; and (3) use or misuse of 4 standard formulas. (MKR)

It has become increasingly possible for mathematics students to include a limited number of approved optional, non-traditional modules in their programs. Surveys coursework in four non-specialist modules over a seven-year period, and examines work in the area of mathematical cognition. (Contains 16 references.) (Author/ASK)

Studies differences in boys' and girls' (N=158) mathematical problem-solving behavior in relation to two types of tasks, computations and applications. Differences were dependent on contents of tasks and gender. Girls rated themselves lower on confidence and attributed bad results more often to lack of capacity and to the task difficulty. No…

Examined the outcomes of academic support programs designed to enhance mathematical and scientific problem solving skills among African American pre-engineering college students. Interventions included weekly scientific reasoning and mathematical critical thinking and problem solving workshops, mentoring by upper-class students, and an interactive…

Exploration of collaboration preferences of six mathematically gifted children (ages 11-12) in solving complex, novel problems found collaboration was preferred only when the task was sufficiently challenging. When collaboration was encouraged there was the development of mutual scaffolding, shared cognition, critical thinking, and discernment and…

Discusses potential pedagogical difficulties arising from using physics-related contexts in high-school mathematics problems. Suggests that such problems should not require any external knowledge of physics by the students; meanwhile, the problems should not contradict the physics knowledge that the students may already have. Presents several…

Investigates the factors that influence the effectiveness of collaboration on open-ended mathematical tasks. Identifies various phenomena that influence cognitive "lifting", "hovering", and "falling"; that is, improvement, no change, and reduction in levels of functioning, respectively. (Author/MM)

This article describes a project in which certain key concepts in probability were explored using graphics calculators with year 10 students. The lessons were conducted in the regular classroom where students were provided with a Casio CFX 9850 GB PLUS graphics calculator with which they were familiar from year 9. The participants in the…

Many students view mathematics as a collection of theorems and facts that were discovered by intelligent mathematicians and all they have left to do is to study them carefully. Some believe it is important to help students change this view (Lavy & Shriki, 2003). One possible way is to enable students to modify the attributes of a given situation,…