Reports a study that investigated the effects of metacognitive instruction in mathematics on low achieving, predominantly Hispanic, elementary school students (grades 3-8). Students were randomly assigned to either experimental (metacognitive) or traditional instruction. Results on learning outcomes showed significant effects favoring students who…

Discusses possible approaches to solving the problem of how many different triangles can be formed on an n x n geoboard and the different geometric concepts utilized to formulate a solution. Approaches include counting strategies, writing a computer program, and using difference equations. (MDH)

Describes three activities that the teacher can employ to help students develop thinking skills through mathematics instruction: (1) memorization using the technique of chunking; (2) higher order thinking with magic squares; and (3) predicting games. Identifies eight facets of the teacher's role in promoting thinking skills. (MDH)

Presents real life vignettes of a fifth grade teacher teaching mathematics. The teacher intended her students to find mathematics engaging, work cooperatively, and solve problems that relate to real life experiences. Noted a questionable focus and outcome for the teaching activities. (BB)

Describes how college students enrolled in a course in elementary algebra apply graphing and algebra to data collected from a seismic profile to uncover the structure of a subterranean rock formation. Includes steps guiding the activity. (MDH)

This article uses a cognitive problem-solving model to explore the application of hypermedia authoring software to mathematics in general and to mathematical problem solving in particular. Hypermedia is presented as a method of exploring alternative solution processes to remediate or prevent learning problems. (JDD)

Discusses factors that influence the shapes of houses built in different cultures. Poses the problem of building a house with optimal floor space given a fixed amount of material for the walls. Discusses students' findings, questions raised during group discussions, and mathematical concepts utilized to solve the problem. (MDH)

The effects of problem solving and peer collaboration as two instructional methods advocated by the National Council of Teachers of Mathematics (NCTM) were evaluated for enhancing mathematics achievement, motivation, and self-concept of 104 low- achieving third and fourth graders. There were significant positive effects for both approaches, as…

This study examined the behaviors and experiences of students who needed assistance while working in peer-directed small groups on mathematics problems and the processes that helped or hindered their learning. Students in 4 seventh-grade classes worked in heterogeneous small groups throughout a 3-week unit on operations with decimal numbers.…

In the past decade, there has been an increased emphasis on the preparation of teachers who can effectively engage students in meaningful mathematics with technology tools. This study presents a closer look at how three prospective teachers interpreted and developed in their role of facilitating students' mathematical problem solving with a…

This study reports on the algebraic generalisation strategies used by two fifth grade students along with the factors that appeared to influence these strategies. These students were examined over 18 instructional sessions using a teaching experiment methodology. The results highlighted the complex factors that appeared to influence student…

This study describes the learning of researchers who engage in mathematics teacher education as an integral part of their practice. As teacher educators working with teachers on the subject of proportional reasoning, the authors reflected on teachers solutions to a standard problem and analyzed answers that would conventionally be considered…

This document contains papers presented at the 19th annual conference of the Mathematics Education Research Group of Australasia. Topics of the presentations include learning research, mathematical representations, problem solving, strategic learning behaviors, algebraic thinking and learning environments, teaching and learning of algebra,…

This study examined whether inclusion of cognitively guided instruction (CGI) in a mathematics methods course for 34 undergraduate preservice teachers at the University of North Carolina at Greensboro would improve their teaching performance, compared to controls. The Beliefs Survey, with four subscales (Role of the Learner, Relationship between…

The first volume of this proceedings contains an introduction and the plenary, research forum, working group, and discussion group papers. Papers include: (1) "Resources as a Verb: Recontextualizing Resources in and for School Mathematics" (Jill Adler); (2) "Markets and Standards: The Politics of Education in a Conservative Age" (Michael Apple);…