A growing consensus holds that preservice K-8 teachers (PSTs) need to experience the modeling process as learners to understand it and envision teaching modeling in their future classrooms. We examine this recommendation by exploring how PSTs construct models and how collaborative learning practices influence them in revising and refining their…

Studies have found that some teacher professional development programs that are based on Cognitively Guided Instruction (CGI) can increase student mathematics achievement. The mechanism through which those effects are realized has been theorized, but more empirical study is needed. In service of this need, we designed a novel measure of…

Previous research has shown that when confronted with missing-value word problems, primary school students strongly tend to use proportional solution approaches, even if these approaches are inappropriate. The authors investigated whether (besides the missing-value formulation of word problems) the numbers appearing in word problems are part of…

Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…

After a year of instruction, 70 kindergarten children were individually interviewed as they solved basic, multistep, and nonroutine word problems. Thirty-two used a valid strategy for all 9 problems, and 44 correctly answered 7 or more problems. Modeling provided a unifying framework for thinking about problem solving. (Author/MDH)

Argues for increased usage of non-linear regression models which could account for a greater percentage of the variance in the data than do linear models in educational studies. (JP)

Examined were the mental processes by which elementary school students work simple multiplication exercises. Ten process models were fit to data obtained in the course of a CAI program in elementary arithmetic. The processes used by students in grade three were compared with those used by students in grade six. (CT)

Characterizes students' function-concept images that arise in interactive environments based on multirepresentational software. Shows that students (a) often use prototypic functions (linear and quadratic) but do not consider them exclusive; (b) use prototypes as levers to handle a variety of other examples; (c) articulate justifications often…

Investigates 6th-grade students' use of equations to describe and represent problem situations prior to formal instruction in algebra. Describes students' preinstructional uses of equations to generalize problem situations and raise questions about the most appropriate curriculum for building on students' intuitive knowledge of algebra. (Contains…

Describes a study of preservice teachers (N=30) that provides confirming evidence that students usually use two rational number operator constructs. Discusses the cognitive models of the students' strategies and the notational system used as an analytical tool. Contains 22 references. (DDR)

Describes an exploratory teaching experiment carried out to test the hypothesis that it is feasible to develop a disposition toward more realistic mathematical modeling in pupils. The learning and transfer effects of an experimental class of 10- and 11-year-old students that were compared to the results of two control groups support this…

A model is proposed in which the quantification of inverse proportionality is developed beyond the initial qualitative relation. Based on a task analysis, the model was tested with 36 eleven-year-old students in a training experiment using a balance task. (MNS)

A concrete and a symbolic approach to learning multiplication in the second grade are studied. The results, indicating that children using the symbolic model performed at a higher level than those using a concrete model, are discussed. (DT)