Twenty-four mathematics teachers were asked to think aloud when posing a word problem whose solution could be found by computing 4/5 divided by 2/3. The data consisted of verbal protocols along with the written notes made by the subjects. The qualitative analysis of the data was focused on identifying the structures of the problems produced and…

The purpose of this study was to replicate and extend a previous study by Burns ("Education and Treatment of Children" 28: 237-249, 2005) examining the effectiveness of incremental rehearsal on computation performance. A multiple-probe design across multiplication problem sets was employed for one participant to examine digits correct per minute…

We confronted 151, 5th and 6th elementary grade pupils with a quantitative problem in a mathematics or religion class, to examine the influence of the context on pupils' understanding and solution of such problems inside and outside the mathematics class. Pupils were first asked to solve a problem about fair sharing either during a mathematics or…

The study of preservice elementary teachers' knowledge of fractions is important because fractions are notoriously difficult to learn and teach. Unfortunately, studies of preservice teachers' fraction knowledge are limited and have focused primarily on division. The present study included all four operations to provide a more comprehensive…

First of three experiments compared third graders who had studied worked, two-step arithmetic word problems to those learning through conventional problem solving. The former grouped showed superior test performance. In experiments two and three, children presented with integrated worked examples outperformed those presented with split-source…

This report analyzes the discursive interactions of four students to understand what heuristic methods they develop as well as how and why they build isomorphisms to resolve a combinatorial problem set in a non-Euclidian context. The findings suggest that results of their heuristic actions lead them to build isomorphisms that in turn allow them to…

Two related studies are reported about the (lack of) activation of real-world knowledge in elementary school students' understanding and solution of school arithmetic word problems. In the first study a set of word problems was collectively administered to 75 fifth-graders during a typical mathematics lesson. Half of the problems were standard…

Classifies children's solution strategies by degree of abstraction and by use of physical objects. Children in grades one, two, and three were given two multiplication and four division word problems that differed in semantic structure. (Author/YP)

Examines the students' understanding of mathematical structure and the relationship between problem solving and the identification of the structure in 13 word problems. Multidimensional scaling and hierarchical cluster analysis were used to assess how subjects organized word problems in their minds. (YP)

Examines whether verbal problem-solving skills in a group of fourth graders would improve if they were specifically taught how to generate their own diagrams when solving word problems. Classifies textbook word problems into three general types and describes them: (1) tabular; (2) geometric; and (3) contingency diagraming. (YP)

This study examines the construct of problem representation and the processes used by learners to construct or modify problem representations in problem-solving situations. Students (n=14) from freshman calculus courses at the University of California at San Diego participated in videotaped interviews in which they were asked to think aloud as…

Studied schemes involved in solving two-step arithmetic word problems in (n=1824) elementary schoolchildren in Israel. Compound schemes and combinations of operations were found to affect the difficulty level of the problems. Appendix includes two versions of the test instrument. (Contains 17 references.) (MKR)

In 1986 the United States (U.S.)-Japan Seminar on Mathematical Problem Solving convened to compare the state of problem solving in the classroom and in research in the two countries. The data and results given in this paper are the results of research conducted in the United States in response to the 1986 seminar. The U.S. and Japanese research…