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…

The great gorilla jump is an activity designed to allow calculus students to construct an understanding of the structure of the Riemann sum and definite integral. The activity uses the ideas of position, velocity, and time to allow students to explore familiar ideas in a new way. Our research has shown that introducing the definite integral as…

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…

Presents a word problem designed to encourage students to create systematic methods for counting and develop probability concepts. Involves sharing eight cookies between three people. (KHR)

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…

Presents activities to incorporate Polya's four-step problem-solving process. (KHR)

Discusses a problem that appeared in the September, 1999 issue of this journal and presents solutions from students in grades 2-6. The question involved using colored cubes rearranged to make different stacked towers. (KHR)

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…

Determines which chessboards contain a chromatic rectangle having all four corners the same color for any black-white coloring. Expands the problem to a three color problem. (YP)

Analyzes fifth graders' approaches for solving the problem of the distance to the horizon. Describes determining the area bounded by the horizon. (YP)

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)

Describes a class activity in which students create word problems associated to specific arithmetic problems that are then edited in their English class. Using the computer laboratory and a word-processing program under the supervision of the media specialist, the problems are compiled in a booklet, printed, and distributed. (MDH)