Presents a study that indicates that second grade students (n=117) do select manipulatives that match the story context in measurement and partition division word problems, that they can solve division word problems, especially when matched manipulatives are used, and that division without remainders are more accessible to solution. (39…

The use of restricted item response models to test hypotheses regarding item difficulty ordering and slope uniformity was demonstrated in a study in which 597 algebra students were asked to solve word problems reflecting various types of cognitive processing. Benefits and limitations of the procedures are discussed. (SLD)

Children's (n=70) solution strategies to a variety of multiplication and division word problems were analyzed to determine performance levels and strategies used. Solution strategies were classified at three levels: direct modeling with counting; no direct modeling with counting, additive, or subtractive strategies; and use of known derived facts.…

Six experiments with 42 kindergartners, 190 first graders, and 15 second graders in Germany investigated why arithmetic word problems with an unknown reference set are more difficult for children than are problems with an unknown compare set. Lack of access to flexible language use makes these problems so difficult. (SLD)

Summarizes 14 mathematics word-problem-solving intervention studies for elementary and secondary students with disabilities or who were at-risk for math failure. Interventions included representational techniques (diagramming), strategy-training procedures (cognitive and metacognitive), task variations (sequencing and word-problem context), and…

Reports a study to examine secondary school students' (n=200) responses to two figurally and spatially similar problems from mathematics and science that require different responses before and after instruction. Results indicated that most students gave the same response to both questions. Reasons for this pattern are discussed. (MDH)

The purpose of this study was to examine the cognitive correlates of RD-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. Third graders (N = 312) were measured on language, nonverbal problem solving, concept formation, processing speed, long-term memory, working memory, phonological decoding, and sight word…

This report describes a computer-based instructional system, the Story Problem Solver (SPS). SPS provides students with instruction about the semantic structure of story problems. It was developed to test a specific schema theory of knowledge organization in long-term memory. For this reason SPS depends explicitly upon a theory of the relationship…

This article describes the Mathematical Problem Solving Assessment-Short Form, an evaluation tool to assess various affective factors, cognitive and metacognitive factors, and strategies associated with mathematical problem solving of middle school students. The theoretical basis for the test is discussed and an actual student protocol is used to…

Describes seven problems designed to enhance the development of four types of student communication in mathematics: (1) describing observations; (2) justifying solutions and solution processes; (3) documenting thinking; and (4) completing or creating mathematical problems. (MDH)

Imagery use in high school mathematics classrooms was studied. A visual image was defined as a mental scheme depicting visual or spatial information, but this definition was not spelled out to teachers or students, in order to learn what they meant by the concept. Subjects were 13 high school teachers and 54 of their students interviewed over 3…

Describes a teaching experiment that evaluated published supplemental materials used to aid preparation of lessons at the fourth grade level involving nonroutine word problems. Lists 12 insights gained that can be useful to teachers using commercially produced problem-solving materials. (MDH)

Presents the results of a survey of 165 seventh grade students asked to respond yes, no, or maybe to 21 metacognitive statements about their cognitive activity on a mathematical word problem. Suggests how to use the responses as a basis for developing classroom activities. (MDH)

Presents a study of 87 second graders to demonstrate that achievement tests in primary mathematics emphasize pupil's lower-order thinking by comparing answers to interview questions from constructivist and traditionally instructed groups. Results indicated that constructivist instructed students demonstrated superior higher-order thinking on tasks…

The purpose of this research was to understand fifth grade children's cognitive behavior as they wrote, solved and then, in small groups, shared original math story problems. Research questions examined children's: (1) beliefs about math in this problem-writing classroom, (2) math story problem-writing behavior, (3) difficulties with their…