Tested three models of children's mathematics word-problem solving based on developmental differences in quantitative conceptual structures: (1) quantitative relations represented as ordered array of mental objects; (2) numbers represented on two tentatively coordinated mental number lines; and (3) numerical operations represented as objects on…

Examined relations between algebraic word-problem attributes and students' strategies, errors, and problem difficulty. Found that constructed responses capture strategy formulation and high-level planning--as do traditional measures of quantitative reasoning--but are more sensitive to individual problem characteristics and procedural errors that…

Investigates gender-related effects of a problem-solving plan for sixth graders (n=155). Analysis indicates a significant interaction effect of occasion of testing, test sequence, and gender. Concludes that females benefited from free exploration, of problem situations followed by an organized exploration whereas males appeared to function equally…

Examines changes in the problem posing strategies of a group of elementary preservice teachers as they posed problems to pupils. Indicates that the teachers' problem posing practices were changed from posing traditional single steps and computational problems to multiple approaches and solutions with open-ended and exploratory problems.…

Explores 80 sixth- and seventh-grade students' self-reported use of 14 categories of strategies for processing mathematical word problems and the relationship of strategy use to academic achievement, problem-solving behaviors, and problem-solving success. A chart of categories of strategic behavior and examples from middle schools students is…

Introduces Hogben's adaptation of Zeno's paradox, "Achilles and the Tortoise", as a thinking and writing exercise. Emphasizes engaging students' imagination with creative, thought-provoking problems and involving students in evaluating their word problem-solving strategies. Describes the paradox, logical solutions, and students' mathematical…

Assesses the effects of explicitly teaching for transfer by broadening the categories by which students group problems requiring the same solution methods and prompting students to search novel problems for these broad categories. This transfer treatment was combined with instruction on solution methods. Improvement on immediate- and near-transfer…

Describes the history of the unsolved moving sofa problem, presents one possible solution, and gives several suggestions for how this problem can be used in the classroom. (Author/NB)

Describes how mathematical puzzles and riddles can be implemented in the classroom to engage students in rich mathematical explorations and logical reasoning. (YDS)

Examines the performance of deaf and hearing-impaired students in Queensland, Australia when solving arithmetic word problems. Subjects' solutions of word problems confirmed trends for learning students but their performance was delayed in comparison. Confirms other studies in which deaf and hearing-impaired students are delayed in their language…

Significant changes in the General Educational Development Math Test require a change in teaching methods. A structured problem-solving approach focused on applying principles and interpreting abstract data will stress process as well as content as required by the test. (SK)

The initial step of a strategic process for solving mathematical problems, "studying the question," is discussed. A lesson plan for teaching students to identify and revise arithmetic problems is presented, involving directed instruction and supervised practice. (JDD)

Experiments in strategy instruction for mathematics have been conducted using three models (direct instruction, self-instruction, and guided learning) applied to the tasks of computation and word problem solving. Results have implications for effective strategy instruction for learning disabled students. It is recommended that strategy instruction…

Discusses social and cognitive influences on understanding and solving word problems. Descriptions of studies with elementary school, secondary school, and college students highlight subject matter-related attitudes; the fact that students can solve problems without understanding them; and contextual expectations, including the issue of authority.…

Given are several examples of seemingly unrelated problems that nevertheless can be solved with a single mathematical idea--the proportion. It is hoped that as students see how a variety of problem contexts can be modeled by a proportion, they will use proportions more frequently in problem solving. (MNS)