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)

Divided into two parts, this article analyzes why some pupils feel reserve about instantaneous velocities and instantaneous flows. The second part relates reactions of pupils facing a problem that implicates the instantaneous rate of change. Describes some characteristics of this problem that enables the authors to explain its instructional…

Reports a correlational study to determine whether teacher's mathematics anxiety might inhibit the introduction of more problem solving and abstraction in elementary schools to enable more ninth graders to enroll in algebra. Correlations on 19 variables for 116 teachers indicated that anxiety decreased with increased mathematics content studied…

This article discusses the analysis of a decision-making process faced by contestants on the television game show "The Price is Right". The included analyses of the original and related problems concern pattern searching, inductive reasoning, quadratic functions, and graphing. Computer simulation programs in BASIC and tables of…

Proposes the use of children's literature as a method to connect language and mathematics. Presents examples of children's books by mathematical topic and methods by which they can be employed in mathematics instruction. (31 references) (MDH)

Discusses the two overgeneralizations "multiplications makes bigger" and "division makes smaller" in the context of solving word problems involving rational numbers less than one. Presents activities to help students make sense of multiplication and division in these situations. (MDH)

Reviews research on (1) schemata acquisition while learning mathematics and techniques for detecting schema in mathematics learners; and (2) assessment of the distribution of cognitive resources while learning mathematics that lead to the design of instructional techniques to facilitate schema acquisition. (26 references) (MDH)

Describes a step-by-step procedure that enables teachers to develop lessons that effectively use software or special calculators in the classroom. Problem-solving strategies and questions are determined that correspond to the technology through which students are able to construct their own knowledge. Illustrates the procedure using spreadsheets,…

This study of 60 eighth grade students found differences among students with learning disabilities and students who were low, average, and high achieving, on perceptions of ability and achievement; attitude toward mathematics; knowledge of mathematical problem-solving strategies; and knowledge, use, and control of problem representation…

Presents activities in which students develop and analyze scatterplots on graphing calculators to model corn growth, decay, a box of maximum volume, and weather prediction. Provides reproducible worksheets. (MDH)

Middle school students' (n=200) solutions to division-with-remainder story problems and their attempts to make sense of their answers were analyzed for evidence that supported or refuted hypothesized semantic-processing models. The models helped explain students' failure to solve these problems in school settings. (Contains 17 references.)…

Guided by Shulman, 1986 and Shulman, 1987 tripartate model of teacher expertise [subject matter knowledge (SMK), pedagogical content knowledge (PCK), and general pedagogical knowledge (GPK)], the present study examined 162 U.S. and Chinese 3rd grade mathematics teachers' expertise in teaching fractions. Results show that U.S. teachers lag…

The purpose of this study was to examine the effects of actively categorizing math problems on the math problem solving performance of students with and without attention deficit disorder (ADD). To this purpose, 52 fifth and sixth grade students were involved in actively categorizing or noncategorizing (control) tasks followed by two problem…

From a very young age, shoes for boys tend to be wider than shoes for girls. Is this because boys have wider feet, or because it is assumed that girls are willing to sacrifice comfort for fashion, even in elementary school? To assess the former, a statistician measures kids' feet. (Contains 2 tables and 3 figures.)

The overall purpose of this paper is to describe a practical and useful approach to mathematics assessment that is meaningful to teachers, students and families. The format is highly flexible, yet specifically designed to provide detailed information as to the performance characteristics of the student and a variety of curricula and instructional…