Despite progress toward gender equity, troubling disparities in mathematical problem-solving performance and related outcomes persist. To investigate why, we build on recurrent findings in previous studies to introduce a new construct, "bold problem solving," which involves approaching mathematics problems in inventive ways. We introduce…

In this article, we use a two-dimensional assessment to examine the experimental impacts of a mathematics learning trajectory-oriented formative assessment program on student strategies for problems involving multiplication and division. Working from the theory that the development of students' multiplicative reasoning involves improvements in…

Although policy documents promote teaching students multiple strategies for solving mathematics problems, some practitioners and researchers argue that struggling learners will be confused and overwhelmed by this instructional practice. In the current exploratory study, we explore how 6 struggling students viewed the practice of learning multiple…

Discussions about school mathematics often address the importance of reasoning and proving for building students' understanding of mathematics. However, there is little research examining how teachers enact tasks designed to engage students in justifying and proving in the classroom. This article presents results of a study investigating the…

This study investigated the ways in which the technological tool, The Geometer's Sketchpad, mediated the understandings that high school Honors Geometry students developed about geometric transformations by focusing on their uses of technological affordances and the ways in which they interpreted technological results in terms of figure and…

Investigates 6th-grade students' use of equations to describe and represent problem situations prior to formal instruction in algebra. Describes students' preinstructional uses of equations to generalize problem situations and raise questions about the most appropriate curriculum for building on students' intuitive knowledge of algebra. (Contains…

Presents research in which mathematics teachers and educational researchers ordered arithmetic and algebra problems according to their predicted problem-solving difficulty for students. Analysis of students' problem-solving strategies indicates specific ways that students' algebraic reasoning differs from that predicted by most teachers and…

Examines the problem solving characteristics, strategy selection and use, and verification actions of African-American eighth-grade students (N=24). Indicates that students displayed approaches attributed to African-American learners, specifically the regular use of holistic reasoning. Concludes that success was correlated highly with strategy…

Students' strategies for solving long division problems under a realistic mathematics approach (RME) at Dutch primary schools were categorized in two ways: (a) according to the level of how students created multiples of the divisor (chunking) to be subtracted from the dividend; and (b) according to their use, or nonuse, of schematic notation.…

Investigated strategies that 7- to 12-year-old children (n=96) spontaneously applied in solving novel combinatorial problems. With experience in solving two-dimensional problems, children were able to refine their strategies and adapt them to three dimensions. Results on some problems indicated significant effects of age. (Contains 32 references.)…

Examines the scope and nature of upper elementary school pupils' difficulties with modeling and solving nonroutine additive word problems. Concludes that many errors result from the superficial, stereotyped approach of adding or subtracting two given numbers without considering the appropriateness of that action in relation to the problem context.…

Students (n=105) enrolled in a college remedial mathematics course participated in a one-semester experiment to determine whether cooperative learning would help students increase their problem-solving skills in mathematics. Results indicated significant differences in favor of students using cooperative learning in solving word problems in…

Discussed are the limitations of teaching general problem-solving strategies and techniques and their relationship to transfer of learning. The lack of evidence for effective teaching strategies, curriculum reform ramifications, and alternative teaching techniques are considered. (KR)

Examined is the relationship between junior high school students' directional reasoning about rates and numerical reasoning on proportion-related word problems. The relationship between the ability to solve context-free fraction exercises and the ability to solve mathematically similar word problems is discussed. (KR)

Described are the general problem-solving strategies and their nature and functions. The importance of integrating different types of general problem-solving strategies with content-specific teaching in mathematics classes is discussed. (KR)