Use of a checkbook can hook even the most reluctant mathematics students into learning mathematical and problem-solving skills. (CB)

Students' reported inner speech during mathematics problem solving was studied. Subjects from grades three to six were assigned to low-task or high-task difficulty groups. Between problems, students reported their inner speech. Both groups maintained an adaptive task-oriented problem-solving stance, with positive affect toward self. (Author/GDC)

Examines principles which can be applied to determine how hints can be used effectively in problem-solving. Conscious and unconscious hints, timing of hints, expected functions, and teaching are discussed. Conscious hints are explained in detail with suggestions and references. Charts are included for types, timing, and expected functions. (DH)

The ratio factors approach involves recognizing a given fraction, then multiplying so that units cancel. This approach, which is grounded in concrete operational thinking patterns, provides a standard for science ratio and proportion problems. Examples are included for unit conversions, mole problems, molarity, speed/density problems, and…

An interdisciplinary unit on investigation guides gifted students up to age 14 through problem solving activities in language arts, mathematics, science, and social sciences. (CL)

Discusses five research areas offering guidance to people concerned about teaching problem solving in elementary schools. Areas are (1) components of problem difficulty; (2) the contribution of reading difficulties to problem-solving deficiencies; (3) characteristics of successful problem solvers; (4) children's use of problem-solving techniques…

The section includes four articles on the use of computers for gifted students. Topics covered include basic information for parents, care and operating routines, a curriculum guide for computer literacy, the computer's role in problem solving, and computer applications for mathematically gifted students. (CL)

The purpose of this study was to introduce the Mole Solver, a computer based system that facilitates monitors and improves students' problem solving skills on mole concept. The system has three distinct modes that: (1) find step by step solutions to the word problems on the mole concept; (2) enable students to solve word problems on their own by…

Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend to blend conceptual physics with mathematical symbolism in a way that profoundly affects the way equations are…

Fact-filled textbooks that stress memorization and drilling are not very good for teaching students how to think mathematically and solve problems. But this is a book that comes to the rescue with an instructional approach that helps students in every grade level truly understand math concepts so they can apply them on high-stakes assessments,…

This study investigates how measured problem solving abilities differ by students' mathematics curriculum, traditional or National Council of Teachers of Mathematics (NCTM) Standards-oriented, when a non-paper-and-pencil test is used as the source of measurement, and if the proposed rubric is efficient and effective for scoring the…

This chapter examines research on the cognitive processes involved in mathematical problem solving. The introduction includes definitions of key terms and a summary of four cognitive processes used in mathematical problem solving: (1) translating; (2) integrating; (3) planning; and (4) executing. Examples are then provided and exemplary research…

Teaching can be understood as acting and deciding in a complex system. On that problem oriented mathematics instruction (POMI) can be characterized as very high complex particularly regarding to mathematical-cognitive aspects. To cope with resulting demands in the long run, the teacher has to be sensitive for this complexity. But what does this…

This book introduces students to the types of problems and processes used throughout the "Reshaping Mathematics for Understanding" series. The problems in this unit deepen students' understanding of mathematics by encouraging them to clarify concepts and challenge their own assumptions. Additionally, by providing opportunities to give and follow…

An action research project, the aim of which was to bring powerful mathematics to females to help them develop a clear conceptual understanding and passion for the subject, and to nurture independent learning skills that will translate into all aspects of their lives, is discussed. This book investigated one strategy for providing girls with…