Reports on a study in which three 3rd grade students were presented with the volume of cuboids. Examines the problem solving actions students demonstrate and analyzes students' strategies and solutions. Explores the connection between spatial structuring and the use of numerical operation. Considers perseverance and control emerging when solving…

Provides a first-person perspective on problem solving in an undergraduate history of mathematics course. Highlights social and material resources for problem solving. Generalizes primary factors affecting perceptions of a problem. Discusses the influence of factors on the personal perceptions of problem difficulty. Includes analyses of resources…

Studied the differences between metacognitive behaviors exhibited by (n=6) graduate students in mathematics and (n=9) freshman college students. Experts possessed and used schemas to solve problems, but schema use did not fully or adequately characterize expertise. Beliefs about cognition played a more important role than control of cognition. (23…

Eighty-six college students studied solutions of simple and complex word problems and then used the examples to construct algebraic equations as the frequency of referral to example was recorded. Students did not always select the appropriate example, and ability to select appropriately did not interact with aptitude. (SLD)

Presents exercises that analyze the additive property of energy. Concludes that if a body has more than one component of energy depending on the same physical quantity, the body's total energy will be the algebraic sum of the components if a linear relationship exists between the energy components and that physical quantity. (JRH)

Reports, in French, an investigation on the use of graphic representations in problem-solving tasks of the type in Spanish Mathematical Olympiads. Analysis showed that the choice and interpretation of the first graphic representation played a decisive role in the discovery of the solution. (34 references) (Author/MKR)

Described is an experience in assigning mathematics problems that have been purposefully selected from professional journals to assist upper level college mathematics students in developing confidence in their ability to contribute published solutions. Several examples are included. (JJK)

Hypothesizes that the incidence of process-oriented thinking increases with the syntactic complexity of the problem presentation. Presents data confirming students' arithmetic preferences in the form of left-to-right translation along with evidence to show the effects of the ordering of data presentation in the problem statements on the…

Discusses a method that uses spreadsheets to calculate the exact distribution of the sum of two or more discrete random variables with arbitrary distributions. Demonstrates how this method can be used to investigate several problems that would be found interesting at the elementary level. (Author/ASK)

Describes a way to assign points to the problem-solving process. Provides a rubric-scoring example. (ASK)

Focuses on changes in attitude toward mathematics and calculator use and changes in how general mathematics students naturalistically solve algebraic problems. Uses a survey to determine whether a student is rule-based. Concludes that the rule-based students used an equation to solve the algebraic word problem whereas the non-rule-based students…

Studies the effects of a course encouraging cooperative problem solving and reflection on thinking activities on students' attitudes. Reports that a majority declared negative attitudes but during the problem-solving course, the changes were almost all in the desired direction. Contains 18 references. (Author/ASK)

Discusses the use of techniques from language experiences in assisting with the learning and assessment of mathematics. Provides a mathematics activity on fractions employing story writing activities. (ASK)

Discusses the importance of writing in mathematics classrooms and offers an alternative to journal writing. Presents "Chris and Pat Writing Activities" designed to help students better understand concepts by making decisions about who has used correct skills to solve a mathematical problem. (ASK)

Lists several problems that have proven to be successful in getting students to think about topics and notions they thought they knew. Indicates that students have not only solved the conundrums (often with help), but also developed them further into research projects. (Author/ASK)