Details a lesson that utilizes trigonometric identities to determine the optimal angle between the atoms of covalent bonds. Generates a proof of the optimal angle for a molecule with four identical atoms bonded to a central atom that has a complete valence shell. (DDR)

Explores how prospective elementary teachers (n=106) enrolled in elementary science and mathematics methods courses used algebraic reasoning to construct and describe relationships among and between variables in the context of solving a problem. Describes specific weaknesses characterized by the teachers' solutions. (Contains 17 references.)…

A study examined the combined effects of class wide instruction on performance assessment tasks and problem solving instruction in ad hoc tutoring in mathematics on six students with learning disabilities. The two interventions led to demonstrable differences over time when compared to students who did not receive this kind of instruction.…

Investigates the effect of collaboration on problem-solving performance and learning in the context of a complex, video-based mathematics problem. High-achieving 6th-grade students (N=96) were assigned to collaborative or individual problem-solving conditions. Results reveal that students in the collaborative condition outperformed students in the…

Studied the relation between reading comprehension and task-specific strategies used in arithmetic word problems. Results with 20 9-year-olds of different competencies in reading and mathematics show a linear relation between reading comprehension and target strategies used in the word problems as well as a relationship between reading and IQ.…

Studied structures and relationships in one-step additive and multiplicative problems solved by 450 students in grades 2, 3, and 4. Results show that the facility ratio of the problems differs by structure, situation, and the sequence of data. The ability to solve one-step problems increases with age, but relative problem difficulty is grade…

Thirty-three college students with deafness and 10 typical students were given 30 mathematics problems to solve, 15 that were word problems. As the complexity of the descriptive information in the word problems increased along with the complexity of the problem situations, the performance of students with deafness decreased. (Contains references.)…

In this study, we investigated the fluency with which first graders of different mathematical achievement levels applied multiple, school-taught strategies for finding arithmetic sums over 10. We characterized children's strategies with the 4 parameters of Lemaire and Siegler's (1995) model of strategy change (strategy repertoire, distribution,…

This research study involved both quantitative and qualitative analysis of elementary teachers' problem-solving skills before and after a focused summer intervention program. Following research-based recommendations for effective professional development, the researchers developed and implemented a program to teach general problem-solving…

This article features NASA's FlyBy Math, a series of six standards-based distance-rate-time investigations in air traffic control. Sixth-grade students--acting as pilots, air traffic controllers, and NASA scientists--conduct an experiment and then use multiple mathematical representations to analyze and solve a problem involving two planes flying…

Genetics is often a fascinating but difficult subject for middle level students. They can see the results of genes in every organism, but trying to visualize what happens at the level of genes is challenging for concrete thinkers. The author discusses an approach that helps students understand how genotypes can translate into phenotypes, then…

Previous studies have shown that even preschoolers can solve inversion problems of the form a + b - b by using the knowledge that addition and subtraction are inverse operations. In this study, a new type of inversion problem of the form d x e [divided by] e was also examined. Grade 6 and 8 students solved inversion problems of both types as well…

This paper describes the problem-solving behaviors of 12 mathematicians as they completed four mathematical tasks. The emergent problem-solving framework draws on the large body of research, as grounded by and modified in response to our close observations of these mathematicians. The resulting "Multidimensional Problem-Solving Framework" has four…

This article describes the results of a year-long exploration of first graders' tool use. It also showcases instructional activities designed to link tool use with quantitative understanding. (Contains 3 figures.)

Technological tools have the potential to offer students the possibility to represent information and relationships embedded in problems and concepts in ways that involve numerical, algebraic, geometric, and visual approaches. In this paper, the authors present and discuss an example in which an initial representation of a mathematical object…