This booklet summarizes the mathematics chapter from "Handbook of Research on Improving Student Achievement", published by the Educational Research Service (ERS). The Handbook is based on the idea that, in order to succeed, efforts to improve instruction must focus on the existing knowledge base with respect to effective teaching and learning. The…

This issue of ENC Focus focuses on the topic of inquiry and problem solving. Featured articles include: (1) "Inquiry in the Everyday World of Schools" (Ronald D. Anderson); (2) "In the Cascade Reservoir Restoration Project Students Tackle Real-World Problems" (Clint Kennedy with Advanced Biology Students from Cascade High…

A problem-solving lesson is described, with a worksheet involving the gauges on a car's instrument panel. (MNS)

Highlights findings from cognitive science which suggest new approaches for science and mathematics instruction, addressing role of naive theories and qualitative understanding of situations in problem-solving. Also considers nature of the learner based on the findings. (JN)

Investigated the effects of individual difference variables of field dependence/independence and spatial visualization ability on the performance of college students in three modes. The extent to which four variables account for variability in retention test performance on certain tasks was also viewed. (MP)

Tenth graders solved mathematical problems assisted by varying amounts of help from their teacher. Significant differences occurred between students receiving aid and the unaided control group. Partial assistance resulted in better immediate performance, but this difference was less observable three weeks later. (Author/GDC)

This article describes the positive outcomes of a 3-week residential program on mathematics problem solving for gifted rising high school seniors. The program incorporated a curriculum that integrated five process standards espoused by the National Council of Teachers of Mathematics including problem solving, reasoning and proof, communication,…

Describes how using spreadsheets helped seventh grade algebra students develop problem-solving skills. Topics include the functional dualism of the spreadsheet as a text, uniting enactive and numeric modeling of word problems, new meanings and reciprocal learning, learning through problem "posing," higher levels of thinking, and decreasing…

This article describes "Hot Math," a third-grade intervention conducted with small groups of students with disabilities or in inclusive classrooms that fosters mathematical problem solving. Hot Math integrates two promising practices to promote mathematical problem solving, explicit instruction about transfer and self-regulation strategies.…

Presented is a study which focused on using turtle graphics programing for geometric problem solving. The goal was to investigate changes in children's mathematical knowledge and results indicate that the LOGO environment enriched children's geometric conceptualizations and sophistication of their geometric thinking. (KR)

Described are activities involving higher order thinking skills developed for gifted students that can be used for all students. Discussed is a framework for designing activities using Bloom's Taxonomy of the Cognitive Domain and William's Student Behaviors. Sample activities are included. (KR)

Discussed is the importance of incorporating calculators and computers into the primary grades. Number concepts, counting skills, place-value, basic operations, problem-solving, and higher order thinking skills can be reinforced by using calculators and computers along with manipulatives. (KR)

Describes teaching strategies that help students improve problem solving skills. Lists three factors good problem solvers were found to possess. Gives step by step instructions for solving problems. (MVL)

Describes Vygotsky's zones of proximal development, the importance of social interaction in learning through problem solving, and the benefits of modeling. Presents three implications for teaching and learning mathematics based on a teaching experiment focusing on these constructs. (MDH)

This article outlines the last step in a five-step process for preparing students to engage in a systematic mathematics problem-solving and decision-making process. The lesson plan teaches students to reread the problem, reexamine the question, check selection of operation, and recheck calculations and compare answers. (JDD)