Proposes that problem scenarios are activities that give students opportunities to employ mathematics across the curriculum by asking them to define problems, identify information needed and potential sources of data, and make related conjectures. Discusses an example of a scenario involving transportation. (MDH)

Presents two spreadsheets for middle school students applying Polya's heuristic to help develop number sense, reasoning abilities, and problem-solving skills. Spreadsheet 1, "the coin problem," allows students to vary coin quantities to total $8.32. Spreadsheet 2, "ratios," develops number relationships while finding 3 3-digit…

Discusses and provides sample lessons of learning by discovery and weekly problem sets, which are presented as alternative methods for teaching college calculus. Both approaches stress conceptual understanding and guide the students to explore the ideas of calculus in small groups in a computer laboratory setting. (JJK)

Presents and discusses assumptions for a general-mathematics problem-solving curriculum that incorporate the belief that all students can do algebra, geometry, and trigonometry, that mathematics must be presented in problem situations, and that students should work cooperatively. Worksheets provide exemplary problem-solving activities. (MDH)

Presents results of 46 randomly selected children's performance measurement and partitive division problems when remainders are zero, nonzero but not used in the solution, and nonzero and used in the solution. Results indicate that children demonstrate an understanding of division prior to formal instruction. (MDH)

N:4$2 N:4$N Reported are results of a Technical Education Research Centers (TERC) project describing telecommunication interactions between groups of students using the computer software unit "Connectany." Polygons are formed through repetitive "jumps" between points on a circle. Investigation questions and results are shared…

Associations between performance-oriented and structure-oriented tasks in elementary school mathematics instruction and achievement were studied for 33 third grade classrooms. A mathematics pretest and posttest were administered, and classroom observations were conducted. Results suggest that performance-oriented tasks promote automatization of…

Presented are four activities that focus on gathering and interpreting data about pizza as a basis for integrating mathematics, health, and social studies. Reproducible sheets for parents to use with their children, class-activity sheets, and a data sheet are provided. Each activity includes the objective, needed materials, directions, extensions,…

Examined cognitive processing and performance of 12 average seventh-grade students during cooperative problem solving. Factors that impeded performance included lack of an experiential framework, imposition of unrequired restrictions, lack of individual monitoring of cognitive activity, and unproductive beliefs. Factors that enhanced performance…

Reports a case study in which a first-grade teacher's instructional decisions were affected by the pedagogical content knowledge concerning problem solving received during a four-week summer workshop on teacher's beliefs about teaching in conjunction with the teacher's beliefs that students can solve any problem they are given. (MDH)

A within-subjects design was used to compare two instructional methods--explicit timing and interspersing--with 187 second-grade students. Students completed two mathematics word problem assignments under differing conditions. In the explicit timing condition, students were told they would be timed while working long mathematics word problems. In…

This article presents essential principles for mathematics instruction for students with disabilities and those who are at risk for school failure. These students have great difficulty in applying algorithmic knowledge to solve problems and even greater difficulty with abstract problem solving associated with higher level mathematics. A procedural…

This paper describes a limited longitudinal study of young children's early numeracy development within three testing cycles, at the mid-point and towards the end of their reception year (at five years-of-age) and again at the mid-point of Year 1 (at six years-of-age), located within the broader context of progress through to Key Stage 1 SAT…

During 3 field experience visits, 23 elementary preservice teachers implemented mathematical problem-solving tasks with grade 3-6 gifted students. Researchers investigated what the teachers learned about gifted students regarding student characteristics, mathematical problem-solving tasks, and pedagogy. Each teacher completed a pre- and…

The National Science Foundation funded Calculators and Mathematics Project, Los Angeles (CAMP-LA) developed curriculum materials focused solely on the use of calculators. The project was developed in three stages. The first stage studied the mathematics curriculums from different states and identified topics that are not included but should be if…