This guide to mathematics education is designed to provide direction for teachers and administrators in the development and evaluation of school mathematics programs. The skills and knowledge of mathematics are seen by the Hawaii Department of Education to be of significant importance in our society, with the Department assuming primary…

Types of strategies used by (n=36) fourth-, sixth-, and eighth-grade students solving comparison of area tasks were identified and classified. Most students used a direct comparison strategy to compare areas. Use of a part-whole strategy increased with the introduction of fractional terms and symbols. (23 references) (MKR)

Thirty-six Korean first graders were interviewed to study their ability solving addition problems with sums of 10, single-digit sums between 10 and 18, and subtraction problems with minuends between 10 and 18. Finger methods to show sums over 10 and the regular named-10 Korean number words supported their learning of 3 efficient recomposition…

Presents a study that indicates that second grade students (n=117) do select manipulatives that match the story context in measurement and partition division word problems, that they can solve division word problems, especially when matched manipulatives are used, and that division without remainders are more accessible to solution. (39…

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…