Compares two experimental programs for teaching mental addition and subtraction in the Dutch second grade (N=275). Discusses realistic program design (RPD) and gradual program design (GPD). Concludes that RPD pupils show a more varied use of solution procedures than GPD pupils. Contains 46 references. (Author/ASK)

This article describes a teacher's techniques and strategies for promoting productive discourse and supporting active learning in the mathematics classroom. The lesson excerpts included are from two days of a workshop with primarily middle-grades teachers. These excerpts demonstrate the teacher's typical progression through defining a problem,…

This article explores how students learned to measure tall objects using a clinometer and some basic calculations. Such activities provide opportunities for students and teachers to learn the usefulness of linking mathematics content and science content to real-world problem-solving situations. (Contains 7 figures.)

This article elaborates on the basics of problem-based learning units and tips for implementation. The problem-based learning unit described focuses on the course of action involved in purchasing a new car. (Contains 2 figures.)

When students are working with hand held technology, such as graphics calculators, we usually only see the outcomes of their activities in the form of a contribution to a written solution of a mathematical problem. It is more difficult to capture their process of thinking or actions as they use the technology to solve a problem. In this paper we…

Relations among patterns of conceptual and procedural knowledge and grade were examined in 90 six- to eight-year-olds in order to explore addition and subtraction development. Conceptual knowledge was assessed by examining children's responses to pairs of problems reflecting various part-whole relations. Children solved related problems as part of…

This article describes a case study dealing with teacher?student reaction and cooperation during problem-solving activities within a class setting. The aim is to familiarize student mathematics teachers with the process of mathematics teaching with computers and to help them re-examine their traditional views of mathematics learning and teaching.…

Integrating mathematics with family and consumer sciences (FCS) has enabled youth to pass the Minnesota 8th Grade Math Basic Skills test. The test focuses on the eight content areas: (1) problem solving with whole numbers and fractions; (2) problem solving with percentage/ratio; (3) number sense; (4) estimation; 5) measurement; (6) tables and…

Many mathematics educators have found that prospective elementary school teachers' beliefs interfere with their learning of mathematics. Often teacher educators consider these beliefs to be wrong or naive and seek to challenge them so prospective teachers will reject them for more generative beliefs. Because of the resilience of prospective…

The study describes students' patterns of thinking for statistical problems set in two different contexts. Fifteen students representing a wide range of experiences with high school mathematics participated in problem-solving clinical interview sessions. At one point during the interviews, each solved a problem that involved determining the…

This document presents ideas and activities for teaching algebra. The section on "Week by Week Essentials" provides seven resources in a weekly format. It includes writing ideas that provide an algebra prompt and requires students to organize their thoughts and present them in a coherent fashion, and connections to the real world that…

The theory of individual preferential choice is a descriptive theory for the resolution of conflict within the individual. If there is only a single peaked preference function, it is relatively easy to find the preference. Under a multipeaked preference function, an optimal choice can be insured only after an exhaustive, costly search. Therefore,…

When mathematics is used to help people cope with real-life situations, a three-stage intellectual process is involved. An operational instrument for assessing how a person moves from the first to the second and third stage is proposed. (Author)

The article suggests possible reasons for difficulties with verbal (word) problems and describes two remediation strategies: re-teaching the introductory sequence for an operation and having students write their own problems. (CL)

This paper reports on the vital role that reflective thinking plays in solving problems involving the mathematics of change and variation particularly multivariable calculus. We report on how reflective thinking is one kind of self-regulatory (in the sense of metacognitive) thought mechanism. We present an outline of the results of a larger study,…