Presents some results of a study on teaching negative numbers. Focuses on the identification of addition and subtraction, the use of the number line, additive problem solving, and the possibility of following several sequences of numerical extensions. Indicates the importance of previous ideas on positive numbers and how these ideas influence the…

Knowledge in academic disciplines is being challenged by the instrumentality of workplace learning. However, the way math is taught in vocational education is often irrelevant or infantilized. To satisfy the need for a creative, problem-solving work force, mathematical disciplinarity is needed. (Contains 68 references.) (SK)

Three sample physics problems are presented in this article. The solutions to the three problems addresses a major student difficulty in problem solving--knowing where to begin. The first suggested step is to begin by stating what is asked for. Step 2 is identifying the fundamental physics that underlies the problem situation. Step 3 is isolating…

Students should be given an opportunity to explore and conjecture with the help of new technology to become good problem solver. Ron Mclister, while using the Geometer's Sketchpad to explore the Pythagorean theorem, came upon a nice result about the relationship of some geometrical patterns.

Students solve a geometric problem of measuring polygons with the help of proportional reasoning. Thus the importance of conceptual reasoning is emphasized as a highly efficient technique for teaching and strengthening mathematical content.

A Mandelbrot mathematical set is an object with endless borders, and in the present exercise a graphing calculator is used to identify and examine the set points. The significance and power of technology is also displayed in the understanding and solving of problems.

The way in which a mathematical problem was used as a vehicle to introduce the joy of mathematical research to a high school student is demonstrated. The student was interested in learning about other classical problems delighting an eager high school student.

Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.

Often after students solve a problem they believe they have accomplished their mission and stop further exploration. The purpose of this article is to discuss ways to encourage students to "look back" so as to maximise their learning opportunities. According to Polya, by "looking back" at a completed solution, by reconsidering and re-examining the…

Five studies examined how interacting with the physical environment can support the development of fraction concepts. Nine-and 10-year-old children worked on fraction problems they could not complete mentally. Experiments 1 and 2 showed that manipulating physical pieces facilitated children's ability to develop an interpretation of fractions.…

Investigates how collaborative interactions influence problem solving outcomes. Analyzes conversations between 12 sixth grade triads using both qualitative and quantitative methods. Describes a dual-space model of what collaboration requires to clarify how the content of the problem and the relational context are interdependent aspects of the…

We argue that to test preschoolers' understanding of counting, one has to use tasks that relate counting to the goal of doing arithmetic, as counting and arithmetic principles are mutually constrained. A naturalistic study in the preschool classroom led to the development of an ''arithmetic-counting'' task, where counting was being related to the…

This paper is a workshop report of an empirical study called DISUM, which deals with appropriate teacher interventions in the course of students' independence-oriented modelling processes. The project aims at developing and investigating corresponding instructional conceptions, based on an intensive analysis of modelling tasks and of students'…

A method for generating sums of series based on simple differential operators is presented, together with a number of worked examples with interesting properties.

This paper focuses on the representation of a proper fraction "a"/"b" by a decimal number base "n" where "n" is any integer greater than 1. The scope is narrowed to look at only fractions where "a","b" are positive integers with "a" less than "b" and "b" not equal to 0 nor equal to 1. Some relationships were found between "b" and "n", which…