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…

In this paper, the properties of tangential and cyclic polygons proposed by Lopez-Real are proved rigorously using the theory of circulant matrices. In particular, the concepts of slippable tangential polygons and conformable cyclic polygons are defined. It is shown that an n-sided tangential (or cyclic) polygon P[subscript n] with n even is…

Specific examples are used to discuss assessment, an integral part of mathematics instruction, with problem posing and assessment of problem posing. General assessment criteria are suggested to evaluate student-generated problems in terms of their quantity, originality, and complexity.

Sixty-five fourth-grade, fifth-grade and sixth-grade teachers in the Midwestern United States participated in professional development opportunities designed to increase their mathematics content knowledge and pedagogical knowledge over a two-year series of workshops. Through the use of pre-tests and post-tests assessing content knowledge and…

This paper offers a tutoring model its objective is to develop and establish the pedagogical-disciplinary knowledge of prospective computer science teachers with respect to guiding learners in problem-solving processes. The paper presents the tutoring model and the research that accompanied its implementation. The research findings indicate that…

This document contains the second volume of the proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education. Conference papers are centered around the theme of "Learners and Learning Environments." This volume features 43 research reports by presenters with last names beginning between Adl…

This study examined the effects of an inductive multimedia program, including graphs, on subjects' ability to create linear functions and conceptualize variables from word problems. Subjects were 98 undergraduate students in two sections of a computer literacy course. Students' achievements were assessed via pre- and posttests, which were parallel…

The purpose of this practicum was to determine if adult students engaged in training for high technology jobs can realize a time savings if customary or metric units of measure are used for practical mathematical calculations. Two quizzes were developed, and validated, using customary and metric units for the same type of problem, and the time to…