A typical form of thinking to approach problem solutions humanly is thinking in analogous structures. Therefore school, especially mathematical lessons should help to form and to develop corresponding heuristic abilities of the pupils. In the contribution, a summary of possibilities of mathematics lessons regarding this shall particularly be…

In mathematics instruction, can a teacher implement surface features of instruction that foster self-regulated learning as well as achieve quality at the deeper level of instruction, that is, focus on higher-order thinking, problem-solving, and mathematical modeling? An educational reform effort in Switzerland, which is based on constructivist and…

To explain human performance on the "Traveling Salesperson" problem (TSP), MacGregor, Ormerod, and Chronicle (2000) proposed that humans construct solutions according to the steps described by their convex-hull algorithm. Focusing on tour length as the dependent variable, and using only random or semirandom point sets, the authors…

This study explored the performance of 75 seventh-grade students with and without disabilities, educated in inclusive mathematics classes, on open-ended, problem-solving mathematics assessments. In the study, approximately half of the students used a graphing calculator on the first assessment and not on the second assessment (n = 35; 46.7%),…

In this article, the authors focus on hypothesis testing--that peculiarly statistical way of deciding things. Statistical methods for testing hypotheses were developed in the 1920s and 1930s by some of the most famous statisticians, in particular Ronald Fisher, Jerzy Neyman and Egon Pearson, who laid the foundations of almost all modern methods of…

When people speak of "the Law of Gravity" they are generally referring to what is more specifically known as "Newton's Law of Gravitation." This law states that the gravitational force (that is, the mutual attraction) between any two physical bodies is directly proportional to the product of their individual masses and inversely proportional to…

The note introduces sequences having M-bonacci property. Two summation formulas for sequences with M-bonacci property are derived. The formulas are generalizations of corresponding summation formulas for both M-bonacci numbers and Fibonacci numbers that have appeared previously in the literature. Applications to the Arithmetic series, "m"th "g -…

This paper examines the use of analogies in statistics instruction. Much has been written about the difficulty social work students have with statistics. To address this concern, Glisson and Fischer (1987) called for the use of analogies. Understanding of analogical problem solving has surged in the last few decades with the integration of…

This document offers instructional materials for a 60-hour course on basic math operations involving decimals, fractions, and proportions as applied in the workplace. The course, part of a workplace literacy project developed by Mercer County Community College (New Jersey) and its partners, contains the following: course outline; 17 lesson…

Two issues were investigated in this study: (1) how well do children do descriptive statistics (i.e., accuracy); and (2) how do they do it. A total of 31 children in third grade (with no formal instruction in statistics) and 31 children in sixth grade (who had learned how to calculate a mean) compared a set of data from two domains: (1) the…

This study compared the performances of college mathematics students on mathematics problems stated in three different contexts: in arithmetical form, in the form of algebraic expressions to be simplified, and in the form of practical situations stated in words. Both single-step and multi-step problems were used. For all three contexts, there were…

The papers in this document follow the order of the meeting and consist of two guest lecturers and reports from four working groups; two topic group presentations are noted but not included. One lecture, delivered by Peter Hilton, discusses the nature of mathematics today and implications for mathematics teaching, while, in the other paper,…

How seven pivotal skills in elementary school mathematics are treated in five current (1981-1983) textbook series for grades 2-4 is described. The report considers the amount of instruction and practice provided, where it is located in the textbook's year-long sequence of lessons, and the extent to which practice is concentrated in one place or…

Investigated was the effect of format variables that describe mathematical word problems in relation to problem-solving difficulty. Changes made by sixth- and eighth-grade students when asked to rewrite problems in a more adequate or easily understandable format were analyzed. Thirty-five sixth and eighth graders enrolled in a Mentally Gifted…

Defines arithmetic, harmonic, and weighted harmonic means, and discusses their properties. Describes the application of these properties in problems involving fuel economy estimates and average rates of motion. Gives example problems and solutions. (CW)