The relationships among types of errors observed during probability problem solving were studied. Subjects were 50 graduate students in an introductory probability and statistics course. Errors were classified as text comprehension, conceptual, procedural, and arithmetic. Canonical correlation analysis was conducted on the frequencies of specific…

Counting books offer children the time and the tools to develop the understanding needed to solve problems. Stimulated by these books, children may use mathematic language and talk about mathematics as they get involved with materials to move and manipulate, as they use supportive aids found in illustrations, and as they interact with materials to…

The question addressed here is how to integrate computational tools, namely interactive general-purpose platforms, in the teaching of process units. Mathematica has been selected as a complementary tool to teach distillation processes, with the main objective of leading students to achieve a better understanding of the physical phenomena involved…

Preschoolers 4 and 5 years of age were found to use four strategies differing in temporal characteristics as they solved simple addition problems with sums of 10 or less. Three strategies had visible and/or audible aspects, and one was covert, involving retrieval from memory. The harder the problem, the more often the children used an overt…

Presents the pro and con of the use of calculators in the classroom. Some feel that calculators make learning mathematics more fun and when used for creative problem solving provide student motivation. Others feel that dependence on the calculators will result in students unable to do simple mathematics on paper. (GS)

The application of the programmable calculator to evaluating complicated formulas is illustrated by considering the formula for finding the area of any triangle when only the lengths of the three sides are known. Other advantages of the programmable calculator are discussed such as freeing the student to explore more challenging problems and…

This document provides abstracts of 20 research reports. Topics covered include: children's comprehension of simple story problems; field independence and group instruction; problem-solving competence and memory; spatial visualization and the use of manipulative materials; effects of games on mathematical skills; problem-solving ability and right…

These student worksheets include activities in counting, place value, estimation, the four operations with whole numbers, number patterns, volume, inequalities, decimal equivalents of fractions, and percents, all to be worked with a calculator. (MP)

Five different ways are outlined in which calculators can be used to develop a student's ability: (1) to solve problems which use real-world data; (2) for solving a greater number of standard word problems; (3) for using different approaches to solve problems; (4) for extending problem situations; and (5) for using the calculator in an…

This experiment was conducted to determine the efficiency of three forms of an algorithm of known effectiveness and the effects of its availability following initial instruction. The dependent variable was time to solve computational problems requiring rule application. The algorithm was presented in three forms: prose, flowchart, and gradual…

Two simple quantitative models were derived from a series of experiments which explored the role of information storage in working memory when performing mental arithmetic. The decay model is a tractable analysis of a complex task which assumes a decay process in working storage. Similar analyses are recommended for problem solving activities…

Defines one approach to problem solving in terms of student use of algorithms to find their solutions and gives examples. Discusses how problems and algorithms relate to each other. Describes strategies for teaching problem solving using algorithms. (CW)

Cryptarithm puzzles are explained and discussed. Examples are provided and reproducible student worksheets are included. (PK)

Four worksheets and teaching suggestions are presented, with the focus on mental computation for levels 2-3; factors, levels 3-4; and nonroutine problems, levels 5-6 and 7-8. (MNS)

The role that food-preparation activities could play in developing understanding of mathematical ideas by middle school students is discussed. Measurement, computation, language, attitudes, and problem solving are addressed. (MNS)