An approach to teaching multiplication and division with negative numbers that focuses on graphs to illustrate concepts is revealed. The material and problems used are presented with comments on the teaching methods applied with 11-year-olds. (MP)

Worksheets are included that use triangular shapes designed to provide practice for addition, subtraction, multiplication, and division of rational numbers. (MP)

Tests of (n=105) ninth-grade algebra students involving the addition and multiplication of monomials found that common, systematic errors made when multiplying monomials were related logically to the symbolism used and the algebraic convention of using an implicit 1 as an exponent. (16 references) (MKR)

In one experiment, subjects from third grade through college relied on memory retrieval rather than on counting to solve multiplication problems. An effect of confusing problems on error rates and reaction times indicated the activation of related information. In a second experiment, subjects demonstrated automaticity of fact retrieval on simple…

The item-response-theory-based (IRT) rule-space model was used to diagnose student knowledge about how exponents behave in multiplication and division in a sample of 431 tenth-grade students. Implications for using feedback from the rule-space model in instruction and assessment are discussed. (SLD)

This article summarizes the basic concepts of multiplication and provides some evidence that the traditional third-grade curriculum and instruction emphasizing memorization of multiplication facts produces much less understanding of the basic concepts of multiplication than a standards-based curriculum and instruction emphasizing construction of…

The author's secondary school mathematics students have often reported to her that quadratic relations are one of the most conceptually challenging aspects of the high school curriculum. From her own classroom experiences there seemed to be several aspects to the students' challenges. Many students, even in their early secondary education, have…

Activities and games which use dominoes to reinforce basic arithmetic skills are presented. Instructions and materials are provided for the activities and games, most of which involve addition and subtraction. Other skill areas which are covered include recognition and matching of domino patterns, multiplication, and division. A seven-item list of…

This document is intended to describe several software learning environments in an order that parallels a reasonable sequence of use by students. It also describes a planned an designed, but not yet implemented, extension of these environments from the discrete to the continuous case. Each of the implemented environments was developed in…

This paper studies the difficulties children have solving word problems that correspond to one of the situations modeled by multiplication; that of a ratio (e.g. "candies per box"), multiplied by an extensive quantity (e.g. "boxes") (I x E). Sixty children were individually observed solving and repeating I x E problems. Various…

These are some of the individual materials needed by students using the Comprehensive School Mathematics Program for the Upper Primary Grades, Part IV. The book of "Worksheets" contains materials that are labeled with the same letter and number as the lessons with which they are to be used. The four "Galaxy of Problems"…

This mathematics textbook, developed for use with slow learners and learning disabled students in secondary school, contains 17 chapters. Among the topics covered are: number words; place value; rounding whole numbers; addition, subtraction, multiplication, and division of whole numbers; reducing fractions; mixed numbers; lowest common…

Presents a tiling problem designed to be solved using the microcomputer, which will give students a context upon which to build meaning for the concepts of factors, common factors, and greatest common factors. (PK)

Discussed are preservice elementary teachers' misconceptions and inconsistent beliefs about multiplication and division with decimals. Sources of inconsistencies and recommendations for overcoming inconsistencies are included. (KR)

This article discusses the classroom use of discovery of number pattern. Provided are examples of a table of squares, multiplications of numbers, and algebraic expressions. (YP)