These self-paced student training modules on linear measurement and whole numbers are two of a number of modules developed for Pre-apprenticeship Phase 1 Training. Purposes of the modules are to teach students the necessary math concepts in linear measurement to enable them to read and use those concepts; and to teach students the necessary math…

This is one of a series of student booklets designed for use in a bilingual mathematics program in grades 6-8. The general format is to present each page in both Spanish and English. The mathematical topics in this booklet include multiplication and division. (MK)

A computer model of memory (based on input, retrieval, and reaction time) was applied to the rapid processing of simple arithmetic facts (addition, subtraction, and multiplication) by 18 educable retarded adolescents when compared with 18 nonretarded fourth graders (of equal mental age) and 18 normal adolescents. Results for addition indicated…

Describes activities for primary grades to practice shape identification, computation, and geometric designs. The materials include reproducible worksheets. (PK)

This study tested the effectiveness of an experimental instructional strategy for writing arithmetic sentences for simple multiplication and division story problems involving nonintegral factors. Significant effects in favor of the experimental group were found on an intermediate test and a posttest. (Author/CW)

Assessed are the extent to which the beliefs, "multiplication always makes bigger" and "division always makes smaller," are explicitly held by preservice elementary teachers. Insight into the sources of preservice teachers' beliefs and into the relationship among preservice teachers' beliefs, computational skills, and performance on word problems…

Five- to six-year-old children estimated the size of Euclidian objects using an addition rule of Height plus Width, rather than a multiplying rule. Within the framework of information integration theory, tested whether intensive handling of objects would facilitate shift from addition rule to multiplication rule. Found that following handling,…

P-adic or g-adic sets are sets of elements formed by linear combinations of powers of p, a prime number, or g, a counting number, where the coefficients are whole numbers less than p or g. Discusses exercises illustrating basic numerical operations for p-adic and g-adic sets. Provides BASIC computer programs to verify the solutions. (MDH)

The author analyzes his 11-year-old daughter's investigation of patterns in multiplication. In an investigation initiated herself, Becca generates hypotheses, discovers patterns, asks questions, and discards procedures that do not produce desired results. Providing a classroom environment that values questioning is a key recommendation. (MLN)

Identifies the types of reasoning involved in middle grade mathematics with regard to multiplicative structures and the difficulties students have with the concepts, why these difficulties might occur, and the interconnections within this content area. Offers four recommendations for the preparation and professional development of teachers.…

Productive pedagogies (PP) is an influential framework for teaching and learning that has featured well in current reforms of teacher education. The present study was designed to examine principles of PP adopted by a cohort of beginning mathematics teachers. A networked online learning environment, WebCT[TM], facilitated the teachers'…

Developed for elementary teachers, this activity unit is designed to teach students the importance of estimation in developing quantitative thinking. Nine ways in which estimation is useful to students are listed, and five general guidelines are offered to the teacher for planning estimation activities. Specific guidelines are provided for…

This module is the fifth in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include calculator multiplication of decimals,…

This set of papers, selected from presentations at the Fourth and Fifth Annual Conferences of the Research Council for Diagnostic and Prescriptive Mathematics, are of primary interest to mathematics educators. In the first paper, Romberg describes a model for diagnosing mathematical learning difficulties which extends the diagnostic process beyond…

The concept of multiplication is described and illustrated using several different representational systems. A conceptual approach to teaching mathematics is compared with the procedural approach commonly found in the school curriculum. Four different methods of representing the multiplication process with numbers larger than ten are presented:…