The Educational Technology Center has attempted to develop a series of computer based learning environments to support the learning and application of multiplicative reasoning. The work and software described in this paper, including the teaching experiment that generated the error phenomena examined, is part of a larger ongoing research project.…

This teacher resource material was written from the perspective that it is possible to improve number fact learning in the primary grades, and in remedial situations beyond those years, in ways that: (1) will help children learn all facts; (2) will emphasize the process as well as the answer; and (3) by capitalizing upon natural extensions of…

Problem Solving in Mathematics (PSM), a program of problem-solving lessons for grades 4-9, is designed to be integrated into the regular mathematics curriculum. Although the content objectives of the lessons are similar to those of most textbooks, PSM emphasizes problem-solving skills and a variety of instructional strategies which foster the…

The purposes of this study were: (1) to develop a skills hierarchy for rational number multiplication using modified intraconcept analysis procedures developed by Uprichard and Phillips in two preview studies, and (2) to evaluate and modify the hierarchy using the Walbesser technique (AAAS) and pattern analysis. Subskills were delineated from two…

These are some of the individual materials needed by students using the Comprehensive School Mathematics Program's Mathematics for the Upper Primary Grades, Part III. 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 booklets "Festival of…

This study attempted to identify the things that help elementary school students solve verbal problems. Among the types of things included for examination were: the attributes of problems, the tools used, and the problem transformations that were possible. The summary of findings is comprised of 29 diverse types of statements grouped under four…

This study was conducted to determine the relative effectiveness of the use of three different combinations of enactive, ikonic and symbolic representation in teaching multiplication to third-grade students. Ninety students in three classrooms were instructed in accordance with the assigned treatment for nine weeks. Groups were equated using the…

This form rates childrens' grasp of basic mathematical concepts and procedures. See TM 001 111 for details of the program in which it is used. (DLG)

First, fourth, seventh, and tenth graders were timed when solving simple and complex addition problems, then were presented similar problems in untimed interviews. Manipulation of confusion between addition and multiplication, where multiplication answers were given to addition problems (3 + 4 = 12) indicated an interrelatedness of these…

The purpose of this study is to examine what effects the mnemonic devices of pictures and stories have on the memorization and recall of multiplication facts. This study was conducted on a fourth grade classroom in which the students were divided into three groups. The first group was given standard flashcards, the second group was given a set of…

This guide is a collection of ideas for mathematics activities which were assembled and tested by primary teachers. The activities supplement the teaching of basic numeracy and include topics such as algorithms, pyramids, magic squares, multiples, and number values. The guide is organized into four sections: (1) addition and subtraction; (2)…

A study of (n=26) prospective elementary teachers' understanding of the area of a rectangular region as a multiplicative relationship between the lengths of the sides resulted in the development of a description of the quantitative reasoning involved. (23 references) (MKR)

The effectiveness of teaching multiplication skills to 2nd graders with disabilities in general education classes was evaluated with 12 students with learning disabilities, 1 student with emotional disability, and 99 normally achieving peers. Students were taught using a concrete to representational to abstract instructional sequence. Students…

Described is an activity that categorizes a two-digit number as "sneaky" if the continued process of taking the difference of the squares of its digits leads to a difference of zero. Other categorizations are determined by whether the difference process ends in a one-digit number or continues in a loop of numbers. (MDH)

Applies the Lesh Translation Model to develop conceptual understanding by showing relationships between five modes of representation proposed by Lesh to learn multiplication of fractions. Presents five teaching activities based on the translation model. (MDH)