This study sought to determine the basis for young children's understanding of fundamental addition and subtraction processes, and to expose any limitations on such arithmetic reasoning. Thirty-six two-year-olds and 36 three-year-olds participated in six experiments which examined children's relational quantity judgments about pairs of arrays in…

This paper reports the formative evaluation of six curriculum units related to initial number sentence writing. These units were used for a coordinated study carried out by the Mathematics Work Group of the Wisconsin Research and Development Center for Individualized Schooling. The units were tried during the 1977-78 and 1978-79 school years at a…

This paper reports the results of the second of a series of collaborative studies examining how children acquire the skills to represent and solve verbal addition and subtraction problems. The purpose of this study was to identify the cognitive processing capabilities of a group of Tasmanian (Australian) children. Fifteen cognitive tests were…

A discussion is presented concerning variables associated with children's representation of certain addition and subtraction problems. Problem components are classified as physical, pictorial, sensual, verbal-spoken, verbal-written, symbolic, or internal. Problems are discussed as abstract (symbolic) or nonsymbolic. Three problem components are…

This curriculum guide for grades K-6 is the first volume of a two-part series. It is meant to provide an ordered sequence of mathematical concepts from which teachers may organize an arithmetic program allowing for individual student progress with the greatest amount of individual attention. Each topic is arranged into levels based on the topic's…

Thirteen different research reports related to mathematics education, plus a set of five studies by one investigator and his associates, are abstracted and analyzed. The set of five studies is primarily concerned with how students deal with ratio. Of the other studies, one focuses on the longitudinal effects of inservice teacher training; five…

This article describes the instructional efforts and success of two first grade teachers who cooperated in a year-long subtraction study with a university research team. Performance profiles of students in the experimental and control groups are presented, and implications for teaching are discussed. (PK)

A newly introduced approach, rule space, can represent large numbers of erroneous rules of arithmetic operations quantitatively and can predict the likelihood of each erroneous rule. The new model challenges the credibility of the traditional right-or-wrong scoring procedure. (Author/PN)

Two experiments investigated how attributional feedback sequence influences children's motivation, attributions, self-efficacy, and performance. Third graders lacking subtraction skills received training and solved problems with one of four ability and/or effort feedback sequences. Children initially receiving ability feedback developed higher…

Results obtained from 11- and 15-year-olds on tests of understanding of decimal place value and its influence on addition and subtraction skills are reported and discussed. (MNS)

In this study, we examined 139 prospective elementary teachers' solution processes to additive word problems for which the solution is 1 more or 1 less than the answer produced by the straightforward application of the addition or subtraction of the two given numbers. For each problem, five aspects of their solution processes were examined: (a)…

A Case Study is presented in this article, where there is a contradiction between pre-algebraic language semantic and syntax used to solve word problems through a negative integers subtraction. Appendix includes answer key. (Contains 1 figure.) [For complete proceedings, see ED500859.]

Presented is a method of teaching adding and subtracting as an interrelated series of patterns using a number line. Examples of the use of this method as well as the materials necessary are discussed. Applications of the method to multiplication and division are given. (CW)

Provides methods of teaching negative number operations, including addition, subtraction, and multiplication. Presents examples and activities for the operations. (YP)

Training with a self-instruction strategy was found to be effective in teaching addition and subtraction to 52 educable mentally retarded and learning-disabled children with arithmetic deficits. Sixteen of the children, who were categorized as impulsive, showed a more reflective cognitive style following the training. (Author/JDD)