The framework of Tharp and Gallimore (1988) was adapted to form a ZPD (Zone of Proximal Development) Model of Mathematical Proficiency that identifies two interacting kinds of learning activities: instructional conversations that assist understanding and practice that develops fluency. A Class Learning Path was conceptualized as a classroom path…

This paper discusses the types of word problems represented in Malaysia's primary one, primary two and primary three mathematics texts based on Van De Walle's model (1998) in the operations of addition and subtraction. A test was constructed to measure students' success based on this model. The data from this study indicates that the Malaysian…

An alternative to the IQ-achievement discrepancy model for identifying students with learning disabilities is the response to intervention (RTI) model. There is a growing literature base in support of the RTI model, and within the reauthorization of IDEA there is an allowance for an RTI approach whereby RTI "may" be used by school…

This book is one in a series of teacher resource books developed to: (1) rescue students from the clutches of computers that drill and control; and (2) supply teachers with computer activities compatible with a mathematics program that emphasizes investigation, problem solving, creativity, and hypothesis making and testing. This is not a book…

This paper documents the achievement monitoring component of a three-year study on the acquisition of addition-subtraction problem-solving skills by young children. A set of performance objectives contained in or ancillary to ten instructional units on sentence-writing for verbal problems and algorithms specified test content. Tests measuring…

This booklet offers teacher instructions and student worksheets on number activities for gifted primary grade students. Three sections are included: (1) "moving numbers" which asks students to supply the missing member or members of addition and subtraction equations; (2) "number trails," which involve the completion of number…

This set of papers was selected from presentations made at the Fourth and Fifth Annual Conferences of the Research Council for Diagnostic and Prescriptive Mathematics because of their pertinence to classroom teachers. The papers concern: (1) "Research and Development Related to Learning about Numerals for Whole Numbers: Implications for…

This paper describes the various procedures associated with the individual interviews that are part of the data gathering processes of the Coordinated Study being carried out by the Mathematics Work Group of the Wisconsin Research and Development Center for Individualized Schooling. The first major section describes the six basic verbal addition…

The purpose of this study was to describe and compare kindergarten and first-grade children's performance on addition and subtraction problems presented in two contexts: verbal (in which problem data were linked to physical referents such as objects or people and their actions), and abstract (in which no such links to physical situations…

This study was designed to follow up earlier work on mapping instruction. The two main goals were to: (1) test the effectiveness of mapping instruction as a general cure for "buggy" subtraction algorithms, and (2) explore two alternative explanations of how this new form of instruction works. It was hypothesized that mapping cures bugs…

Following instructions provided in the teacher's manual, the SCOPE Mathematics Achievement Test booklet for grades K-1 presents 11 mathematical concepts. Testing items include: building appropriate sets; matching equivalent sets; reproducing a given pattern; selecting and/or making an object that is bigger than or smaller than a given object;…

Two experiments tested the idea that the means by which children acquire efficacy information can produce different levels of task motivation and self-perception of competence. In Experiment 1, children periodically received either ability attributional feedback, effort feedback, ability plus effort feedback, or no attributional feedback. Although…

Most of the research on mathematical and scientific thinking has been concerned with uncovering knowledge structures and reasoning processes in people of different levels of competence. How these structures and processes are acquired has only recently become a major concern. Thus, some of the major research on mathematical and scientific thinking…

The use of counting for subtraction was investigated. Counting for subtraction is related to counting-on for addition and to four skills: the ability to use the subtrahend cardinality to gain entry into the count sequence, the ability to use the minuend cardinality to gain entry into the count sequence, the ability to use the count sequence to…

A new system of order analysis, developed by Takeya and called Item Relations Structure Analysis (IRSA), was described and used for examining the structural relations among a set of 24 items on the addition and subtraction of fractions. A diagraph showing 16 chains of items that had discernibly common features was generated by this method, and…