Relating natural language to mathematical language is an important component of elementary mathematics education. This paper describes new steps toward a computerized database of addition and subtraction word problems that could provide teachers and students with access to critical natural language terms and expressions for mathematical…

Instructions and exercises on the use of checking accounts are provided for students in grades 6-12. The following topics are included: (1) reasons for opening a checking account; (2) how to open a checking account; (3) how to fill out deposit slips; (4) the elements of a check and how to write a check correctly; (5) checking account rules; (6)…

Types of errors made by children in addition and subtraction are presented and discussed. Suggestions are given for testing, diagnosing, and prescribing for instruction. (MNS)

This paper proposes a semantic analysis in which meanings of word problems are structures that include class and order relations, and suggests a hypothesis of developmental levels that can account for children's performance of these problems at various ages. The different kinds of problems vary in the complexity of semantic structures and the…

A probabilistic approach is introduced to classify and diagnose erroneous rules of operation resulting from a variety of misconceptions ("bugs") in a procedural domain of arithmetic. The model is contrasted with the deterministic approach which has commonly been used in the field of artificial intelligence, and the advantage of treating the…

Preschool children's problem-solving strategies on structured and unstructured number tasks were compared in this study. Participants were 20 four-years-olds and 20 five-year-olds. Each child was administered a number conservation, addition and subtraction, and division task. The addition and subtraction task contained trials which were designed…

Developed by the Initial Learning in Mainstreaming Project, the manual presents an instructional program to teach mainstreamed handicapped elementary school students borrowing (regrouping) in subtraction. In addition to detailed teaching instructions and accompanying tape recordings for students, the manual includes tests, worksheets, and pages to…

The document presents a criterion referenced test of basic math skills, including division, multiplication, addition, subtraction, fractions, decimals, time, and measurement. (DLS)

This study investigated the effect of initial instruction on the processes children use to solve basic addition and subtraction verbal problems. Prior to instruction and following a 2-month introductory unit on addition and subtraction, 43 first-grade children were individually tested on verbal problems representing different models of addition…

THIS BOOKLET, ONE OF A SERIES, HAS BEEN DEVELOPED FOR THE PROJECT, A PROGRAM FOR MATHEMATICALLY UNDERDEVELOPED PUPILS. A PROJECT TEAM, INCLUDING INSERVICE TEACHERS, IS BEING USED TO WRITE AND DEVELOP THE MATERIALS FOR THIS PROGRAM. THE MATERIALS DEVELOPED IN THIS BOOKLET INCLUDE (1) NUMBER RELATIONSHIPS, (2) EQUIVALENT FRACTIONS, (3) ADDITION AND…

A 20-task learning hierarchy for subtraction of fractions was deductively derived using Gagne's task analysis. To test this analysis empirically, composite items were written for each level and administered to students in grades 3-6. Test results were analyzed by the Walbesser Technique and Pattern Analysis; the acceptance levels developed by…

Reported are the results of a study to determine if specific errors in subtraction occur when students demonstrate ability to apply selected decimal numeration system principles. A secondary purpose was to examine and compare errors made by various subsets of the sample population characterized by grade level, arithmetic achievement, mental…

This study explored the effects of visual (vertical and horizontal) and oral presentation modes upon simple mathematical computations (addition, subtraction, and multiplication). Seventy-two undergraduate education majors were employed as subjects. The placement of the process sign (left, middle, right) and whether a one or two digit number…

The use of two different colored beans or chips to represent positive and negative charges is discussed as a method of demonstrating operations with integers. (MP)

An instructional sequence in which number lines and beads are used to illustrate addition and subtraction of directed numbers is described. (SD)