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…

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…

An overall schema of interpretation for programming instructors is given, so that the misconceptions students develop in programming can be determined more readily. Types of language-independent and -dependent bugs, how they can be identified, and how to help students overcome them are addressed. (MNS)

A test of logic using implicational and disjunctive sentences was given to Chinese and English speakers. No differences were found on "if-then" sentences, but differences were found on "or" sentences. (MNS)

The process of transition from a novice's state to that of an expert, in the domain of decimals, is described in terms of explicit, intermediate, and transitional rules which are consistent yet erroneous. Data from students in grades 6-9 are included. (MNS)

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)

A computer program named BUGGY is described. The program is designed to duplicate "traditional" student mathematical mistakes; pupils are to identify the nature of the errors the computer makes. (MP)

Computer software with graphic representations of functions can teach algebraic concepts, or can blur or obscure concepts of great importance. Making good use and bad use of visual imagery are each discussed. Then a general theory of interpretation of graphs is proposed, and a list of examples is presented. (MNS)

This booklet is a catalog of error patterns found in basic arithmetic and algebra courses. It is intended to be used as a resource by instructors and tutors teaching these concepts. The material is divided into major concept headings with subheadings. The error patterns are named and given a brief general description followed by a specific example…

The Concepts in Secondary Mathematics and Science (CSMS) and Strategies and Errors in Secondary Mathematics (SESM) research projects based at Chelsa College, England, have shown the marked reluctance of secondary school students to use fractions when solving mathematical problems, even though they have been taught the topic for a number of years.…

Data from 32 state assessments in mathematics (conducted in 1984 and earlier) are analyzed in this document. The high degree of variability across the states is stressed, with some of the points of variation in the test development, administration, and analysis process noted. Information is then presented on topics on which students are doing well…

Recent research on solving addition and subtraction word problems has resulted in the construction of theoretical models of children's problem-solving processes. Some of these models have been translated into computer programs. Characteristics and predictions of the theoretical analysis developed by Riley, Greeno, and Heller (1983) are discussed…

This study sought to evaluate a measure of dyscalculia to determine its validity and reliability. It also tested use of the instrument with seventh graders and ascertained where errors attributed to dyscalculia were also present in an average sample of seventh graders. Results varied. (MNS)

Delineates and describes four types of questions which may help teachers learn more about student understanding, namely, silent questions, oral questions, written questions, and students' questions. (PK)

Reports on a study to determine if having students write about the work required in doing three types of exercises from elementary algebraic fractions would affect the students' error patterns on quizzes. The study involved six developmental studies in elementary algebra classes. (PK)