What is the optimal penalty for errors in infant skill learning? Behavioral analyses indicate that errors are frequent but trivial as infants acquire foundational skills. In learning to walk, for example, falling is commonplace but appears to incur only a negligible penalty. Behavioral data, however, cannot reveal whether a low penalty for falling…

The study compared the written expression of 56 fourth to fifth grade remedial readers and achieving readers. Significant differences favoring the achieving readers were found in three areas: productivity, syntax, and level of ideation. Remedial readers tended toward the same kinds of errors as achieving readers but with an increased frequency.…

Proposes a method for describing the relationship between writing error and style shifting rates across communicative situations. Finds that errors diminished in proportion to the tendency of students to select grammatical features that are shared by Black American English and Standard American English in formal communicative situations. (RAE)

Recommendations for remediation of 28 distinct common error patterns in arithmetic computation are described. (SD)

Examples of four interviews are presented to serve as sample evidence in support of more comprehensive diagnostic procedures in assessing reliably and validly the weaknessess and strengths of learners. The search for computational errors is seen to go beyond standard paper and pencil tests. (Author/MP)

In a two-year study, frequencies and descriptions of systematic errors in four algorithms in arithmetic were studied in regular and special education classrooms. (Author/SD)

This study compared the error patterns of third- and fourth-grade children on addition, subtraction, and multiplication exercises in horizontal and vertical formats. The research design used parallel eight-item tests for each operation; the only difference between items on parallel forms was the formal (horizontal or vertical) of the computational…

The study of computational errors among sixth grade students included identification and classification of errors, investigation of the effects of two feedback treatments and of classwork and homework on error patterns, and investigation of the relationships of error patterns with intelligence, mathematics achievement, attitudes toward…

Four basic types of student errors in computation are noted and described. These are: (1) mechanical, (2) careless, (3) conceptual, and (4) procedural. It is felt many teachers deal with all errors as if they were of the unhabituated procedural type, with not enough attention given to other possibilities. (MP)

Research on error patterns associated with whole number computation is reviewed. Details of the results of some of the individual studies cited are given in the appendices. In Appendix A, 33 addition errors, 27 subtraction errors, 41 multiplication errors, and 41 division errors are identified, and the frequency of these errors made by 352…

Recall of multiplication number facts is a major educational objective in elementary grades, yet some children never acquire total mastery. A microcomputer multiplication number facts training program was developed which incorporated programmed instructional features including feedback, positive reinforcement, vanishing, branching and pairing.…

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…

A new diagnostic modeling system for automatically synthesizing a deep structure model of a student's misconceptions or bugs in his/her basic mathematics skills provides a mechanism for explaining why a student is making a mistake as opposed to simply identifying the mistake. This report consists of four sections. The first provides examples of…

The procedures used for locating documents on diagnosis and prescription in mathematics are described, and the coding system used in reporting the documents is explained. Appendices include lists of basic documents, basic sources, frequently cited authors, and relevant phrases and concepts; a partial bibliography of documents concerned with…

This report illustrates a network of procedures which can be used to solve problems involving the addition and subtraction of fractions. This network, which is based on a skills hierarchy, is used to classify seven levels of student competency. The determination of student competency depends upon the careful construction of error-diagnostic tests.…