We report on an innovative design of algorithmic analysis that supports automatic online assessment of students' exploration of geometry propositions in a dynamic geometry environment. We hypothesized that difficulties with and misuse of terms or logic in conjectures are rooted in the early exploration stages of inquiry. We developed a generic…

Recent federal education policies and reports have generated considerable debate about the meaning, methods, and goals of "scientific research" in mathematics education. Concentrating on the critical problem of determining which educational programs and practices reliably improve students' mathematics achievement, these policies and reports focus…

Reasons for college students making reversal errors translating a sentence to an equation were explored in six studies. The principal sources were haste, failure to check, failure to base the equation on the sentence meaning, and use of nonalgebraic symbols. Students could successfully check when prompted. (MNS)

Common mistakes pupils make when adding fractions are categorized and analyzed. (MP)

Five types of errors in an information-processing classification are discussed: language difficulties; difficulties in obtaining spatial information; deficient mastery of prerequisite skills, facts, and concepts; incorrect associations; and application of irrelevant rules. (MP)

An exploratory investigation of various incorrect solution procedures used by students attempting to solve a variety of forms of open sentences is reported. The study identifies specific incorrect strategies, indicates their relative frequency of occurrence, and attempts to offer some explanation for certain of the incorrect procedures used. (MK)

Sixth graders wrote solutions to the word problems in the Metropolitan Achievement Test. Errors were analyzed and classified. At least 52 percent of errors were computational or clerical and could not be attributed to reading difficulties. (SD)

An operational definition of careless errors was provided and used in an investigation of 50 children attending an international primary school in Lae, Papua New Guinea. Results indicated that mathematically competent and confident children tend to make a greater proportion of errors than other children. (MP)

Data indicate that relatively advanced science-oriented college students can experience serious difficulties in symbolizing certain meaningful relationships with algebraic equations. Reversal errors in formulating equations were seen to stem from two main sources: (1) a syntactic word order matching process and (2) a semantic static comparison…

A content-oriented analysis of written solutions to test items in Israeli high school graduation examinations in mathematics yielded six error categories: misused data; misinterpreted language; logically invalid inference; distorted theorem or definition; unverified solution; and technical error. (Authors/MNS)

A model of subtraction development and the computing difficulties and research issues suggested by the model are outlined. Demands of simultaneous processes, difficulties with informal subtraction, and the impact on the counting-up procedure are discussed. (MNS)

Interviews conducted with each of 35 sixth graders who made errors on the Metropolitan Achievement Test showed little evidence that poor reading abilities affected children's success on word problems. (DT)

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)

Four methods of solutions and 12 calculative strategies were found from introspective reports of 15 skilled and 15 unskilled students in grades 11 and 12 doing mental multiplication. Unskilled students used strategies more suited to written than mental computation, while skilled students used strategies based on number properties. (MNS)

Analyzes error patterns of kindergartners' mental addition task. Eight weeks of computational practice affected the errors of unpracticed combinations on a retest. Seven of 10 children mastered previously unknown combinations involving zero by learning a relationship rather than the practice and memorization of individual facts. (Author/YP)