We identify and document 3 cognitive obstacles, 3 cognitive affordances, and 1 type of integer understanding that can function as either an obstacle or affordance for learners while they extend their numeric domains from whole numbers to include negative integers. In particular, we highlight 2 key subsets of integer reasoning: understanding or…

In this article we report 3 experiments demonstrating that a simple booklet containing self-explanation training, designed to focus students' attention on logical relationships within a mathematical proof, can significantly improve their proof comprehension. Experiment 1 demonstrated that students who received the training generated higher…

Written questionnaires were given to (n=213) preuniversity students to assess their judgments of association and their solution strategies with contingency tables in statistics. Compares results with previous psychological research. Qualitative analysis found three misconceptions concerning statistical association. Includes questionnaire.…

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)

Formative validation methods were used with over 90 mathematics teachers in Utah to design an assessment of the mathematical and mathematics teaching cognitive competencies of underprepared middle and secondary school mathematics teachers. A summative validation study using 47 subjects indicated that the test was valid and reliable. (Author/PK)

Described are procedures followed in developing, administering, and scoring a set of mathematical problem-solving superitems and examining their construct validity through a recently developed evaluation technique associated with a taxonomy of the structure of learned outcomes. Data strongly support the validity of the underlying theoretical…

Describes the development and validation of a short form of the My Class Inventory (MCI) assessing classroom psychosocial environment. Reports a case study involving the use of the short form of MCI in attempts to improve a sixth-grade mathematics class. Provides all 25 items of the short version of MCI. (YP)

Analyzed questionnaire responses of 152 prospective secondary mathematics teachers, 10 of whom were interviewed, to investigate their knowledge of the concept of function. Results indicated that many did not have a modern concept of function, a limitation that influenced their pedagogical approach. (Contains 45 references.) (MDH)

Reports on conceptual understanding and solution strategies for percent problems of (n=31) students representing 2 ability levels from grades 5, 7, 9, and 11. Strategies evolved from intuitive to formal and increased in diversity with increasing age. Appendix includes concept and computation interview questions. (Contains 15 references.) (MKR)

Examined inconsistencies in secondary school students' reasoning about the probability concept of equally likely events. Results of two studies suggest that the number of students who understand the concept of independence is much lower than the latest National Assessment of Educational Progress results indicate. (Contains 22 references.) (MDH)

Assessed were second grade students to determine whether their beliefs about causes of success in mathematics were related to their personal goals in mathematics. One class that experienced mathematics instruction consistent with a constructivist view rated higher than traditional classes on Task Orientation, attempting to gain understanding.…