This study aims to evaluate cognitive conflict in constructing mathematical concepts, based on thinking errors. The data were collected through observations of words or sentences, leading to the derivation of qualitative outputs. Furthermore, the results showed that the two selected subjects experienced cognitive conflicts regarding thinking…

Researchers and instructors have only recently embraced the role of errors as vehicles for learning in the algebra classroom. Studying a mixture of correct and incorrect worked examples has been shown to be beneficial relative to correct worked examples alone. This study examines the effectiveness of having students generate, or anticipate, errors…

Probability theory has long been taken as the self-evident norm against which to evaluate inductive reasoning, and classical demonstrations of violations of this norm include the conjunction error and base-rate neglect. Many of these phenomena require multiplicative probability integration, whereas people seem more inclined to linear additive…

In this research, we examined overall performance and gender differences in measurement skills in elementary-school students from low-income families. In Study 1, accuracy and error patterns were analyzed in a large sample of fourth-graders; in Study 2 error patterns and strategy usage were examined with a smaller sample of fourth-graders. Study 1…

Certain misunderstandings in science, mathematics, and computer programing reflect analogous underlying difficulties. These misunderstandings are examined through four knowledge levels: (1) content; (2) problem-solving; (3) epistemic; and (4) inquiry. Analysis of several examples shows that misunderstandings have causes at multiple levels, and…

Tests can identify the strengths and weaknesses of the child, not only in terms of right and wrong answers, but also in terms of how and why the child succeeds or fails to meet significant mathematical standards. (JD)

In the study of mathematics instruction the focus has changed from the outcomes of learning to the cognitive processes involved in mathematics learning. This new emphasis presents a serious challenge for curriculum design, but it may also lead to more success for students in learning mathematics. (Author/VM)

Much valuable information can be gained by analyzing the students' wrong responses. When a student answers a free response item she/he gives the response which she/he considers to be the correct one. Therefore, diagnosing the algorithm that led the student to his/her answer provides an important source of information for assessing his/her…

An overview is presented of information processing analyses of knowledge and performance in three areas of the elementary mathematics curriculum: basic addition and subtraction facts, complex procedures such as multicolumn subtraction, and the solution of word problems. Theories of the knowledge associated with "expert" performance are discussed.…