5th graders (n=527) were randomly assigned to self-explain worked examples (WE) or solve problems during a yearlong study. WE students learned more algebra skills when given algebra worked examples on an end-of-year transfer measure. Comparing attempts, conceptual, and mechanical correctness by condition, results demonstrated that the condition…

To improve mathematics achievement, students' errors should be treated as a source to stimulate their understanding of the conceptual and procedural basis of their errors. The study investigated 20 Chinese and 20 U.S. high school teachers' interpretations and responses to a student's errors in solving a quadratic equation. The teachers' responses…

The goal of this study was to understand errors that student make when simplifying exponential expressions. College students enrolled in four college mathematics courses were asked to simplify and compare such expressions. Quantitative analysis identified three persistent errors: interpreting negative bases, negative exponents, and parentheses.…

Verbal protocols were collected from math-anxious and math-comfortable college students while they solved algebra problems. These protocols were then examined for differences in problem-solving processes. Differences occurred in the use of two basic strategies: generating values and symbolic transformations. Math-anxious students generated more…

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…

This study investigated how students processed information obtained by reading a passage related to inertial reference frames. Two groups of 10th-grade students (one group consisting of students identified as potential National Merit Scholars and another consisting of students enrolled in level-I biology) read a science text passage and answered a…

This study examined how engaging calculus students in Writing to Learn Mathematics affected the types of conceptual and procedural errors that the students made on their examinations. Students in two sections of an introductory college calculus course in Fall 1994 were the respondents in this study. A classification system was developed that…

Seven graduate students in a seminar on classroom computing received instruction in LOGO programming. Programming protocols were collected periodically and examined for errors and misconceptions; in-depth interviews were conducted in order to understand specific misconceptions better. As novice students transit from instruction to experience in…

Defining a "misconception" as an error of translation (transformation, correspondence, interpolation, interpretation) between two different kinds of information which causes students to have incorrect expectations, a Taxonomy of Errors has been developed to examine student misconceptions in an introductory biology course for science…

A seriation task (assembling a set of nesting cups) was used in this study to examine developmental changes in young children's ability to restructure a situation. Forty young children, eight each at 18, 24, 30, 36, and 40 months of age, participated in the study. Each child was presented with five nesting cups and was told he or she could play…

This research is aimed at diagnosing the problem-solving skill of elementary school children and subsequently improving their competence in early mathematics. To reach this goal, a computer assisted instruction (CAI) program on open sentences, incorporating knowledge about students' problem solving strategies and misconceptions, was constructed.…

This paper analyzes "confused history" on the part of students and where that confusion might originate. The study is based on a modified form of content analysis of articles by R. Lederer. The articles offer a compilation of student errors in history and geography. Two major categories of errors are recognized: (1) Type I, represented by errors…

Advances the idea that performance errors should contribute positively to the process of learning. Argues that errors do not occur randomly and that instructional theory should not condemn errors, but seek them. (PK)