The process of pairing a name with representations or peculiar properties permeates many mathematics classroom situations. In school, many practices go under the label 'definition', even though they can be very different from what mathematicians conceive as a formal definition, and in fact there are substantial differences between these different…

Selection bias is a persistent, and often hidden, problem in educational research. It is the primary obstacle standing in between increasingly available large education datasets and the ability to make valid causal inferences to inform policymaking, research, and practice (Stuart, 2010). This article provides an accessible discussion on the…

Unlike in elementary schools, high school teacher effects may be confounded with unobserved track-level treatments (such as the AVID program) that are correlated with individual teachers. I present a strategy that exploits detailed course-taking information to credibly estimate the effects of 9th grade Algebra and English teachers on test scores.…

This document presents a first approximation for a model for student performance in solving linear equations. First, characteristics of a model of student performance for solving linear equations is discussed. It is noted that there is a need for some theoretical structure to support and organize the bits and pieces of information provided by…

This document contains 53 plenary and contributed papers presented at the eighth Psychology of Mathematics Education (PME) meeting. Two plenary addresses focused on mathematics research in Australia and Japan, and problem solving and symbolism. Contributed papers were classified under 13 headings including: teaching and learning theory; cognition;…

This document contains plenary and contributed papers presented at the seventh PME meeting, held near Jerusalem, Israel in July 1983. Three plenary papers focused on implicit models in solving problems, discussions with teachers and children, and heuristics. Contributed papers were classified under seven headings: learning theories…

Given only correlation coefficient, one cannot infer causality. This lesson has been lost on Secretary of Education Richard Riley, who recently intoned that "taking rigorous mathematics courses ... early in secondary schools is a gateway to college and future employment." Students taking such classes have probably already been identified…

Suggests ways researchers can use international comparisons to improve student learning, using math performance of U.S. and Chinese sixth-graders on four types of tasks. Chinese students did better on computation; U.S. students excelled at process (open performance) assessment tasks. U.S. kids need to develop symbolic and algebraic thinking. (MLH)

To probe beyond declarative knowledge about real numbers in secondary school, the authors interviewed students in Grades 9, 10 and 12. The main question seems to be whether the length of a decimal expansion is "indefinite" or "infinite." It blurs the mental representation of rational numbers as well. (Contains 3 footnotes.) [For complete…

Programs for computer-assisted instruction (CAI) which were developed at Stanford University from 1963-70 are described, and prospects for CAI in the 1970's are considered briefly. The programs include ones in arithmetic, logic, and reading for elementary grades and in basic Russian and remedial algebra for college students. Of these, the logic…