Learning progressions have become an important construct in educational research, in part because of their ability to inform the design of coherent standards, curricula, assessments, and instruction. In this paper, I discuss how a learning progressions approach has guided our development of an early algebra innovation for the elementary grades and…

The authors' purpose was to determine the effects of computer-based practice and conceptual interventions on computational fluency and word-problem solving of fourth- and fifth-grade students with mathematics difficulties. A randomized pretest-posttest control group design found that students assigned to the computer-based practice intervention…

In experiment 1, novice fourth-grade students (N = 92) who compared multiple examples that separately varied each critical aspect and then simultaneously varied all critical aspects developed better conceptual knowledge about the "altitude of a triangle" than students who compared multiple examples that did not separately vary each critical aspect…

Traditional mathematics education focuses on teaching rote procedures to solve problems, though these procedures are not usually motivated by goals. As a result, students have trouble flexibly using procedures and generalizing their knowledge to solve novel problems that differ from the problems they practice during instruction. In the following…

Previous research has shown that--due to the extensive attention spent to proportional reasoning in mathematics education--many students have a strong tendency to apply linear or proportional models anywhere, even in situations where they are not applicable. This phenomenon is sometimes referred to as the "illusion of linearity". For example, in…

Mathematical tasks calling for relational thinking were given to 60 children of Indian, Pakistani, or Bangladeshi origin who had spent their school lives in England, 60 who had arrived within the past 3 years, and 60 British children. Differences in the ability to abstract, hypothesize, and generalize were studied. (KC)

This volume of the 30th annual proceedings of the International Group for the Psychology of Mathematics Education conference presents: plenary panel papers; research forum papers; short oral communication papers; and poster presentation papers from the meeting. Information relating to discussion groups and working sessions is also provided.…