Gap reasoning is an inappropriate strategy for comparing fractions. In this article, Patrick Sullivan and Joann Barnett look at the persistence of this misconception amongst students and the insights teachers can draw about students' reasoning.

This article explores some of the common mathematical difficulties that 11- to 16-year-old students experience with respect to their learning of physics. The definition of "understanding" expressed in the article is in the sense of transferability of mathematical skills from topic to topic within physics as well as between the separate…

This study investigates Chinese and U.S. teachers' cultural beliefs concerning effective mathematics teaching from the teachers' perspectives. Although sharing some common beliefs, the two groups of teachers think differently about both mathematics understanding and the features of effective teaching. The sample of U.S. teachers put more emphasis…

Investigates the concepts of ratio and proportion constructed by grade 9 students by investigating their proportional reasoning schemes and procedures on three types of tasks: missing value, numerical comparison, and qualitative reasoning. Indicates that students frequently used additive reasoning--that is, a comparison of two numbers by…

Assesses the ability of tenth grade students (n=364) to acquire meanings of graphs that are frequently used in their biology textbooks. Indicates that the main source of failure to process information equally well from tables and graphs was not a lack of basic analytical skills but rather a lack of understanding of the relationship between…

This study investigated the perception of university teachers regarding what critical thinking skills are needed for successful undergraduate study, and determined the relative importance of these skills within and across academic disciplines. A total of 31 university teachers in 6 academic disciplines of Physical Sciences, Biological Sciences,…