Students may be able to set up a relevant proportion and solve through cross multiplication. However, this ability may not reflect the desired mathematical understanding of the covarying relationship that exists between two variables or the equivalent relationship that exists between two ratios. Students who lack this understanding are likely to…

This article illustrates the kinds of mathematical discussions that should occur with students in classrooms. The authors use a sample from professional development to show discussions that focus on the relationships of events within a problem that led to each representation, the connections between the ways participants chose to represent those…

Students learn to use linear algebra covered in their first algebra course to design mobiles like those created by artist Alexander Calder. (Contains 17 figures and 2 tables.)

This study describes a conceptual teaching approach that helps students make connections between their everyday activities and mathematical word problems. It includes a brief review of the importance of teaching for understanding and describes four principles of conceptual teaching: (1) use cooperative groups; (2) allow students enough time to act…

This article describes a series of mathematics activities based on the book "A Grain of Rice," which are designed to help students understand powers of 2. Ideas for activities in other disciplines are also provided. (Contains 3 tables.)