In light of conceptual metaphor theory, historical mathematicians' and students' difficulty with negative numbers reveals that the collecting objects metaphor may be a cognitive obstacle to those first learning about negative numbers. Moreover, consistency of physical motions with targeted ideas is a factor of cognition. Thus, this…

This paper discussed the use of structured observations as a research strategy in two recently completed studies that investigated students thought processes and behaviors in a microcomputer-based laboratory (MBL) environment and in other instrument-based laboratory environments. In the first study, students' behaviors and thought processes were…