Undergraduates often are aware of and able to apply the facts required to prove a statement but still fail to prove it. By comparing doctoral students and undergraduates constructing proofs in abstract algebra, four types of strategic knowledge are hypothesized. Found that doctoral students had knowledge of how to choose which facts and theorems…

Compared tutoring episodes where tutoring did and did not cause learning in university physics students to inform design of intelligent tutoring systems. Found that when students were not at an impasse, learning was uncommon regardless of the tutorial explanations employed. When students were at an impasse, tutorial explanations were sometimes…

The processes by which conceptual knowledge is constructed during mathematical problem solving were studied, focusing on the cognitive activity of learners (i.e., the ways they elaborate, reorganize, and reconceptualize their solution activity). Underlying this research is the view that learners' mathematical conceptions evolve from their activity…

Two cases are described in which alternative assessments have been successfully employed in college mathematics. Case 1 describes an alternative assessment applied in a class of 10 elementary school teachers studying Euclidean geometry as required by state teacher-certification requirements. One student asserted that he already had an adequate…

The psychological mechanisms that underlie human question asking and answering during comprehension and complex learning were studied. The transcripts of 83 tutoring sessions on research methods for college students and 22 algebra tutoring sessions for seventh graders were collected and analyzed. It was estimated that student questions were about…