We report on an innovative design of algorithmic analysis that supports automatic online assessment of students' exploration of geometry propositions in a dynamic geometry environment. We hypothesized that difficulties with and misuse of terms or logic in conjectures are rooted in the early exploration stages of inquiry. We developed a generic…

Children learn arithmetic procedures by rote, rather than by constructing them with an understanding of numbers. Rote learning produces lack of flexibility, nonsensical errors, and other difficulties. Proposed is a theory of conceptual understanding and its role in learning and executing arithmetic procedures. The basic hypothesis is that…

Results do not support Piaget's explanation of object conceptualization. (MB)

Article reveals that positive instance errors arose more often from memory deficits and from choice of irrelevant dimensions. Negative instance errors arose when interpreting information about present stimuli and the relevant dimension. (Author)

Four examples of student misunderstandings from algebra and trigonometry are presented, and their implications are discussed. (MP)

Studies in the past have shown that reinforcements independent of the subjects actions may induce a feeling of helplessness. Most experiments on learned helplessness have led researchers to believe that uncontrollability (non-contingency of feedback upon response) was the determining feature of learned helplessness, although in most studies…