This paper describes an emerging approach to the design of task sequences and the theory that undergirds it. The approach aims at promoting particular mathematical concepts, understood as the result of reflective abstraction. Central to this approach is the identification of available student activities from which students can abstract the…

The purpose of this study was to develop and evaluate procedures for validating a learning hierarchy from test data. An initial hierarchy for the computational skills of adding rational numbers with like denominators was constructed using Gagne's task analysis. A test designed to assess mastery at each of the 11 levels in this hierarchy was…

Engineering students use spatial thinking when examining diagrams or models to study structure design. It is expected that most engineering students have solidified spatial thinking skills during K-12 schooling. However, according to what we know about geometry learning and teaching, spatial thinking probably needs to be explicitly taught within…