Higher order rule characterization of heuristics for compass and straight edge constructions in geometry

Understanding and procedural knowledge in mathematics instruction1

“…The best introduction to the use of production systems in psychological analysis is Newell and Simon's (1972) book, Human Problem Solving, although an article by Hunt and Poltrock (1974) gives a sound presentation of the major concepts in a much shorter form. Scandura (1973) has given an extensive meta-theoretical discussion that urges the feasibility of this kind of theorizing.…”

The Role of Automation in Instruction

“…Higher order and lower order knowledge played a central role in this research from its inceptions -with emphasis on the central role of higher order knowledge in problem solving (Scandura, 1971(Scandura, , 1973(Scandura, , 1977. Early SLT research also focused heavily on indentifying what individual learners do and do not know relative to what needed to be learned (e.g., Durnin & Scandura, 1974;Scandura, 1971Scandura, , 1973Scandura, , 1977.…”

On the Mechanization of Straightedge and Compass Constructions

“…The work of Scandura et al seems to be the first one to describe a systematic way, with higher order geometric rules, to solve RC-constructions problems [Scandura et al(1974)Scandura, Durnin, and Wulfeck II]. The geometric aspects are derived from Polya's work [Polya(1965)], but this work is more focused on pedagogical considerations about structural learning. To our knowledge, there is no implementation of this study.…”