Demonstrates that an elementary understanding of computer programing and the development and illustration of the structure of computer program analysis will be valuable assets in the understanding and teaching of mathematics and may be used as modeling devices to simulate the stages of learning. (Author)

A study to investigate one of the mechanisms teachers may use to convince themselves incorrectly that students have learned science concepts requiring formal operational ability is presented. The investigation indicates instructors may actually teach and test for memorization of algorithms rather than understanding. (MP)

Addresses the distinction between conceptual and algorithmic learning and the clarification of what is meant by a second-tier student. Explores why novice learners in chemistry and physics are able to apply algorithms without significant conceptual understanding. (DDR)

Three perspectives of instruction that reflect applications of cognitive theory are transportation of knowledge, application of algorithms, and transfer of responsibility. To determine what kind of instructional theory is appropriate for vocational education in a rapidly changing, technological, and increasingly complex society and what…

Structural learning theory and the Rasch model measured learning gain, retention, and transfer in 1,037 students, grades 7-10. Students learned nine functional relationships with either spontaneous or synthetic algorithms. The Rasch model gave the better description of the data. The hypothesis that the synthetic method was superior was refuted.…