Studied the interpretation of mathematics in terms of algorithmic or coherent views of 1,287 teachers from 12 countries using responses to items from the Third International Mathematics and Science Study (TIMSS). Teachers from four high-achieving Asian countries were more likely to see mathematics as algorithmic than were teachers from four…

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.…