This chapter reports 11 experiments that were done to determine whether Guided Cognition-designed homework facilitates learning middle school mathematics, and if so, to determine how it helps and what is learned. Experiments were performed in two middle schools and included 8th graders in two experiments and 7th graders in nine experiments. Mathematics topics ranged from fractions to integers to geometry. As in the literature experiments, students were in their normal school environment following their regular curriculum and were unaware that their learning was being observed. Guided Cognition design was found to be effective for learning mathematics. Working story problems that were enriched with cognitive events such as role play, divergent thinking, visualizing and illustrating, and relating to prior experience raised scores on unexpected quizzes by about a letter grade. Another unexpected quiz found that the improvements in problem-solving performance persisted for 6 months. Guided Cognition homework was also found to be efficient in that students who worked eight problems and then performed four cognitive events performed as well on unexpected quizzes as students who worked 24 problems in the same time interval. Another pair of experiments determined that modest gains could be made from merely reading completed examples of cognitive events, but that these gains were not long lasting. Performing the cognitive events was found to be most effective for long-term performance. Another experiment found that experiencing cognitive events after working some mathematics problems can help consolidate knowledge of how to work such problems.
