Instructional gaming as a means to achieve skill in selecting ideas relevant for solving a problem

Two pilot studies investigated the effects of using IMP (Instructional Mathematics Play) kits, pamphlets with which individuals may play the mathematical game EQUATIONS against a computer programme. The highly‐branched 105‐kit series presents a total of 21 mathematical ideas ‐‐ five versions of each idea. Twenty‐nine junior high school students in a high‐ability mathematics class completed varying numbers of the kits in five 48 min sessions during a 2 week period; 10 junior high school mathematics teachers in a leadership training programme worked through the entire series at their individual paces during a 21/2 month period. Pre‐ and post‐tests focusing on the IMP kit ideas were designed by the investigators to evaluate the subjects’ abilities to detect the relevance of a particular idea for purposes of solving a problem and to evaluate a mathematical expression involving that idea. On the relevance/selecting pre‐test the students achieved solutions to 3.86 (mean) of the 21 problems; teachers achieved solutions to 8.50. On the post‐test students increased their performance by 4.03 solutions to 7.90, and teachers increased theirs by 7.80 to 16.30. Both increases were significant at the 0.0005 level. Students were also administered straight computation post‐tests involving the same 21 ideas: they solved 69 per cent of the problems on the computation test, as compared with their solution of 40 per cent of the problems on the relevance/selecting post‐test. The magnitude of the changes in performance after exposure to the IMP kits suggests that significant effects may be anticipated with somewhat less competent subjects than those involved in the pilot studies. A surprising result was the significant amount of ‘ unencountered learning ‘ by students ‐‐ that is, the number of ideas that a student missed on the pre‐test, did not encounter in going through the IMP kits, but did correctly on the post‐test. The distribution of the unencountered learning rate suggests, the usefulness of research directed to assessing individual learning styles (e.g., specifics‐learners as contrasted with general‐izers) in order to find more effective means of individualizing learning. The pilot studies point to controlled experiments for further investigating whether effective ways can be devised to improve skill in selecting relevant ideas for solving problems.