The performance of students from three intelligence levels at grades 4, 5, 6, and 7 on certain discovery tasks in arithmetics are examined. Results indicate that students should be given from 3 to 6 instances to make discoveries of the type tested and that students of lower intelligence levels can form generalizations. (FL)

Reported is a study which compared two instructional methods involving discovery learning and a verbal didactic instructional method. The verbal didactic method was significantly better for immediate learning; the verbal didactic method and a guided discovery method were better for retention. No differences were noted regarding transfer. (CT)

A discovery approach was used with seven fourth grade classes while nine classes were taught by an expository methods. Expository pupils were significantly better in computation and discovery pupils significantly better in retention of ability to apply mathematics. Attitude improved more for those taught by the discovery approach. Some interaction…

Students in three mathematics classes were assessed on two aptitudes, field independence and general reasoning, and randomly assigned for a discovery treatment. There was a significant interaction with general reasoning on the retention test. There were no interactions with field independence. (Author/MK)

Two studies investigated the effects of verbalization of discovered generalizations on the retention of those principles. (SD)

A lecture method was compared with a method based on questioning sequences that guided students to discover mathematical principles. Students with high levels of mathematics anxiety had significantly lower achievement. Students with high anxiety benefited more from the expository approach; those with low anxiety benefited more from the discovery…

Elementary School Teachers were instructed on finding number patterns in a figure in one of three groups: individual discovery, group discovery, and expository. They were tested for recall, retention, and transfer. The expository groups did better on recall, but group discovery was more effective for retention and recall. (SD)

The learning of mathematics is presented as a cognitive process rather than as a behavioristic one. A generative model of mathematics learning is described. Learning with understanding can occur with discovery or reception treatments. Relevant empirical research is discussed and implications for teaching mathematics as a generative process are…

Investigated strategies that 7- to 12-year-old children (n=96) spontaneously applied in solving novel combinatorial problems. With experience in solving two-dimensional problems, children were able to refine their strategies and adapt them to three dimensions. Results on some problems indicated significant effects of age. (Contains 32 references.)…

Investigated were the effects of five verbalizing methods (subject speaks, reads, writes, listens, or does not verbalize) on short-term retention of the ability to use discovered generalizations. No significant differences were found among the effects of the verbalizing methods for a retention test. (JP)

The results of this field experiment support the conjecture that when learning tasks involve the development of a mathematical structure, guided-discovery techniques involving dialectical dialogue may be a more viable alternative to conventional instruction than individualized instruction through expository or programmed packages. (MN)

No significant interaction was found between two instructional treatments and two aptitude variables in this study, but they did find four disordinal interactions, two using one predictor variable and two using two predictor variables. (MN)

Fifth graders performed better than third graders on discovering the function rule relating two number pairs. Task difficulty and mode of presentation (graphic or symbolic) varied by function. The children seemed ready to relinquish a hypothesis in the face of disconfirming evidence. (MNS)

Twelve middle school students, working in pairs, used a computer microworld to explore introductory geometric transformational concepts. Despite a tendency for symbolic overgeneralization, the students were able to use visual feedback from the microworld and discussions with partners to correct their own mistakes. (Author/JJK)