**ERIC Number:**ED115711

**Record Type:**RIE

**Publication Date:**1974-Jun-14

**Pages:**18

**Abstractor:**N/A

**Reference Count:**0

**ISBN:**N/A

**ISSN:**N/A

How Does Mathematics Learning Take Place?

Scandura, Joseph M.

In a study of mathematics learning, taking a rule-oriented approach, students were taught to trade objects of type A for objects of types B and C. Children ranging from ages 7 to 9 were given rules for converting A to B and B to C and were then presented with the task of converting A to C. Of the 30, 6 succeeded. Of the 24 who failed, half were taught via a higher order rule to link arbitrary pairs of compatible rules. The other 12 pupils were not given this training. Then, all of the students were presented with a new pair of compatible rules for converting A to B and B to C. Finally, they were presented with a corresponding A to C task. The results showed that all of the students who received training succeeded whereas not one of the other students did so. The results, it is stated, indicated that knowing the components of a solution (rule) for a task is not sufficient. Integrating components is accomplished by applying higher order rules to lower order ones (e.g., component rules). Component rules and higher order rules, although behaviorally sufficient for problem solving, are not logically sufficient. Presumably, it is asserted, the learner must have some innate capability which tells him when and how the various rules are to be used in attacking a problem. With regard to the last point, an innate mechanism which is basic to a structural learning theory is then discussed. (Author/JM)

**Publication Type:**Speeches/Meeting Papers

**Education Level:**N/A

**Audience:**N/A

**Language:**N/A

**Sponsor:**N/A

**Authoring Institution:**N/A

**Note:**Based on an invited talk given at a general session of the National Council of Teachers of Mathematics, Inc. (Bozeman, Montana, June 14, 1974)