The interplay of creativity, failure and learning in generating algebra problems

Abstract

Typical mathematics instruction starts with a teacher explaining a worked example, followed by students’ practicing isomorphic problems. Because such instruction may not optimally help students notice the critical features of the concept, an alternative way is to have them generate their own examples across a range of contexts. One hundred and sixty four students participated in three algebra-learning studies, where they completed several worksheets, each targeting a specific algebraic manipulation principle. Each worksheet started with worked examples presenting the targeted principle, after which the students had to generate their own examples. Student-generated examples varied from being only superficially different from the worked-examples, to creative ones that differed on a structural level. Path analyses revealed significant indirect and direct effects of structural creativity. The indirect effect revealed that structural creativity was associated with a higher error rate, which, in turn, negatively influenced immediate learning. Interestingly, in spite of the indirect effect, and what was a relatively simple and short intervention embedded in a longer instructional program, the direct effect of structural creativity on delayed posttest outcomes was positive and significant. We situate our findings in the extant literature on the role of failure in mathematical creativity and learning.