Structuring worked examples to be an effective form of feedback in mathematics classes

摘要

Worked examples have been extensively investigated in cognitive load theory research and found to be a highly ef fective learning strategycompared to conventional problem solving, especially for novice learners. Feedback is w idely accepted as a powerful learning tool and can takemany forms. Although w orked examples are commonly used during feedback in mathematics classrooms, this combination has not beensystematically researched. Hence, the main aim of this study w as to bring together these tw o successful strategies to facilitate learning.Specif ically, several presentation formats of worked examples w ere compared to f ind the most ef fective version.Four experiments w ere conducted in authentic mathematics classrooms w ith 13-14 year students studying the topic of linear equations.Each experiment follow ed the same procedure in that students w ent through an initial learning acquisition phase and then w ere tested on the topic.In line w ith the dif ferent feedback conditions investigated, the following day students received their test papers with specific feedback commentsw ritten on their papers w hich included a set of w orked examples to study as a further form of feedback. Finally students w ere retested on thetopic. In each experiment participants w ere assigned to groups according to a randomization process.Overall results indicated that the best form of feedback occurred when students were given a complete w orked example pair using thealternation strategy of studying a solution to a problem and then solving a similar problem, on problems w here learners had previously madeerrors. It did not matter if the errors w ere indicated by the teacher, or students found the errors themselves by consulting a complete list of w orkedexamples. Results also indicated that using partial w orked examples in the form of completion problems, or changing the w orked examples toinclude new problems instead of the original problems, w ere less ef fective. Furthermore, it w as found that problem-solving pairs also matched theef fectiveness of full worked examples. Evidence w as also collected that w orked examples w ere an ef fective alternative to standards-based andnorm-based feedback procedures. It w as concluded that worked examples could be an ef fective form of feedback in realistic mathematicsclassroom settings.