Author(s):Rijkje Dekker and Marianne Elshout-Mohr

Publication type: journal article

Online: link (full-text for subscribers only)

Authors' abstract. This article addresses the issue of helping students who work collaboratively on mathematical problems with the aim of raising the level of their mathematical understanding and competence. We investigated two kinds of teacher interventions aimed at helping students. The rationale of these interventions was based on a process model for interaction and mathematical level raising. One kind of interventions focused on the interaction between the students, the other – on the mathematical content of the tasks. The effects of the two kinds of interventions were investigated using a pre-test – post- test comparison of students’ learning outcomes and analyzing the transcripts of students’ verbal utterances and worksheets. Our analyses point to interventions focused on students’ interactions as more effective in terms of students’ learning outcomes. Theoretical and practical implications of the research are discussed.

I've discussed a similar study (by Pijls) before. That study was partially a follow-up of the study currently under review. Also here students are supposed to do discovery learning in small groups (triples in this case). No computers are used in this study however. Also here there are two experimental conditions: a process-help condition and a product-help condition. In the process-help condition the teacher is not supposed to talk about mathematics in any way. In the product-help condition he was allowed to give hints. This is what the authors have to say about the product-help condition.

Being used to collaborative learning as instructional arrangement, the teacher habitually limited himself to hints, avoided direct instructions or lengthy explanations, and gave help only when this was manifestly needed.

So it is important to note that this is in no way a comparison between discovery learning and instruction; it's a comparison between two kinds of discovery learning in small groups. I got curious about this study because the study by Pijls that I reviewed before claimed that the study currently under review showed that process-help was better than product-help (a result that Pijls was not able to replicate). The authors of the current study indeed claim that they show this, but they don't. To see why they don't we look at the statistics. The authors state:

A pre- and a post-test were constructed to measure the results of students’ learning. The tests consisted of different items, but were parallel in relevant aspects.[...] Maximum total scores were 25 for both pre- and post-test.

In between the pre- and the post-test the students followed 2 sessions of 65 minutes. The authors go on to say:

The hypothesis about the post-test scores was that these would be

higher in the process-help condition than in the product-help condition.

This hypothesis was confirmed (p < .05).

Using the diagrams that the authors provide it is possible to deduce the pre- and post-test scores of all students in both conditions. So we can exactly redo the statistics. Did you carefully read the first sentence of the preceding quotation? That's were the answer lies, the authors did a one-sided statistical test. If they did the usual two-sided statistical test, then the hypothesis would have been rejected (p=0.08). It seems they just applied the test that gave them a statistically significant result.

More interesting information can be deduced from these diagrams. Using the usual statistical test, it cannot be shown that the students in the product-help group 'on average' improved (the t-test for the gain from pre-test to post-test has p=0.15). Actually 6 of the 15 students in the product-help group did not improve their score. In the process-help group this is the case for 4 of the 20 students. Now of course 2 sessions of 65 minutes are not a lot of time to learn something new. It keeps amazing me how education researchers seem to think that you can learn significant material in such a short amount of time....