Learning from worked-out examples has been proved to be very effective in initial skill acquisition. In order to fully exploit the potential of example-based learning, teachers should know how to effectively employ such examples in classroom instruction. Therefore, we designed a computer-based learning environment in which mathematics and science teachers learn how to effectively use worked-out examples. The computer-based learning environment was deployed in a workshop on example-based classroom teaching. Participants (25 maths-teachers) first learned about example-based classroom instruction and afterwards received either the computer-based learning environment or the standard workshop materials (i.e., a printed version of the workshop-foils) for follow-up course-work. A comparison of the training with and without the computer-based learning environment showed that teachers who had the opportunity to deepen their knowledge with the computer-based learning environment had significantly more knowledge about this topic. Furthermore, teachers who were given the computer-based learning environment rated the intenseness of their follow-up course-work higher. However, they did not spend more time with follow-up course-work. Thus, the differences in learning success are supposed to be based in the more intensive follow-up course-work to which the participants were encouraged by the computer-based learning environment.

Worked-out examples consist of a problem formulation, solution steps and the final solution. To fully exploit the potential of example-based learning, not only one but several examples are best presented before problems to-be-solved. Several studies found that students typically prefer learning from worked-out examples. Students learning with worked-out examples usually need less time for learning, are faster when they solve problems on their own and make fewer mistakes. According to these very promising results we challenge teachers to “Give them time to think it over!” This means that the teachers should provide their students the possibility to study worked-out examples before imposing problem solving demands.

 

Based on a needs analysis examining classroom videos, schoolbooks and interviews with teachers (for details: Hilbert, Renkl, Schworm, Kessler & Reiss, 2006), we developed a computer-based learning environment on example-based classroom teaching. This computer-based learning environment was deployed for follow-up course-work in a workshop for mathematics and science teachers on how to effectively employ worked-out examples in classroom instruction. To test the benefit of the computer-based learning environment, the workshop was carried out with and without offering participants the computer-based learning environment for follow-up course-work. The following specific research questions were addressed:

1. Does the computer-based learning environment help teachers gain more knowledge about example-based classroom teaching than standard workshop materials?

2. Do teachers being offered the computer-based learning environment spend more time with follow-up course work than when being offered the standard workshop materials?

3. Do teachers being offered the computer based learning environment assert that they did more intensive follow-up course work than teachers being offered the standard workshop materials?

 

In a workshop on example-based teaching, 25 mathematics-teachers learned about how to effectively use worked-out examples in their classrooms and how example-based learning can be supported by self-explanation prompts. The workshop lasted two sessions of approximately four hours at intervals of three weeks.

In the first session, teachers learned about theoretical issues of example-based learning and teaching. At the end of the first session, teachers either received a CD-ROM with the computer-based learning environment (n = 15) or were offered the standard workshop materials (i.e., a printed version of the workshop-foils, n = 10). Both groups were asked to use the computer-based learning environment and the standard workshop materials respectively for follow-up course work.

Three weeks after the first session, teachers attended the second session of the workshop. On this date, practical issues of example-based issues in the mathematics classroom were discussed. In the beginning of the first session, teachers were asked to fill in a questionnaire on knowledge about example-based teaching consisting of five items (maximum score: 15 points; e.g., “How can self-explanations when learning with worked-out examples be fostered?”). Additionally, participants were asked, how many minutes they spent learning with their follow-up course work-material and how intensively they did so on a rating scale from 1 (very superficial) to 6 (very intensive).

 

An alpha-level of .05 was used for all statistical analyses. As an effect size measure, we used Pearson’s correlation coefficient r – qualifying values of about .10 as weak effect, values of about .30 as medium effect, and values of about .50 or bigger as large effect.

On average, teachers who were given the computer-based learning environment for follow-up course work achieved better results in the questionnaire on knowledge about example-based teaching (M = 5.06, SD = 3.35) than teachers who were given the standard workshop materials (M = 2.85, SD = 2.10). This difference was significant, t(21) = 2.57, p = .018, r = .24.

Unfortunately, only 12 teachers gave particulars on how long they learned with their follow-up course materials and only 13 stated how intensively they did so (eight in the group with the computer based-learning environment, four and five respectively in the group with the standard workshop materials). We found no significant difference for the time spent with follow-up course work, t(10) = 1.04, p > .10, r = .10. On average, teachers spent 27.50 minutes with follow-up course work, when they were given the computer-based learning environment (SD = 10.00). Teachers who were given the standard workshop materials spent M = 19.00 minutes with follow-up course work (SD = 18.99). The intensity with which teachers did their follow-up course work also did not significantly vary between groups, t(11) = 1.93, p > .05; however, it did represent a medium sized effect r = .25.

 

Clear effects of the kind of follow-up workshop materials on learning success were found in this study: Teachers learned more about example-based teaching when they had the opportunity to use the computer-based learning environment than when they were given the standard workshop materials. However, this result could not be attributed to differences in the time spent with the workshop materials which also speaks in favour for the profitableness of the computer-based learning environment. Furthermore, we found a medium effect of the workshop materials on the intensity of teachers’ follow-up course work. However, one problem with this study was that many teachers refused to answer the questions on the time and intensity of their follow-up course work. Also, there is no information on the reliability of teachers’ statements. Future studies on the benefits of the computer-based learning environment should take greater care to control the conditions. Nonetheless, our conclusion of this field-study is that the computer-based learning environment is a profitable addition for the workshop on example-based classroom teaching.

 

Literature

Hilbert, T. S., Renkl, A., Schworm, S., Kessler, S., & Reiss, K. (2006). Learning to teach with worked-out examples: A computer-based learning environment for teachers. Manuscript submitted for publication.

Renkl, A. (2005). The worked-out-example principle in multimedia learning. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning. Cambridge, UK: Cambridge University Press.