A secondary mathematics course, such as algebra, often employs the use of worked examples as an instructional device. The role of a worked example serves as a key component to understanding the problem type being taught and can be presented to the class in multiple ways. Under the behaviorist tenet, a teacher presents the worked examples, explains the necessary procedures to obtain the solution, then through guided practice the students utilize the worked examples to work similar problems upon which the students receive feedback regarding their progress. Using a constructivist approach, the instructor provides students the opportunity to construct mathematical ideas by posing real world problems as examples. Here the goal would be for the students to realize the procedure to solve the given problem through exploration and discussion as facilitated by the teacher. In either case, the instructional goal for the lesson would be schema development of the problem type in the student’s long term memory that enables the transfer of information learned to novel problems.
Comprehension of the material is governed by factors such as presentation, relevance, and difficulty level of the content. However, retention and retrieval are regulated partly by the effectiveness of structure of the lesson design and partly by the individual memory of the student. To design effective worked example presentation it is important to consider the individual memory of the student. Marsh and Butler (in press) concur in their article stating, “It is key to consider what type of processing different learning strategies encourage.” The psychological perspective of memory is important to regard when designing instruction using worked examples.
Atkinson et al. (2000) suggested that highlighting certain subgoals of the problem increase the likelihood that learners will be able to transfer the problem’s structure to novel problems. Hence implying the problem schema has been formed in the student’s long term memory. Marsh and Butler (in press) discuss similar strategies in their article. The human brain has the innate ability to create logical connections between related parts and the bigger picture. Labeling and visually isolating certain features of the worked examples can direct the learner’s attention to the structural nature of the problem and helped students form connections thus further facilitating schema acquisition.
Regardless of what theoretical approach is taken when designing worked example instruction, the strategies employed should minimize superfluous material and optimize training opportunities to facilitate schema constructions.
Atkinson, R. K., Derry, S. J., Renkl, A., & Wortham, D. (2000). Learning from Examples: Instructional Principles from the Worked Examples Research. Review of Educational Research, 70(2), 181-214.
Marsh, E. J., Butler, A. C. (in press). Chapter 29: Memory in Educational Settings.
Simon, M. A. and Schifter, D. (1991). Towards a constructivist perspective: An intervention study of mathematics teacher development. Educational Studies in Mathematics, 22(4), 309-331.
Your phrase about the human brain's innate ability to create logical connections between related parts and the bigger picture stood out to me. Do all brains respond the same way? Are we constantly forming connections or must connections be drawn? Do some people have the greater facility of connecting than others? Several of the readings make a strong argument for the power of connections in memory as opposed to memory being a gift, per se, but are there innate differences in the facility for forming connections? Does someone with more life experiences also have a better memory?
ReplyDeleteI like your idea that a constructivist version of a worked example would be a real world problem facilitated by trial and discussion. I think Kirchsner et al. article left out that idea and acted as if the student were on their own. What you posited still seems like an effective method of algebra instruction and gave me more ideas of how constructivism and allowing students to make their own meaning can be more than just mininally guided instruction. What did you think of the Kirchsner article? Do you think constructivism can still be effective?
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