Example-rule coordination

Brief statement of principle

Instruction that combines or helps students' combine learning from examples and learning of or from rules tends to be more effective than instruction that does not.

Description of principle

Example-rule coordination refers to a class of instructional methods that involve combining instructional examples with other forms of instruction including self-explanation, problem-solving practice, analogical comparison. Coordination support may occur through explicit prompting for self-explanations, interleaving worked examples and problems, fading assistance from worked examples to problems.

Examples

Studies exploring various forms of example-rule coordination include: Butcher's integrated hints in Geometry, Booth's corrective self-explanation in Algebra, McLaren's worked example interleaving in Chemistry, Eskenazi's vocabulary example personalization in English, Ringenberg's example-based help in Physics, Anthony's worked example interleaving in Algebra, Noke's analogical comparison of examples in Physics, Renkl's example fading in Geometry.

Experimental support

See the pages listed above the examples section for studies providing experimental support. See also the references below.

Theoretical rationale

Combining examples and rules can enhance refinement toward better feature validity of knowledge components. That refinement may be supported or enhanced by various instructional methods and learning processes. By prompting students to engage in self-explanation of an instructional example, students are more likely to try to express the more general rules inherent in the example and thus focus on the deep, relevant features rather than shallow, perceptual features that are irrelevant to correct application of the target knowledge component.

Another way combining instructional examples and rules may enhance refinement is through self-supervised learning processes similar to co-training whereby a learner may draw on complementary strengths and weaknesses of learning by induction from instructional examples versus learning by comprehension of instructional text or rules. More specifically, a learner may identify and eliminate errors in induction from an instructional example by noticing an inconsistency with his or her comprehension of a given verbal rule. Or, conversely, a learner may identify and eliminate errors in comprehension of a rule by noticing an inconsistency with his or her induction (or analogical reasoning) from an example.

Variations (descendants)

worked examples, self-explanation, analogical comparison

Generalizations (ascendants)

coordinative learning

References

References that need to be added:

1. worked example references (Sweller, Renkl, etc.)
2. specific papers on studies that combine example and rule instruction by Nisbett, Holyoak etc.
3. self-explanation references (Chi etc.)
4. analogical comparison refs (Gentner, Nokes, etc.)

• Blum, A., & Mitchell, T. (1998). Combining labeled and unlabeled data with co-training. In Proceedings of Eleventh Annual Conference on Computational Learning Theory (COLT), (pp. 92–100). New York: ACM Press. Available: citeseer.nj.nec.com/blum98combining.html
• Holland, J. H., Holyoak, K. J., Nisbett, R. E., & Thagard, P. R. (1986). Induction: Processes of inference, learning, and discovery. Cambridge, MA: MIT Press.
• Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346–262.
• Rittle-Johnson, B., & Koedinger, K. R. (2002). Comparing instructional strategies for integrating conceptual and procedural knowledge. Paper presented at the Psychology of Mathematics Education, National, Athens, GA.