the incredible power of analogy

THE 3 A’S OF KNOWLEDGE TRANSFER: ACQUIRE, ANALOGISE, APPLY PT 2

This is the third instalment of a 4 part series aimed at assisting an educator in designing a sequence of learning that drives towards the ultimate goal of knowledge transfer. The intro post is here and the post on the first stage of developing a context of transfer, acquiring knowledge, is here

PT 2: Analogous examples 

The importance of presenting analogous examples to students to facilitate transfer is made apparent by Gentner and Ratterman (1991), who purport that people learning from a single example of content tend to encode it in a context-specific manner, with the result that later remindings are often based on more obvious surface aspects. Applying knowledge to a new context from only seeing one example of the learning is significantly harder compared to providing an analogy for students, but as Reeves and Weisberg suggest, it is not enough to simply provide a single analogous examples to your students. 

The beginnings of analogical reasoning

 Karl Duncker was a quite remarkable German psychologist.

He dedicated considerable energy into exploring how learners approach problem solving, and his thesis on how it happens is here. His candle problem highlighted the notion of Functional Fixedness, which highlighted that once a learner has established a schema for a certain function, it is difficult for the ‘function’ to be applied in another context. Before his tragic death, suicide at 37 years of age, Duncker created the ‘radiation problem’, where he established that learners asked to solve the problem could only do so 10% of the time. It is this very low number that paved the way for considerable research into how to assist the problem solving dilemma of functional fixedness.

Gick and Holyoak are perhaps the most notable of researchers to shed light on how to mitigate functional fixedness. They found that when students were given an analogy to the Duncker tumour problem that had the same underlying structural properties, the number of students who were able to solve the problem rose from 10% to 30%. Incredibly, when they experimented by providing a 2nd analogy prior to exposing students to the radiation problem they found that 80% of students could then solve the problem. When they provided a underlying principle to students, when only a single analogy was used it did not assist students, but when 2 analogies were given, the underlying principle increased student success to 82% with a verbal principle, and 92% with a diagrammatical principle.

Of particular note however, was Gick and Holyoak’s attention to the quality of a student’s schema when applying the analogies to the problem. What they found, consistently, was that when a student presented a good quality schema, found by having students articulate the similarities between analogies, 100% of students were able to solve the problem. This has enormous implications for the need to ensure that a well-developed schema is present when asking students to apply or transfer knowledge into a new context.

It highlights the fact that it is the bank of mental models and patterns that a student has that allows them to search and seek connections from the schema to the new learning context. If they have a good understanding of the general principles of a problem, characterised by identifying the deeper relational structure of a problem, then it is more likely they will be able to see the same structure in a new problem. As Duncker states, ‘one can transpose a solution only when one has grasped its functional value, its general principle, i.e., the invariants from which, by introduction of changed conditions, the corresponding variations of the solution follow each time.’

Gick and Holyoak’s work has been validated by other researchers. Alfieri, Nokes-Malach and Schunn conducted a meta-analytic review of research using comparison examples to assist problem solving, and found conclusive evidence that analogical reasoning using several comparisons benefits the transfer of knowledge. Jacobson et al report that providing students’ opportunity to search for the similarities of analogy structures improves problem solving and transfer capability, and adding to the weight of evidence, Markman and Gentner suggest that directing students to the structural similarities is what eventually builds the schema that the student will use to connect to new learning contexts.

So, analogy greatly assists students in being able to transfer knowledge into a new context. Providing at least 2 analogies and explicitly pointing students to the similarities appears to be the optimal context for developing the relevant schema for transferring and applying knowledge.

How to exploit this ability to transfer and apply knowledge will be the basis of the next post.

References

Language and the career of similarity. Gentner, D., & Rattermann, M. J. (1991). In S. A. Gelman & J. P. B yrnes (Eds.), Perspective on thought and language: Interrelations in development (pp. 225-277).New York: Cambridge University Press.

Learning Through Case Comparisons: A Meta-Analytic Review. Louis Alfieri,Timothy J. Nokes-Malach &Christian D. Schunn. Pages 87-113 | Published online: 20 Apr 2013

Schema abstraction with productive failure and analogical comparison: Learning designs for far across domain transfer. Jacobson, M., Goldware, M., Lai, P. 2020. https://www.sciencedirect.com/science/article/pii/S0959475218301506

Structural Alignment during Similarity Comparisons. Markman, A.B., Gentner, D. (1993). https://www.sciencedirect.com/science/article/pii/S001002858371011X

The role of content and abstract information in analogical transfer. REEVES, L. M., & WEISBERG, R. W. (1994). Psychological Bulletin, 115, 381-400.

I’m Paul Moss. I’m a learning designer at the University of Adelaide. Follow me on Twitter @edmerger

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