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Publish at 07 décembre 2021 Updated 16 décembre 2021

Learning analogies in problem solving

An effective technique, with its limits

Humans have a good memory, but it doesn't compare to some of our animal counterparts. Indeed, birds are able to follow the same migration routes, elephants retain watering holes, and dogs retain smells in their heads for years. Yet, short of being able to store material indefinitely in our thinking, we are champions at making connections.

Analogies simplify knowledge (too much)

For some, this is what makes our species strong. Language quickly adopted images. This became poetry and many other things; this strength can be used in education. Our brains are very good at making analogies and thus decoding the world around it. Of course, this requires a certain amount of gradation in young children. For example, a teacher talking about carnivores should perhaps compare a lion and a tiger before making the similarity with a shark.

Since the use of analogies can harm as well as help learners. In fact, according to the opinion of some, it would be better if teaching did not rely solely on this type of approach, because, yes, it simplifies complex phenomena but it can also lead to misunderstanding or misconceptions held throughout life. Let's take the example of the atom, which is always shown in textbooks as a nucleus of protons and neutrons around which electrons gravitate. Yet this ultra-familiar form is wrong and in no way represents the real picture of atoms that physicists are working on.

The problem is mainly that the analogy is seen as an explanation rather than a simplification. It is also wrong if it is used to generalize complex concepts. Thus, the risk is to miss the complexity of things. One only has to look at the "understanding" in immunology of many Internet users since the arrival of covid-19 to understand that analogies sometimes lead to misinformation. By the way, an analysis by Toronto researchers demonstrates the limits of analogy in mathematics when it comes to teaching this science. It can work, but they should not be the only teaching method.

Mathematics + intuitive analogies = winning recipe

It is true that if there is one subject in which analogies are frequently found, it is math. We're talking about a very abstract science that would be hard to get across without having to use various examples. Yet, as shows in this speech, the formulation of a problem will not create the same image in students. "There are five birds and three worms. How many more birds are there than worms?" This problem seen by prep students will be more difficult than this version, "There are 5 birds and 3 worms. How many birds will not have worms?" Why? Because even though it is the same operation to solve (5-3=2), the extra-mathematical knowledge used will not be the same. Children will have an easier time grasping the concept that birds eat worms, that usually in their living situation, food is present equally, etc.

So, a big part of the teacher's job will be to build on the intuitive analogies that learners have so that they understand concepts. Substitute analogies have more effect in a problem than the term subtract. It is better to use "lose", "take away", "remove" that the child can associate with their daily life. Some scenarios may also be better suited to different arithmetic operations. For example, it will be more difficult to divide 12 oranges by 4 apples to find out how many more times the citrus fruit is present. On the other hand, taking those 12 oranges and separating them into 4 baskets will be an easier image to get across. This explains why textbooks in mathematics try to be as consistent and as little discordant as possible.

This analogical reasoning will, of course, grow over the years with algebra and more advanced mathematics. The use of analogies will then be able to come from students themselves who will use different images in order to be able to solve complex equations. The creation of associative structures becomes almost mandatory in order to successfully pass the initial difficulty of the problem. However, again, analogy is not everything and they must also be able to understand algebraic elements to avoid falling into the trap of ease.

Illustration : Annie Spratt on Unsplash

References :

Duane Hicks, Michael. "Describing Students' Analogical Reasoning While Creating Structures in Abstract Algebra." Digital Collections at Texas State University. Last updated May 2021. https://digital.library.txstate.edu/handle/10877/13500.

"Le Rôle Des Analogies Dans La Résolution De Problèmes Aux Cycles 2 Et 3." Centre Alain Savary - Education Prioritaire - Ifé. Last updated: June 4, 2021. https://centre-alain-savary.ens-lyon.fr/CAS/mathematiques-en-education-prioritaire/compte-rendus-formations-de-formateurs-mathematiques/session-2019-2020/le-role-des-analogies-intuitives-dans-la-resolution-de-problemes-arithmetiques-aux-cycles-2-et-3.

Morgan, John. "How Analogies Support Learning." Tes. Last updated: February 26, 2021. https://www.tes.com/magazine/article/how-analogies-support-learning.

Rivier, Catherine. "Intuitive Analogies In Arithmetic Problems With Verbal Statements For Cycle 2 Students In France." UNIGE Open Archive. Last updated: April 20, 2021. https://archive-ouverte.unige.ch/unige:151078.

Sarina, Vera, and Immaculate K. Namukasa. "(PDF) Nonmath Analogies in Teaching Mathematics." ResearchGate. Last updated: January 25, 2010. https://www.researchgate.net/publication/248607025_Nonmath_analogies_in_teaching_mathematics.

Suresh, Arun. "Why You Shouldn't Use Analogies to Learn." Medium. Last updated: January 16, 2021. https://medium.com/curious/why-you-shouldnt-use-analogies-to-learn-89a2db42f282.


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