How should one go about trying to teach students to "unlearn" a previous skill/principle they believe is correct but is actually wrong?

Hypothetically speaking as a really basic situation, if your student was adamant that the formula for the area of a rectangle is 2*l + 2*w, even though you tried to explain that is instead the formula for the perimeter, and explained to them the definition of area vs. perimeter, but they are overly confident that they are right, how can you gently guide them to the right direction? What is best practice?

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    Ask the students to draw a 1 m^2 (or whatever unit length/area is common to them) square on the board and explain why they do as they do and then ask them to calculate its area. Clearly they should arrive at the same result both times. That should give you a foundation for evaluating their logical skills and maybe start turning their minds. May 5, 2014 at 10:22
  • Apart from the answer I gave below, your example might indicate a confusion between area and perimeter. I think I would try taking it out of the abstract, by letting them calculate how long it would take to walk around a polygon and many small tiles it would take to cover a floor, or something to that effect. May 5, 2014 at 13:09

2 Answers 2


I these cases the direct approach is seldom constructive. It's tempting to start constructing logical examples that show they must be wrong, but this is much more a matter of psychology than of logic.

Basically, the stronger you argue, the harder they will dig their heels in. With your example you may actually force a situation where they have no other way out than to admit that they're wrong, but in most scenarios they'll find a way to stick to their guns, and the more you push the issue, the harder it becomes to admit they were wrong all along.

So the trick here is small commitments. Don't ask them to accept the whole thing in one go, but get them to accept a small part of it, something they can agree on without admitting defeat. Then just stand back and let them come round on their own.

My favourite example of this principle is trying to convince a rabid anti-Apple consumer to buy an apple laptop instead of a regular PC. If you argue on quality of hardware, or value for money, or user experience, it won't do you any good (regardless of whether those are valid arguments). What you should do is buy them something very cheap and tiny, like an iPod nano, for their birthday. Once they commit to that, the anti-Apple stance is no longer a point of principle, but they're somewhere in the grey area, free to move around.

It's all about breaking down the principled stance and the ties to their pride. Only once you've got rid of that should you come in with the logical arguments.

  • @Peter thanks for the suggestion! Great Apple metaphor too (coming from someone who switched from Android/PC to Apple). I will try this out. Given the example, what would you say is a small enough commitment?
    – Lisa
    May 6, 2014 at 8:29
  • The smaller the better I'd say. It really depends on the scenario. I'd try to find small commitments by creating concrete and specific examples and stayiong away from the connection to the abstract. Really anything that they can agree to without agreeing to the main point. In your example, you might talk about a bathroom floor and how many tiles you need to cover it versus how much caulk you need to line the edges. After they've worked that out, you can slowly let them draw their own conclusions. May 6, 2014 at 21:06

I've tracked down a research paper on this very mathematical issue, which apparently has been stumping people since Plato:

De Bock, D., Van Dooren, W., Janssens, D., & Verschaffel, L. (2002). Improper use of linear reasoning: An in-depth study of the nature and the irresistibility of secondary school students' errors. Educational Studies in Mathematics, 50(3), 311-334. and http://en.wikipedia.org/wiki/Meno%27s_slave

To generalize, it is advantageous to try the following in order to create "cognitive conflict" in the student's own mind:

  1. Recognize that students' "fast thinking" (in a Kahneman sense) will be their first response. Requiring them to slow down and justify their answer will be frustrating and painful for them.
  2. Create an environment where the student is comfortable changing their answer. No attacks in front of an audience of their peers, etc.
  3. Give examples of "what other students answered," perhaps in the form of a table that shows many people chose the linear response, while others recognized area increases as the cube of length. This reduces shame at their own answer and may increase interest about why another answer was so often chosen.
  4. Give examples of the reasoning of correct students, and ask the incorrect student to justify their disagreement.
  5. I would recommend giving the student time to think, and then asking them to discuss it again another day.
  • thanks for the suggestions! I will definitely implement them. Hopefully this will bring some improvement. Thanks for the book tip too; I will be adding Kahneman's book to my reading list.
    – Lisa
    May 6, 2014 at 8:40
  • @Lisa, You might find this video helpful in avoiding firm commitment to incorrect answers. It asks students "what do you notice" before allowing them to solve a problem. youtu.be/WFvYZDR4OeY
    – Adrienne
    May 6, 2014 at 18:05

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