Time to Unlearn

I don’t recall now but I remember someone pointing out that a lot of the things learned in life later are just really about unlearning things taught to one earlier. While the vein of truth was evident there, it was just earlier when my wife and I were taking a look at the contents of my daughter’s Math book for the incoming school year did the impact of the truism there strike me.

When I was in college I remember a written communications mention how she found it hard to interact with high school teachers given their fondness of what she referred to as common errors. From time to time she made it a point to correct every error we had both written and spoken. Maybe it was her way of promulgating correctness the way she deemed apt.

Back then I didn’t care really because I was there only for the credits. With the following though, I think I now got to understand more what she had already realized then.

Preposition or Conjunction?

If you add 1 to 19, the result is an even number. (Yes/No)

I might be the only one to notice but adding 1 to 19 is not the same as adding 1 and 19. It might be plausible that the latter is school kid material but I’d have a hard time believing n(n+1)/2 has just been rendered grade 1 stuff already in my lifetime that fast.

Theories

If you put together two even numbers, the answer is also an even number. (Yes/No)

Unless they actually expect grade 1 pupils to prove that assertion from a given definition, (which should require at least basic knowledge in algebra,) I see no point in asking this theoretical question here. Sure the kid could get away with thinking of two even numbers, say 0 and 2, and adding them to check whether the statement holds.  In the example given it expectedly turns out true. It in fact comes out true for any two even numbers for the particular question.

I find an issue however with how this inculcates and effectively encourages a common mistake among students: proof by example. I have seen for a fact how even a lot of graduates resort to such kind of reasoning. It doesn’t mean it’s right however.

First there’s no actually such thing, (maybe they had proof by counterexample in mind, I don’t know.) Second and more to the point as my Math professor in college told someone when asked why the student’s proof for a proving question in an exam was wrong. Upon knowing that an example was presented he quickly pointed out and emphasized in class that:

An example is not a proof. What may be true for some members of a given domain may not be true for its other members.

Well at least that’s how I remember how he worded the point. At least for me, it would be best not to let kids start off with something they will have to eventually unlearn in the future. After all it shouldn’t be long before they would eventually encounter ambiguity in pushing for such mindset when they resolve a claim that all prime numbers are odd.

What if someone gets to think of 2?

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