
Why (5x3 = 5+5+5) Was Marked Wrong - kp25
https://medium.com/i-math/why-5-x-3-5-5-5-was-marked-wrong-b34607a5b74c
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dalke
> If the teacher has not covered the commutative property, then it might be
> unwise to let a student continue with this line of thought.

Built in to this is the idea that only the teacher provides knowledge to the
student. Consider that the student may have learned it from a parent or
someone else, or from a book.

Thus, the author regards this not as a test of the student's math skills, but
as a test of being able to repeat a specific teacher's math pedagogy.

I like (and agree with) some the comments:

> I have to disagree with this. Your intepretation of the Wikipedia article is
> fallacious: Wikipedia says “The multiplication of two whole numbers is
> equivalent to adding as many copies of one of them, as the value of the
> other one.” They did not define “one” as being the first number in the
> problem a x b, nor “other one” as being the second.

> Whoa, so now we’re making first graders confused about the commutative
> property because of category theory? Nice

~~~
dozzie
Commutativity is somewhat subtle property. I wouldn't expect a child to
understand its implications right away and be able to act as the
multiplication _was not_ commutative.

The child could also simply not remember which way was multiplication defined,
especially that it doesn't matter for natural numbers.

~~~
dalke
The essay suggests that covering the commutative property is possible at this
age level. In any case, at this level that property means "with addition and
multiplication of numbers, it doesn't matter which one goes first."

The problem is that the test can't distinguish between two possibilities.

Here's an account I once heard. An elementary grade state-level test for
general science asked something like "of the following materials, which are
used to make plates to test mineral hardness? a) wood, b) glass, c) porcelain,
d) plastic".

The answer in real life is b) and c), but only one answer was allowed. In one
class, some students picked b) and others picked c). When the teachers
complained, the state said that glass was too dangerous for an elementary
school, so isn't part of the curriculum, so the student shouldn't know that.

The problem is, a geologist had visited the class and showed different types
of plates used in real life. The students, in essence, were penalized for
knowing more than they were expected to know.

I can make the similar case here. A good test shouldn't penalize a student for
knowing too much.

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nikolay
I disagree with the author. He confuses Math with Computer Science. In Math, a
x b and b x a are both equal and equivalent. The division example with
switching places is ridiculous. Learning from mistakes is part of the process.
Even kids who suck at Math won't switch places when dividing or subtracting!

~~~
dalke
In math, a x b and b x a are equivalent only when dealing with commutative
(a.k.a. _Abelian_ ) operations. If a and b are matricies then the above does
not hold. Consider:

    
    
       a = [1, 2]
       b = [ 3 ]
           [ 4 ]

~~~
nikolay
Again, Computer Science! There's no such thing as "dynamic type variables" in
Math!

