5 ms·

Why (5x3 = 5+5+5) Was Marked Wrong

6 points by kp25 11y ago

tech_crawl_ 11y ago
Honestly had no idea about this.
dalke 11y ago
> 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 11y ago
  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 11y ago
    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.
- Leynos 11y ago
  Agreed. This exemplifies approach of hiding information, and subsequently attacking and vilifying those who sought it out through alternative channels, taken by many teachers. It is one of the reasons I came to despise much of the teaching in school.
nikolay 11y ago
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 11y ago
  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 11y ago
    Again, Computer Science! There's no such thing as "dynamic type variables" in Math!

6 points by kp25 11y ago

Honestly had no idea about this.

dalke 11y ago

> 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 11y ago
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 11y ago
  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.
Leynos 11y ago
Agreed. This exemplifies approach of hiding information, and subsequently attacking and vilifying those who sought it out through alternative channels, taken by many teachers. It is one of the reasons I came to despise much of the teaching in school.

nikolay 11y ago

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 11y ago
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 11y ago
  Again, Computer Science! There's no such thing as "dynamic type variables" in Math!