Are you smarter than a second grader?
Late last week I was checking my son's math homework when a "simple" assignment, turned far more complicated.
The great thing about helping your children with their homework is that it forces you to review things that you may have learned 10, 20 or even 30 years earlier. This latest assignment involved faces, edges and vertices. Basically, the homework was asking the student to give the number of these values given a different object. For example, a cube has 6 faces, 12 edges and 8 vertices.
But what about a sphere? How many faces does a sphere have? This simple question has opened up a can of worms in my house.
The second grade answer is zero, but I believe the answer is actually approaching infinity. I'm pretty good with math, but I needed more proof than just myself.
I checked with my father in-law who has a master's degree in mathematics and he gave me a very eloquent answer. Take the two dimensional approach of polygons. A triangle has 3 sides, then a square has 4, then a pentagon with 5, and then an octagon with 8. You begin to see that as you add sides, the polygon gets rounder and rounder as the size gets smaller. Therefore, one can deduce that a circle has an infinite number of sides with their length approaching zero.
In the three dimensional world, think of a pyramid, a cube, a soccer ball (32 faces). The same concept here. The more faces, the more spherical the object becomes with the area of each face approaching zero.
So, even though my son said "infinity", he was told that the answer is zero. I checked with the school about this. I was informed that the curriculum for second grade only covers concrete concepts and that abstract concepts aren't yet covered, therefore the answer is considered wrong, even though it's right.
My son's principal is going to take my concern about the curriculum to the central office and I plan on asking them myself.
But doesn't it seem wrong to teach the wrong answer and then correct it a few years later? Doesn't it seem wrong to not have enough flexibility with the curriculum to accept the mathematically correct answer because it's beyond the current grade level? Shouldn't our schools be fostering this enhanced understanding instead of making a 7 year old think he's wrong?
I have told my son to write down "infinity" on any test he may get, because that is the correct answer and I believe that the correct answer, even if it will be marked incorrectly, is the only one you can give.
The great thing about helping your children with their homework is that it forces you to review things that you may have learned 10, 20 or even 30 years earlier. This latest assignment involved faces, edges and vertices. Basically, the homework was asking the student to give the number of these values given a different object. For example, a cube has 6 faces, 12 edges and 8 vertices.
But what about a sphere? How many faces does a sphere have? This simple question has opened up a can of worms in my house.
The second grade answer is zero, but I believe the answer is actually approaching infinity. I'm pretty good with math, but I needed more proof than just myself.
I checked with my father in-law who has a master's degree in mathematics and he gave me a very eloquent answer. Take the two dimensional approach of polygons. A triangle has 3 sides, then a square has 4, then a pentagon with 5, and then an octagon with 8. You begin to see that as you add sides, the polygon gets rounder and rounder as the size gets smaller. Therefore, one can deduce that a circle has an infinite number of sides with their length approaching zero.
In the three dimensional world, think of a pyramid, a cube, a soccer ball (32 faces). The same concept here. The more faces, the more spherical the object becomes with the area of each face approaching zero.
So, even though my son said "infinity", he was told that the answer is zero. I checked with the school about this. I was informed that the curriculum for second grade only covers concrete concepts and that abstract concepts aren't yet covered, therefore the answer is considered wrong, even though it's right.
My son's principal is going to take my concern about the curriculum to the central office and I plan on asking them myself.
But doesn't it seem wrong to teach the wrong answer and then correct it a few years later? Doesn't it seem wrong to not have enough flexibility with the curriculum to accept the mathematically correct answer because it's beyond the current grade level? Shouldn't our schools be fostering this enhanced understanding instead of making a 7 year old think he's wrong?
I have told my son to write down "infinity" on any test he may get, because that is the correct answer and I believe that the correct answer, even if it will be marked incorrectly, is the only one you can give.
posted by Howard Bernstein, 9 Weather Now at
11:59 AM
3 Comments:
The answer to this question, as I have discovered, is hotly debated. The discrepancy seems to lie in the definition of "side."
How many sides does a circle have?
It could have 1 curved side (along the circumference).
It could have 2 sides (inside and outside surfaces).
It could have infinite sides. Each side being very very small.
And if a side is defined as a straight line, it could have zero sides.
Personally, I see this as a limit question as the number of sides approaches infinity. But this begs the question, if the school is only looking for absolute answers, why are they asking abstract questions?
I did not attend local schools, but I too encountered difficulties with how math is taught in schools. Many years ago, an answer I gave on a test was marked incorrect because I used the formula y=mx+b to arrive at the solution instead of plotting points. Schools should encourage children to excel in math instead of punishing them for thinking outside of the narrow curriculum that they are taught.
Hi Howard,
I teach Geometry at Skyline HS in Front Royal. Very interesting view on spheres and circles. I never thought of it that way. The best way to explain "sides" is "how many segment" which need to be straight. The best way to explain "faces" would be "how many flat parts." If a circle or sphere had sides or faces, no matter how small they are, then it is not a circle or sphere.
Or a circle could be defined as an infinite number of points in a plane that are equidistant from one central point.
If we define it that way, then adjacent points would be line segments (sides), although there length would be just about zero.
Same argument for a sphere, just that the points are in all planes from one central point.
Howard (hbernstein@wusa9.com)
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