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A “simple” 3rd grade problem

math.stackexchange.com

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Re: A “simple” 3rd grade problem

#121

Post by dhimes »

Sunlis wrote: post #85
wtallis wrote: post #77

Earlier quoted context omitted.

You're not convinced this actually happened? When I was in elementary school, I regularly (ie. several times per semester) got into arguments with my math and science teachers over stuff this dumb. There's no need to make up something like this when you can find it in the real world so easily.

In grade school I had an argument with my science teacher about wheels. She said that a point along the outside of a wheel moved faster than a point nearer to the center (which is absolutely correct). However, she followed that up by saying that the outside of the wheel makes more revolutions than the inside. I tried to correct her, but she wasn't having any of it. So I grabbed my bike from outside, brought it into t…

At least she admitted it- bravo for her (and you!)

Re: A “simple” 3rd grade problem

#122

Post by dhimes »

jneen wrote: post #86
dhimes wrote: post #43

Earlier quoted context omitted.

My god, this looks more like a 4chan troll post than stackexchange. I'm not convinced this really happened. Is this the only kid in the class that got it right? Did the teacher not then notice when the brighter kids were coming up with 20 min that there may be something to it, and reconsider the question himself/herself? So much fail in so little space. Ugh.

In high school geometry, I remember my teacher making some assertion that was plainly false - I think it was that 3 planes always intersect in a line. After arguing with him for like 15 minutes, I walked to the front of the class and wrote a proof on the board. I spent the rest of the class period sitting outside.

If only there was a way to get those teachers reprimanded and retrained.

Re: A “simple” 3rd grade problem

#123

Post by chacham15 »

dos1 wrote: post #106
sillysaurus wrote: post #101

Earlier quoted context omitted.

It seems likely that no one taught those students how to think about math. I.e. teaching students the steps to solve a math problem is not teaching them how to think about the problem. I instantly knew 12/13 + 7/8 was ~2 because I visualize two pie charts in my head, both of which are mostly full. This is in contrast to the other way to solve the problem, converting the fractions to a common denominator and then divi…

It's always interesting to hear how people go about solving math problems. You mention a pie chart visualization and then the much more labor intensive (but maybe "correct"?) method. I used a third way, which was thinking that 13/13 would be one, so 12/13 is pretty close, so that's ~1. And 8/8 would be 1, so 7/8 is pretty close and also ~1. 1 + 1 = 2 :) I imagine there are myriad other ways people approach estimation…

I did it that way too. And while I agree that the best teacher for a person is that person themselves, this is such a basic understanding of math that I think that even the less motivated need to know this.

Re: A “simple” 3rd grade problem

#124

Post by [deleted] »

gizmo686 wrote: post #55
randlet wrote: post #30

Earlier quoted context omitted.

I think the joke is: "There are only two hard things in Computer Science; cache invalidation, naming things and off by one errors".

Whats the joke? The hard things are: 0) cache invalidation 1) naming things 2) off by one errors Looks like he counted right to me. EDIT: fixed newlines

[deleted]

Re: A “simple” 3rd grade problem

#125

Post by dhimes »

tokenadult wrote: post #97

I read all the comments on the math.stackexchange.com submission and all the comments here before starting to type this reply. There are a lot of issues here, and I will try to add the perspective of a mathematics teacher. The reason I can gain paying clients for my mathematics lessons even though I have no degree in mathematics and no degree in teaching is that I can produce results that many elementary school teach…

It in no way detracts from your point, but I believe that asking a 'number sense' problem like the estimation or fraction problem you gave is a different issue than teaching the more algorithmic procedure of solving fraction problems.

One doesn't seem to preclude the other, nor does it seem to mean you won't have success in a science or technology career. I think you'll find a lot of people who know how to solve, say, 'circular motion problems,' but don't really understand what they are doing.

Re: A “simple” 3rd grade problem

#126

Post by chacham15 »

SiVal wrote: post #117
dos1 wrote: post #106

Earlier quoted context omitted.

It's always interesting to hear how people go about solving math problems. You mention a pie chart visualization and then the much more labor intensive (but maybe "correct"?) method. I used a third way, which was thinking that 13/13 would be one, so 12/13 is pretty close, so that's ~1. And 8/8 would be 1, so 7/8 is pretty close and also ~1. 1 + 1 = 2 :) I imagine there are myriad other ways people approach estimation…

I use the heuristic that many of us here probably use, consciously or not, after our years of experience with math problems: if it's a math problem, as opposed to problem in some other domain that ends up requiring math (science, accounting, carpentry, etc.), there will be some degree of artifice in the problem. Somehow, the numbers will just happen to end up being integers or perfect squares or exact multiples or wh…

I've been tutoring 1 on 1 middle school kids (at the 8th grade level) in underprivileged areas and what I find is that they have little understanding for what fractions are/represent at all. For example, I asked a student what the decimal value of 1/2 was (I had explained what decimal values were beforehand) and she didnt know. I was shocked (maybe its because we're cs people we have a special affinity for 2s). As a further test I gave her a piece of paper and asked fold the paper in half and she knew it instantly. I then asked where on the paper the 1/4 mark was. Again, she didnt know. This came from a further problem of not understanding that (1/2)/2 is 1/4. After playing with the paper folding it in so many ways she started to internalize what these fractions meant.

Re: A “simple” 3rd grade problem

#127

Post by dhimes »

randlet wrote: post #35
jrabone wrote: post #27

Earlier quoted context omitted.

It is ABSOLUTELY open for debate, and part of the clue is in the question "if she works just as fast" ie. the cutting rate is constant. Then, it is ambiguous since the SIZE of the pieces is not mentioned. It's not the teacher's fault, per se; the question is unanswerable. The student picked one interpretation but the (likely) correct one is shown in the answer http://math.stackexchange.com/a/380007

It's only open for debate if you're being extremely pedantic. There is even an illustration demonstrating exactly what the cuts look like! Yes, if you want to be very nit-picky the question is undefined, but this is a third grade math test and the only reasonable answer is 20min. The student was absolutely correct.

I agree. If I am the principal and the student protests to me and the teacher gives some bizarre-ass interpretation of the problem to me, the teacher will have a problem with me.

I've seen enough of that in high-school physics where the teacher literally doesn't understand what the hell the problem is asking to piss off the Good Humor man.

Re: A “simple” 3rd grade problem

#128

Post by jules »

driverdan wrote: post #52

I have to laugh at how much play this got at Stack Exchange and here. This is simple, scare quotes are unnecessary. The teacher made a mistake. They're not perfect, they make mistakes just like the rest of us. End of story.

It's called bikeshedding. The more trivial the problem, the larger the population able to discuss it.

https://en.wikipedia.org/wiki/Parkinsons_law_of_triviality

Re: A “simple” 3rd grade problem

#129

Post by drtse4 »

randlet wrote: post #38

Anybody talking about how this problem is ambiguous or under-specified are of course technically correct. By making that claim though, you are ignoring the context of the problem! This is a 3rd grade math test that even includes an illustration of how the cuts are made! Within that context, the answer is unambiguously 20 minutes.

Not sure about that under-specified... adding more info/clarification would mean simply giving the answer. Clicking that link i was expecting something unintuitive, but that was not the case, i agree, it's really just a 3rd grade problem.

Re: A “simple” 3rd grade problem

#130

Post by Jack000 »

Total_Meltdown wrote: post #98
downandout wrote: post #15

The student is absolutely correct. I don't think it's even open for debate. Cutting anything in half requires exactly one cut; cutting in thirds requires two. It's as simple as that. The teacher that crafted the question, or worse yet, the publisher of a textbook that may have provided the test question, needs to take a hard look at whether or not they are in the correct profession. The fact that the teacher not only…

It is open for debate. The question does not say cut "into thirds," it says "into three pieces." This - http://i.stack.imgur.com/kEjP0.png - is a perfectly reasonable answer which, assuming the rate of cutting is constant, would result in 15 minutes. It's a bad question. Edit: That said, I would have given the same answer as the student, because I think that's the most reasonable interpretation, especially considerin…

this was my first thought, but then I realized the teacher gave justification for his answer.

the problem is poorly formulated. The teacher would have been correct if it had said "it took 10 minutes to cut away 2 pieces from a very large board (thus resulting in 2 cuts, 3 pieces total)", whereas the student's answer assumes a single cut, which is more reasonable.

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