Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

A “simple” 3rd grade problem

math.stackexchange.com

Post reply on HN
Print view View original

141–150 of 174 posts

Re: A “simple” 3rd grade problem

#141

Post by alok-g »

s_kilk wrote: post #26
auctiontheory wrote: post #20

A friend of mine teaches school in rural North Carolina - here's what she tells me. Her school has to meet certain percentage-based "standards" - I forget the exact numbers, but let's say 75% is the cutoff. So now when Joey gets 5 answers right out of 10, the resulting 5/10 is defined as "75%." We're doomed.

Wait... How on earth do they justify redefining 50% as 75% ? (or whatever the actual numbers are)

My undergrad professor in electrical engineering asked us to calculate voltage on a diode as part A of a problem. This came out as 0.7V. The part B was to convert this to percentage! (Don't ask me how and why the answer was 70%).

Re: A “simple” 3rd grade problem

#142

Post by alan_cx »

For me this question is more about careful reading that actual mathematics. A valuable lesson, IMHO.

As for the teacher, well, I and my entire class once spent half a lesson arguing with our maths teacher who was swearing blind that 1x1=2. She wasn't an idiot or any thing, actually usually a very good teacher, but she just had one of those silly mind blocks. Once it clicked in her head she basically realised how mad she looked and took it with great humour. So, fair enough. Only human.

Re: A “simple” 3rd grade problem

#143

Post by waps »

Periodic wrote: post #120
SiVal wrote: post #117

Earlier quoted context omitted.

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…

When I did my undergraduate degree in physics I think one of the best things I learned early on was estimation skills. I was used to doing things precisely and finding the tricks. Our professors made jokes about things just needing to be right to "within an order of magnitude", and it wasn't for two years that I internalized that. When you deal with the real world there are always a lot of errors and uncertainty in m…

I remember this from my first university physics class. We would derive a movement equation for a cannonball, to find the optimal angle to shoot a cannon for maximum travel. Everybody knew the answer of course, but we'd always just used the formula. This time we'd start with the obvious integration equation, movement + attraction between 2 point masses, integrate over flight time, and find the point where it crosses the ground plane.

And then the teacher just took the range from the integration, and the formula, multiplied the two and put a ~= sign between them. I believe I actually stood up and said you can't do that and we had the first of many discussions about exactness.

That was scary.

That was my first run-in with what I considered the central article of my then faith : that you can derive the structure of the physical world from first principles. Throwing away terms in an equation in order to arrive at correct physics laws, I don't know, I considered it sacrilege or something. Of course I've since learned that deriving all of physics from it's own basic laws doesn't work, and the way we fix that is that we delete "inconvenient" terms in the equations when required. Deriving physics from a few mathematical laws is completely impossible. You can't even correctly derive the (mathematical) fields used in physics, so the very numbers that one uses to do physics aren't actually valid mathematical numbers.

So the relation between physics and mathematics is not that one is based on the other, because that was tried and didn't work out, and people have almost completely given up. So it was replaced by a marriage of convenience (this works ! Sure it won't validate mathematically but the numbers look really similar), ignoring at least a dozen elephants that stood in the way, and we just act like they don't exist.

Re: A “simple” 3rd grade problem

#144

Post by WildUtah »

keithpeter wrote: post #68
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…

Yes. This is the '10 posts, nine spaces' problem. Here is another version: A fence is made using 15 posts spaced equally along a straight line. There are 3m between each post. What is the distance between the first and last post? When I'm teaching this kind of thing, we go out and walk around the building site opposite with a few 15m measuring tapes. The physical walking out and measuring helps.

+1 for arranging your question so that it has The answer.

Re: A “simple” 3rd grade problem

#145

Post by rsl7 »

RivieraKid wrote: post #89

Perhaps the teacher or the author of the question understood the problem differently – we are cutting off small pieces from a long stick. So to cut off 2 pieces, we need 2 cuts, not 1.

very clever. this ambiguity shows how difficult it is for creative students and how important it is to be graded on the process as well as the conclusion. The process would show your divergent thinking and why you arrived at a different answer.

Re: A “simple” 3rd grade problem

#146

Post by serginho »

It' just an interpretation of a language. If it was - to cut out 2 pieces from an infinity board - then a teacher is correct. If it was - to cut into 2 pieces a board to get nothing from a board in the end - then a student is correct.

Re: A “simple” 3rd grade problem

#147

Post by ubernostrum »

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…

Most likely, whoever produces and publishes the question sets changed the question for a new edition and did not notice that the new question also changed the answer.

In the previous edition it was probably something like "Marie works in a factory which makes cars; it takes her 10 minutes to finish two cars. How long will it take Marie to finish three cars?"

And the answer to that would be 15 minutes, and the reasoning in the answer (based on reducing fractions, which is what it's probably supposed to teach) would be correct.

But probably in the next edition the question changed from putting things together to cutting them apart, and the author/editor simply didn't realize that these are not interchangeable. The teacher, meanwhile, probably didn't look too closely at it, and simply applied the answer and reasoning supplied in the teaching materials for the question set.

None of which implies that the teacher can't do the math; rather, it implies systemic problems in the way the materials are produced and in the methods used by teachers to grade the work.

Re: A “simple” 3rd grade problem

#148

Post by oneeyedpigeon »

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

[ "cache invalidation", "naming things", "off by one errors"].length != 2

Re: A “simple” 3rd grade problem

#149

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

#150

Post by rmrfrmrf »

dfc wrote: post #116
rmrfrmrf wrote: post #114

Earlier quoted context omitted.

Unless you have some kind of vice holding that piece of wood together, you're making 3 cuts.

As I stated downthread: If you ask me to make these cuts I am plugging in my chop saw (or mitre saw if you prefer) I am making 1, 2 and 2 cuts. Where one cut is defined as pulling the trigger on the saw arm and pressing the handle down. Your "vice" will be my left hand pushing the wood against the fence and towards the stop block. Do you do a lot of woodworking?

Yes, actually. I was just going by the clear-as-day diagram showing a hand saw. Feel free to continue laying on the snark, though.
Post reply on HN