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

161–170 of 174 posts

Re: A “simple” 3rd grade problem

#161

Post by bigiain »

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.

Now - all those "smarter than this schoolteacher" programmers who've never put code with an off-by-one error into production put your hands up.

Yeah, my hand is firmly down too…

Re: A “simple” 3rd grade problem

#162

Post by dfc »

rmrfrmrf wrote: post #150
dfc wrote: post #116

Earlier quoted context omitted.

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.

It was not snark. I was just trying to ascertain if you were unfamiliar with working with lumber or just being difficult. Would you really make three cuts?

Re: A “simple” 3rd grade problem

#163

Post by doorhammer »

jodrellblank wrote: post #90
doorhammer wrote: post #63

Earlier quoted context omitted.

I agree with this. I think it's a pretty decent example of the fundamental attribution error. The context of the problem clearly sets it up as one of those "everyone gets this wrong, so make sure you think a second" situations (I had to think a second, anyway). I'd extend that to the publisher as well, though (or at least it's individual employees creating the book). First off, assuming the answer key has "15", I'm n…

On the topic of how math textbooks are created, you might like this commentary from Richard Feynman when he served on a school-math-textbook recommendation committee: http://www.textbookleague.org/103feyn.htm

That was an awesome read. Thanks for the article. It makes me think about how corporations work a lot of the time.

Re: A “simple” 3rd grade problem

#164

Post by _ZeD_ »

sillysaurus wrote: post #101
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 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…

this isn't about high level math... this is about penny pinch... doesn't no-one go to open-air market?

Re: A “simple” 3rd grade problem

#165

Post by jimmahoney »

reeses wrote: post #157
jimmahoney wrote: post #134

Earlier quoted context omitted.

In terms of your fraction problem, given that this is HackerNews I'm surprised that no one claimed that the answer should be zero. :) $ python >>> 12/13 + 7/8 0

Yet another reason Lisp > Python! [1]> (+ (/ 12 13) (/ 7 8)) 187/104

(If (speak you (polish reverse) naturally)).

Re: A “simple” 3rd grade problem

#166

Post by jimmahoney »

mrdmnd wrote: post #140
jimmahoney wrote: post #134

Earlier quoted context omitted.

In terms of your fraction problem, given that this is HackerNews I'm surprised that no one claimed that the answer should be zero. :) $ python >>> 12/13 + 7/8 0

You must not be using python 3, then.

Perhaps you prefer ruby?

  $ irb
  >> 12/13 + 7/8
  => 0

Re: A “simple” 3rd grade problem

#167

Post by keithpeter »

noamsml wrote: post #95
keithpeter wrote: post #69

Earlier quoted context omitted.

"When grading things, ppl usually face hundreds of copies at a time and it's very tedious." Oh, yes, been there and I have the video. Don't you work from pre-written and checked marking schemes?

It depends. In algorithm classes, there are often many right answers, including ones you haven't thought of before. Same goes for most college math.

"In algorithm classes, there are often many right answers"

I accept this, but I'm assuming the original algorithm that a creative student produces will pass tests/produce same output as the 'textbook' solution. My understanding of the original article is that a correct final answer was marked wrong.

"Same goes for most college math."

Absolutely. My favourite from 16+ maths (GCSE in UK) is the area of a trapezium. Most find the mean length of the two parallel sides and multiply that by the distance between the parallel sides (so make a rectangle of the same area). About 1 in 15 break the trapezium up into two triangles and add the areas.

Re: A “simple” 3rd grade problem

#168

Post by keithpeter »

shrikant wrote: post #151
keithpeter wrote: post #68

Earlier quoted context omitted.

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.

Surely I can't be the only one who wondered if the posts were of non-negligible thickness!

OK, you got me!

Change "There are 3m between each post." to "The distance from one post centre to the next is 3m"

Which illustrates the general point: you need teams working the test and checking their answers against what the writer thought the answers were. You also need English specialists checking the wording of the questions.

Re: A “simple” 3rd grade problem

#169

Post by keithpeter »

jasomill wrote: post #131
keithpeter wrote: post #68

Earlier quoted context omitted.

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.

So does considering simpler cases of two posts (3), three posts (3 + 3), and four posts (3 + 3 + 3), then discovering the pattern (3(n - 1)).

Yes when teaching GCSE here in the UK where there is an algebra component.

I've also had students in Functional Maths classes just sketching arrangements of posts and counting the spaces.

Post reply on HN