91–100 of 174 posts
If you want to see how good you are at writing test questions with unambiguous answers, I challenge you to write a full set of questions for a trivia night at your local bar/church/whatever. I wager you will be pleasantly humbled.
Earlier quoted context omitted.
It's called grading on a curve, and it's (imo, unfortunately) very common in undergraduate courses in the US :)
it was used by many of my math & science classes here in canada, and i'm unsure why it is a problem? The prof would make the test very hard so the average was around 50-70 and then use a curve to get grades.
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…
You can't tell if it was a simple "whoops, I thought this question belonged to a problem category X, and I overlooked that it does not" typo-like mistake, meaning the teacher would instantly realize his/her mistake if you point it. Or if they wouldn't get it even after you try to explain it to them (what you're trying to imply here). When grading things, ppl usually face hundreds of copies at a time and it's very ted…
As it is, this is one case among many (not all about grade schoolers and not all 'stories on the Internet' by a long shot) and the professor doesn't always acknowledge they were wrong. Speaking as an engineer, the work is hard enough when you do understand the math.
Earlier quoted context omitted.
While, given the picture presented the child's solution makes the most sense, there is another close scenario in which the teacher is correct[1]. So its not really "as simple as that." [1] http://math.stackexchange.com/a/380007
Yes, the question did not account for unknown specifics. There is also a 3rd answer which in which the answer accounts for the person making the cuts having to answer the phone half way through the job.
Earlier quoted context omitted.
You can't tell if it was a simple "whoops, I thought this question belonged to a problem category X, and I overlooked that it does not" typo-like mistake, meaning the teacher would instantly realize his/her mistake if you point it. Or if they wouldn't get it even after you try to explain it to them (what you're trying to imply here). When grading things, ppl usually face hundreds of copies at a time and it's very ted…
"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?
The problem at hand is "what are you supposed to do" vs the actual problem at hand. At first I had a difficulty seeing why 20 should be wrong, but then it dawned upon me: The teacher set out to create a word problem for a specific mathematic solution strategy. Students probably were inundated with this strategy for weeks before the test, so for them it is very clear what they were supposed to do.
Absolutely. The test was probably written by the person grading it to cover fraction/ratio problems. The question shown is a poor rewrite of something like, "If it takes 10 minutes to fill two buckets, how long does it take to fill three buckets?"
I think, this is a good example why you should not divide math problems in rigid cetegories. Things become worse when badly taught high school students go to college, and fail to do simple arithmetics and algebra.
http://www.ams.org/notices/200502/fea-kenschaft.pdf
reports on her work in teacher training programs for in-service teachers in New Jersey. "The understanding of the area of a rectangle and its relationship to multiplication underlies an understanding not only of the multiplication algorithm but also of the commutative law of multiplication, the distributive law, and the many more complicated area formulas. Yet in my first visit in 1986 to a K-6 elementary school, I discovered that not a single teacher knew how to find the area of a rectangle.
"In those innocent days, I thought that the teachers might be interested in the geometric interpretation of (x + y)^2. I drew a square with (x + y) on a side and showed the squares of size x^2 and y^2. Then I pointed to one of the remaining rectangles. 'What is the area of a rectangle that is x high and y wide?' I asked.
. . . .
"The teachers were very friendly people, and they know how frustrating it can be when no student answers a question. 'x plus y?' said two in the front simultaneously.
"'What?!!!' I said, horrified."
Professor Kenschaft's article includes other examples of the mathematical understanding of elementary schoolteachers in New Jersey. In this regard, New Jersey may actually set a higher standard than most states of the United States, so all over the United States, there is risk of learners being misled into incorrect mathematical conceptions by their schoolteachers.
The problem is not ideally written, to be sure. In February 2012, Annie Keeghan wrote a blog post, "Afraid of Your Child's Math Textbook? You Should Be,"
http://open.salon.com/blog/annie_keeghan/2012/02/17/afraid_o...
in which she described the current process publishers follow in the United States to produce new mathematics textbook. Low bids for writing, rushed deadlines, and no one with a strong mathematical background reviewing the books results in school textbooks that are not useful for learning mathematics.
But if you put a poorly written textbook into the hand of a poorly prepared teacher, you get bad results like that shown in the submission here. Those bad results go on for years. Poor teaching of fraction arithmetic in elementary schools has been a pet issue of mathematics education reformers in the United States for a long time. Professor Hung-hsi Wu of the University of California Berkeley has been writing about this issue for more than a decade.
In one of Professor Wu's recent lectures,
http://math.berkeley.edu/~wu/Lisbon2010_4.pdf
he points out a problem of fraction addition from the federal National Assessment of Educational Progress (NAEP) survey project. On page 39 of his presentation handout (numbered in the .PDF of his lecture notes as page 38), he shows the fraction addition problem
12/13 + 7/8
for which eighth grade students were not even required to give a numerically exact answer, but only an estimate of the correct answer to the nearest natural number from five answer choices, which were
(a) 1
(b) 19
(c) 21
(d) I don't know
(e) 2
The statistics from the federal test revealed that for their best estimate of the sum of 12/13 + 7/8,
7 percent of eighth-graders chose answer choice a, that is 1;
28 percent of eighth-graders chose answer choice b, that is 19;
27 percent of eighth-graders chose answer choice c, that is 21;
14 percent of eighth-graders chose answer choice d, that is "I don't know";
while
24 percent of eighth-graders chose answer choice e, that is 2 (the best estimate of the sum).
I told Richard Rusczyk of the Art of Problem Solving about Professor Wu's document by email, and he later commented to me that Professor Wu "buried the lead" (underemphasized the most interesting point) in his lecture by not starting out the lecture with that shocking fact. Rusczyk commented that that basically means roughly three-fourths of American young people have no chance of success in a science or technology career with that weak an understanding of fraction arithmetic.
The way this is dealt with in other countries is to have specialist teachers of mathematics in elementary schools. Even with less formal higher education than United States teachers,
http://stuff.mit.edu:8001/afs/athena/course/6/6.969/OldFiles...
http://www.ams.org/notices/199908/rev-howe.pdf
teachers in some countries can teach better because they develop "profound understanding of fundamental mathematics" and discuss with one another how to aid development of correct student understanding. The textbooks are also much better in some countries,
http://www.de.ufpe.br/~toom/travel/sweden05/WP-SWEDEN-NEW.pd...
and the United States ought to do more to bring the best available textbooks (which in many cases are LESS expensive than current best-selling textbooks) into many more classrooms.
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…
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 considering the illustration. But the keyword there is "interpretation." The question is ambiguous.
(My argument is taken from this answer: http://math.stackexchange.com/a/380007 )
Earlier quoted context omitted.
The answer to this question is open for debate. You see you didn't specify whether you cut all the way through resulting in two halves of a person with one cut on one of them. And which one!
You would call that one cut?
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…
These are released.
People can make corrections.
For something like math this could have significant impact not just in the US and EU but in the developing world too.
PS: About the fraction multiple choice: There's probably a bad joke about 24% being what we'd expect if we let the students chose at random. I'm not funny enough to think what it is. (The punchline being that there are 5 options, not 4.)
