I actually saw a post where a math educator stated that this problem (top blue box), which has caused yet another firestorm among the unwashed masses over on Facebook, can be interpreted in several ways. No, really not...there's only one correct way to "interpret" this problem.
I blame Thorsen Vreeland for making me even aware of this. Thanks for nothing, pal. ;-)
You're right: A whole coconut = 2xC = 2. ;-)
ReplyDeleteThe picture section looks a lot like my first grade math workbook, in 1971-72. Except they'd have used triangles, squares, circles, rods. The concept was exactly the same: one shape (or color) representing a multiple of another. Only they never followed through algebraically until much later, maybe too much later. As a six year-old, I'd have seen the coconut halves as separate units, rather than halves of a whole, because I'd have been seeing them in context with previous lessons.
ReplyDeleteYou put the lime in the coconut and shake it all up.
ReplyDeleteThe dangers of random representation messing with preconception.
ReplyDeletePresenting a lesson without the presenter (teacher) is generally a poor idea. Unfortunately too many educators think it is normal.
Perfectly valid mathematics. Symbols are arbitrary.
ReplyDeleteThe correct answer are fruit salad or smoothy.
ReplyDeleteVery good for maths, very bad for physics: don't add tomatoes and bananas !
ReplyDeleteOlivier Malinur what? You don't like tomato and banana salad?
ReplyDeleteChristof Harper care to read this?
ReplyDeleteEric Mintz hrm? Looks like a visual word problem from elementary school.
ReplyDeleteChristof Harper my thought exactly.
ReplyDeleteI've seen math students prank their professors by using oddball symbols (rubber stamps, stickers, and the like) on their homework. Provided the math was right, nobody ever objected.
Eric Mintz, I avoid adding power with energy, speed and acceleration or volts and amperes.
ReplyDeleteOlivier Malinur apples and bananas go together very well, though.
ReplyDeleteEric Mintz I suppose the problem here is that I don't know what firestorm the "unwashed" lit. There's nothing here except basic mathematics. no enforced estimation or making people do backwards somersaults to get the wrong answer and say it is right.
The little detail oriented bit with the berries (yes) makes this a "brain teaser" and not something I would have found in a regular textbook back in the 70s. But I started doing brain teaser booklets on my own around 2nd grade.
Eric Mintz: In Estonia, the canonical uncanonical thing to do by math students is to use the diacriticised letters: õ, ä, ö, ü, š, ž, č. Somebody does it every couple of years, apparently. And then, the lectors tell people about it and everybody has good time.
ReplyDeleteConsidering that addition is explicitly marked, shouldn't juxtaposition of two coconuts be treated as multiplication rather than addition?
ReplyDeleteAndres Soolo It's a set. Plus, the math doesn't work out if 4 bananas = B^4
ReplyDeleteRichard Taylor berries. Both of them.
ReplyDeleteAndres Soolo it's defined as a set in the example, though. If you reversed problems 3 and 4, leaving the two coconut problem as the blank solving exercise, then you could argue for the alternate interpretation.
ReplyDeleteAnd the student (assuming this is a prison school system textbook problem) would be correct in any valid interpretation, provided the answer for that interpretation was correct. (But the guard/instructor may not be able to function at that level of creative ability. One of the prison school problems.)
Pretty sure that the number of bananas or coconuts in a picture is irrelevant. Otherwise they wouldn't have made the picture too small to see clearly on a phone screen and they would have had to use "bunch of eight bananas" as a picture and not "bunch of four plus bunch of four". They're just using multiples to fill out the screen for esthetics, plus to confuse you.
ReplyDelete(In other words, the answer is 16)
ReplyDeleteum. no. My young son can see the pictures fine. And I just used him as an empirical example and he immediately got the 4 versus 3 bananas.
ReplyDeleteJasper Janssen well, why isn't one apple = 30? WHY waste all that space doing addition? (since you think that they would have made a single bunch of 8 bananas if the number mattered.....)
Christof Harper that's right, they would also have made it "bunch of three apples equals 30", exactly. So clearly they're either not thinking of it in that way or they're using inconsistent notation.
ReplyDeleteSo I definitely didn't pay attention to the quantities of fruits when I tried to solve it. I think it's interesting how just by changing the formatting, it would reduce all ambiguity. If instead of natural looking changes , the the 2 coconuts were just 2 pictures of the same coconut in close proximity, it would be immediately clear that it's not just an artistic thing, and they want you to realize the number of them matters.
ReplyDeleteDepending on your distance from the screen and such, the bananas can actually be hard to make out.
I'll admit I was wrong because I misunderstood what was significant and what wasn't. I'm used to school textbook questions being so focused on clarity that a question like this would never be asked quite this way.
Jasper Janssen Christof Harper the best math teacher I have ever met, Mr. Howatt, my seventh grade teacher in the Ithaca, NY public schools, always listened carefully to alternate interpretations. Teachers, like all people, come in all sizes, shapes, colors, and dispositions.
ReplyDeleteTeaching has a real problem in the US. If you can do the job well, you are probably overqualified. Someone who understands mathematics deeply enough to teach it well can get a far better paying job with better working conditions than teaching in a public school. Since most private schools operate under the public schools' cost umbrella, they often pay less, offering better working conditions to compensate.
I understand that Finland professionalized its public school teachers, and that their students' math comprehension skyrocketed as a result. I don't know the details; Oh, for time!
When I glanced at this, I saw:
ReplyDeleteApple = x
Bunch of bananas = y
Coconuts = z
Noticing that there were 3 or 4 bananas didn't seem relevant, same with the coconut halves.
If the math didn't work out to whole numbers in both cases, it would have flagged my attention.
I view this as a badly designed problem.
Jasper Janssen no. They aren't. You just don't like it
ReplyDeleteAaron Wood the individual bananas are hard to see, especially for an old guy.
ReplyDeleteChristof Harper by the way, using your young son as evidence that it's easy to see is stupid. You do know that sight is at its most acute in the young, right? Of course your young son can see it.
ReplyDeleteThere isn't any text with this maths problem? Just this picture?
ReplyDeleteEric Mintz I disagree. You do not need a top 5% math MSc or DSc to teach this.
ReplyDeleteYou do not need super specialist professional classes.
You need freedom and ability, yes. But those are a human birthright.
Jasper Janssen are you, seriously, using eyesight on a phone screen to determine what you feel is an objective analysis of intent and design of a mild brain teaser?
ReplyDeleteAaron Wood that's one common defining characteristic of a brain teaser or "gotcha" problem. What you call "bad design" used as a simple trick to force attention to detail for a solution.
So, yeah. Pretty much bad design. But that's the point.
Christof Harper I respectfully disagree. The more the teacher knows about the subject, the better he or she can teach.
ReplyDeleteMath is tricky. The simplest sounding problems can be the most difficult to solve. Here's one. Please forgive me if I repeat myself.
Pick any integer greater than 0. If it is even, divide it by two. If it is odd, multiply it by three and add one. Eventually, you will end up repeating the following values: 4, 2, 1, 4, 2, 1, ...
Math geniuses have been trying to prove this for decades. Paul Erdos, possibly the best number theorist who ever lived, called this problem "a monster."
Kids often stumble over problems like this just by fooling around with numbers. The typical grade school teacher will blow the question off. A teacher who knows math will understand its significance.
Aaron Wood And that's why the shuttle blew up. :-/ Well, that and metric conversions.
ReplyDeleteBad design of the presentation of the failure of orings? Definitely. Design matters. These should be examples of bad design, not "gotcha" things.
ReplyDelete