Timeline for Why do some students struggle so much with fractions?
Current License: CC BY-SA 4.0
21 events
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| Jan 16, 2023 at 4:11 | comment | added | user18187 | One of the best answers I've read on this site so far! | |
| Dec 30, 2022 at 1:05 | comment | added | Thierry | I like H. Wu but I think his (and others') complaints about multiplying pizza slices are misguided. Of course it makes sense to model fractions with pizzas, at least as much as modeling them with points on a number line. Those points are represented by a clump of ink molecules, so to multiply fractions we have to multiply a clump by a clump? I don't know about you, but I multiply numbers, not clumps. Obviously nobody can learn fractions this way! Not exactly a fair criticism, of course, but neither is it when we switch clumps with pizza slices. | |
| Dec 28, 2022 at 18:17 | history | edited | WeCanLearnAnything | CC BY-SA 4.0 |
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| Jul 14, 2020 at 5:04 | comment | added | WeCanLearnAnything | @zipirovich - Thanks! I'm not sure which part of Example 3 contradicts the notion of fractions as numbers. In the big picture, students need to learn roughly in this order: (1) Fractions are numbers, (2) Equivalent Fractions, (3) Fractions as Quotients [quotients are just particular type of number], (4) Fractions and quotients as ratios, rates, and probabilities. And, yes, $\frac{x+3}{x+4}$ can be all of those things. | |
| Jul 12, 2020 at 15:40 | comment | added | zipirovich | I've only stumbled upon this thread today. Such a great answer!! I especially love Example 3! But then, this part seems to contradict your claim that fractions are just numbers -- unless I'm misunderstanding something. (And I admit that I haven't read Wu's book, although I plan to now.) Probably that's one of the reasons why fractions are difficult -- because it's a multi-faceted concept. I'd say that introducing fractions as numbers at first makes sense. But then the concept must be extended into understanding fractions as ratios. After all, $\frac{x+3}{x+4}$ isn't a number, is it? | |
| Jul 12, 2020 at 6:09 | history | edited | WeCanLearnAnything | CC BY-SA 4.0 |
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| Feb 27, 2019 at 21:31 | comment | added | Chris Cunningham | @RustyCore I don't appreciate your comment; there are about a dozen links on that page that have to do with fractions. The person who wrote this answer was probably thinking of a specific one of those as a jumping off point. If not, fine. The one you picked out is probably a reasonable place to start. | |
| Feb 27, 2019 at 19:14 | comment | added | Rusty Core | @ChrisCunningham There is a link clearly identified as "Teaching fractions in elementary school: A manual for teachers". | |
| Feb 26, 2019 at 17:16 | comment | added | Chris Cunningham | @WeCanLearnAnything I was hoping to head down the paths of "teach actual math instead of gobbledygook" and "In the realm of fractions, that means teaching that fractions are numbers" ... | |
| Feb 26, 2019 at 15:39 | comment | added | WeCanLearnAnything | @ChrisCunningham . Which aspect of math education did you want to learn about? | |
| Feb 26, 2019 at 14:10 | comment | added | Chris Cunningham | Can you (or anyone else) suggest a place to start in reading the many, many things on this page: math.berkeley.edu/~wu ? | |
| Feb 24, 2019 at 21:17 | comment | added | Timothy | own that despite that, you still care about making your answer better, feel free to edit your answer. Editing it just by adding in what you added in the comment probably still wouldn't make me feel like it was good enough to put a check mark beside it. Without realizing it, I might be making it so that no way of writing the answer will make it worthy of a check mark. | |
| Feb 24, 2019 at 21:14 | comment | added | Timothy | @WeCanLearnAnything Don't worry about your answer not being good enough. The fact that I didn't put a check mark beside it doesn't mean you did something wrong not making it a better answer. It just means I'm trying to help the Stack Exchange community research which types of answers tend to solve people'e problems by not indicating that that it solved my problem. It's totally fine with me that you gave more detail in a comment instead of editing your answer. I just don't want to put a check mark beside the answer when the answer itself is in its current form. If you happen to decide on your | |
| Feb 24, 2019 at 8:03 | comment | added | WeCanLearnAnything | @Timothy . To answer your question more directly, then, the psuedo-math in Examples 1-4 represent what many students experience in school. In contrast, what I wrote about fractions being numbers that must mentally integrated with whole number knowledge - that is something many students never experience deeply. Even if exposed to the critical notion that a fraction is a number, it is rarely emphasized and even more rarely graded, so students do not expend the mental effort to internalize it. | |
| Feb 24, 2019 at 7:55 | comment | added | WeCanLearnAnything | @BenCrowell . I tend to work 1-on-1 with students so I do assign problem sets like the one I recommended. I've never tried it in a classroom setting, but I'm pretty sure one way to build up to that is "assessment as learning". Sadly, this would require teachers to create tons of material by hand, because you won't find tough stuff like that online! "Assessment as learning" exercises, if graduated properly, would help teachers master fractions as well. This is mostly conjecture, though, until I try it in a classroom in a few weeks... :) | |
| Feb 24, 2019 at 2:13 | comment | added | Timothy | I'm not complaining about your answer but I did upvote it but didn't put a check mark beside it because your answer doesn't give a more detailed description of why some students struggle so much with fractions that you explained clearly. | |
| Feb 23, 2019 at 19:58 | comment | added | user507 | [...] that quite a large fraction of K-6 teachers do not themselves understand fractions and division well enough to do this exercise. | |
| Feb 23, 2019 at 19:57 | comment | added | user507 | Create a word problem and draw a picture for each of the following: This sounds like a great exercise, and if you are teaching kids of this age and assigning stuff like this and giving kids feedback on it, then you're a hero and I hope my grandkids can be in your class someday. But I suspect that very few K-6 teachers are willing to read this amount of written work and write detailed feedback on it, especially given that in the US they may have classes with 35 or 40 kids. There is also the issue of teachers' own mathematical competence, which is not addressed in this answer. I suspect [...] | |
| Feb 22, 2019 at 18:56 | history | edited | WeCanLearnAnything | CC BY-SA 4.0 |
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| Feb 22, 2019 at 18:49 | history | edited | WeCanLearnAnything | CC BY-SA 4.0 |
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| Feb 22, 2019 at 18:40 | history | answered | WeCanLearnAnything | CC BY-SA 4.0 |