Timeline for Are fractions hard because they are like algebra?
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
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| Aug 19, 2021 at 22:56 | comment | added | user10552 | I agree with your thesis. | |
| Mar 11, 2020 at 2:03 | comment | added | Timothy | myself but maybe if you state in a reply to these comments what your question actually was, somebody else might be able to figure out an answer that solves your problem. | |
| Mar 11, 2020 at 2:01 | comment | added | Timothy | I can't figure out what your question is. Is your question whether it is because algebra is hard in and of itself and some people find it hard to do algebra even when they know how to work with fractions? Is your question whether it's because some kids unconsciously are assuming "How is it possible that there is a solution to $(1 \div 6) \times 4$ which $\frac{4}{6}$ technically means but can also be shown to equal $4 \div 6$? I believe the answer to the first of those questions is no and the answer to the second is yes. I don't have enough knowledge to figure out the answer to the question | |
| Dec 25, 2018 at 11:58 | comment | added | guest | Yes. But that doesn't mean anything wrong with it. Some parts of arithmetic have some pre-algebra training naturally embedded in them. And you still need fractions or even "advanced arithmetic" in general, for life. | |
| Apr 28, 2016 at 23:39 | comment | added | Bill Dubuque | Certainly one reason for the steep learning curve is that this is usually the first time students encounter equivalence relations and quotients of algebraic structures. It is quite a conceptual leap to comprehend the collection of equivalence fractions into a single equivalence class and to view that collection as a new "number" and, further, to comprehend that the usual arithemetical (ring) properties extend to these new numbers in a way that does not depend on the choice of representative (this is not done rigorously until much later - when one studies quotient fields and/or localization). | |
| Mar 3, 2016 at 3:41 | answer | added | John | timeline score: 0 | |
| Feb 25, 2016 at 17:34 | answer | added | Jenna | timeline score: -2 | |
| Apr 9, 2015 at 1:49 | comment | added | schremmer | @DavidButlerUofA Come to think of it, I did miss the question because, even though it is not a good reason, I refuse to spend any class time on fractions. And I will think a bit more about it before I consider answering. | |
| Apr 9, 2015 at 0:37 | comment | added | schremmer | @DavidButlerUofA You are of course correct but algebra is a large field and, given the sparse time usually allocated to it, I can think of more important things to deal intelligently with than fractions. | |
| Apr 8, 2015 at 23:33 | history | edited | DavidButlerUofA | CC BY-SA 3.0 |
further clarification
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| Apr 8, 2015 at 22:38 | answer | added | user1815 | timeline score: 11 | |
| Apr 8, 2015 at 19:51 | comment | added | DavidButlerUofA | I'm not sure what your point is @schremmer. To see the "command" 33/7 as an object in its own right and to operate on it as it stands sounds very like algebra to me. | |
| Apr 8, 2015 at 18:45 | comment | added | schremmer | I disagree: fractions are inherently artificial. $\frac{13}{7}$ is essentially the command "Divide 7 into 33". That we can operate on the code itself may occasionally be helpful but certainly not crucial in the real world. As engineers are wont to put it, ``The real real numbers are the decimal numbers''. And, even in an arithmetic course, there things a lot more important to deal with. Of course, though, you may be mandated by your state. | |
| Apr 8, 2015 at 12:50 | history | edited | DavidButlerUofA | CC BY-SA 3.0 |
clarification of the nature of the question
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| Apr 8, 2015 at 12:48 | comment | added | DavidButlerUofA | Interesting paper in the link, thanks @BenjaminDickman. I am aware of the fact that the literature on rational number is overwhelmingly large, and I'm not interested in all of the reasons they are hard. I'm just interested in whether researchers think this particular idea is reasonable as one of the many reasons. Still, thanks for the link, it's very interesting. | |
| Apr 8, 2015 at 8:15 | comment | added | Benjamin Dickman | There is an enormous literature on fractions and rational numbers in mathematics education. Recently, I have been looking through some of the literature on hypothetical learning trajectories for which rational numbers crop up repeatedly. Try Wright (2014) and, especially, its references (no pay-wall to see the list, at least) for a tip-of-the-iceberg on why fractions are "hard." | |
| Apr 8, 2015 at 8:06 | answer | added | Karl | timeline score: 9 | |
| Apr 8, 2015 at 7:37 | history | asked | DavidButlerUofA | CC BY-SA 3.0 |