Timeline for Why do some students struggle so much with fractions?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Mar 2, 2022 at 5:12 | comment | added | Daniel R. Collins | Anyway: My answer is in the context of actual curriculum students face (as noted, "In most school situations..."), not some hypothetical alternative. | |
| Mar 2, 2022 at 5:11 | comment | added | Daniel R. Collins | @MadeleineBirchfield: To my knowledge, the work of Wu (with whom I've corresponded) doesn't actually get used in schools. Your proposal requires students working with larger numbers in the intermediary step, which is why it's opposite the advice in any widely used textbook of which I'm aware. | |
| Mar 1, 2022 at 22:49 | comment | added | user19584 | @DanielR.Collins that's why the last step (6) is still required, i.e. find the GCD of $a \cdot d + b \cdot c$ and $b \cdot d$, and divide the numerator and denominator by the GCD to get a simplified fraction. See i.e. the process as given in Wu's textbook Pre-Algebra Sec. 1.3 and 3.1 | |
| Mar 1, 2022 at 22:18 | comment | added | Daniel R. Collins | @MadeleineBirchfield: Not really relevant, because any school situation or book I've seen expects the answer to be simplified, which your proposed result isn't. E.g., see the process as given in OpenStax Prealgebra Sec. 4.5, which is standard, and finding LCDs a highlighted first step. | |
| Mar 1, 2022 at 21:53 | comment | added | user19584 | @DanielR.Collins The LCM of $b$ and $d$ is not needed beforehand for adding rational numbers $\frac{a}{b}$ and $\frac{c}{d}$. One can simply multiply the numerator and denominator of the first fraction by $d$ and the numerator and denominator of the second fraction by $b$, and add the two numerators together to get $\frac{a \cdot d + b \cdot c}{b \cdot d}$. | |
| Aug 2, 2020 at 18:49 | comment | added | Daniel R. Collins | @Timothy: Regardless of how it's taught, introduced, or intuited... at the end of the day, yes, students need to hold all those rules in their mind. Many people can't, and the various rules for different operations cross-contaminate each other. | |
| Jul 17, 2020 at 16:34 | comment | added | Timothy | about the reason. | |
| Jul 17, 2020 at 16:33 | comment | added | Timothy | I can't quite figure out what you're saying. To a young and inexperienced person, it would appear that you're assuming they are able to take the rules on how to perform calculations on fractions as a given, and they just have trouble holding all those rules in their mind. I think the way they learn them best is to introduce them to them using a student centered approach. Give them an intuition on why non whole numbers exist. For example, start with teaching them only how to add fractions with the same denominator and how to right multiply one by a whole number. I don't think you're quite right | |
| Jul 17, 2020 at 1:52 | history | edited | Daniel R. Collins | CC BY-SA 4.0 |
Add link to working memory capacity estimates
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| Jul 16, 2020 at 1:44 | history | answered | Daniel R. Collins | CC BY-SA 4.0 |