Timeline for Why unlike terms cannot be simplified?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 27, 2015 at 21:26 | comment | added | Benoît Kloeckner | @Jason: it seems you understood the question as if it was about how to help a struggling student. I read it as how to explain "why" to a student who understands the rule but is not satisfied without a deeper explanation. The former interpretation is right for most questions at matheducator, but the comment of Behzad tend to show the latter is what is meant here. | |
| Dec 16, 2015 at 15:55 | comment | added | Jason | Then you could mention that every once in a while $x$ and $x^2$ will have the same value, but since we usually don't know what the value of the variable is, we should assume that they have different values until we see other evidence. Also, if the kid has been exposed to non-integer square roots and is able to see the contradiction, they're likely not going to be struggling with the rules of simplification. | |
| Dec 16, 2015 at 15:49 | comment | added | Benoît Kloeckner | To make my criticism of this answer clearer: a good answer should make clear the difference between $x+x^2$ not simplifying, and $\sin^2 x + \cos^2 x$ simplifying to $1$. Short of this, the core point has not been explained. | |
| Dec 16, 2015 at 15:44 | comment | added | Benoît Kloeckner | The reasoning proposed here is not invalidated by finite fields, as it uses division by integers which may be zero in a given finite field. However, this answer really assume that $x$ and $x^2$ are fundamentally not interchangeable, which is basically what is asked to be explained. Also, the "breaking into parts" point of view may provoke misconceptions, as not all numbers are rationals. If the kid has been exposed to non-integer square roots, or is to be exposed to them, it may conflict with what he or she will be or has been told. | |
| Dec 16, 2015 at 14:33 | comment | added | Dag Oskar Madsen | I am only saying that some of the simplest arguments cannot be logically sound since they are contradicted in other (admittedly more abstract) mathematical settings. | |
| Dec 16, 2015 at 14:02 | comment | added | Jason | Finite fields? I thought OP wanted to help frustrated eight graders with basic algebra. Most of these answers seem like they belong in math.stackexchange, not matheducators.stackexchange. | |
| Dec 16, 2015 at 12:38 | comment | added | Dag Oskar Madsen | There must be something more going on, since the statement is false in finite fields. See Benoît Kloeckner's answer. | |
| Dec 16, 2015 at 2:21 | review | First posts | |||
| Dec 16, 2015 at 2:44 | |||||
| Dec 16, 2015 at 2:18 | history | answered | Jason | CC BY-SA 3.0 |