Timeline for Logic in symbols or words
Current License: CC BY-SA 3.0
17 events
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Jan 11, 2016 at 10:50 | answer | added | Ieuan Stanley | timeline score: 5 | |
| Aug 25, 2015 at 4:34 | history | edited | Joonas Ilmavirta | CC BY-SA 3.0 |
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| Aug 25, 2015 at 0:52 | answer | added | vonbrand | timeline score: -3 | |
| Jul 24, 2015 at 16:05 | comment | added | user21820 | My personal opinion is that it does not matter whether you use words or symbols in the mathematical language you write in. Rather what matters is consistency. If you are inconsistent the student cannot successfully learn the intended semantics of the language constructs, nor can they learn to follow syntax rules in derivation. The first is what makes most students think that mathematics is opaque. The second is what makes most students unable to create and check their own proofs unaided. A secondary issue is what kind of formal language you select. I think the best is natural deduction style. | |
| Jul 23, 2015 at 15:33 | comment | added | Joonas Ilmavirta | @AndrewSanfratello, the second example contains no "purely logical symbols" (implication arrows, quantifiers and such), but it does contain "not purely logical mathematical symbols" (variables, set names, operations of the reals). This is intentional. Of course there are many degrees of spelling things out in words instead of symbols and one could (and should) study them. My main focus is on the "purely logical symbols", but results in more generality are welcome. | |
| Jul 23, 2015 at 8:59 | comment | added | Andrew Sanfratello | Did you purposely make your second example a mixture of words and symbols? I feel like a rigorous study would write out that statement completely with words. | |
| Jul 23, 2015 at 7:34 | comment | added | Joonas Ilmavirta | @BenjaminDickman: That looks interesting. Thanks! Others: I don't want to discuss the wording of my examples. The point is communicating and teaching logic when teaching mathematics. Please try not to digress. | |
| Jul 23, 2015 at 7:31 | history | edited | Joonas Ilmavirta | CC BY-SA 3.0 |
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| Jul 23, 2015 at 7:28 | comment | added | user173 | Or further, 3. Every real has a positive $\delta$ which bounds its distance to any rational. | |
| Jul 23, 2015 at 7:19 | comment | added | Benjamin Dickman | Maybe take a quick look at this paper ("Strict Logical Notation Is Not a Part of the Problem but a Part of the Solution for Teaching High-School Mathematics") and see if chasing the paper down in either directions (its references, or those that referenced it) turns out to be useful. (You may find it especially interesting insofar as it concerns research at a Finnish high school...) | |
| Jul 23, 2015 at 0:46 | comment | added | JRN | For your example 2, you might want to use more words: "such a positive number $\delta$," "any rational number $x$," "the absolute difference of $y$ and $x$ is less than $\delta$." | |
| Jul 22, 2015 at 19:36 | comment | added | Joonas Ilmavirta | @GerhardPaseman, the impediment I had in mind was difficulties with logical statements, not not seeing the connection. I added some parentheses to make it more clear what the main impediment is. Some students have big problems with simple logical statements after years of mathematical education, but most of these problems occur in the first year or two. | |
| Jul 22, 2015 at 19:32 | history | edited | Joonas Ilmavirta | CC BY-SA 3.0 |
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| Jul 22, 2015 at 19:20 | comment | added | user5402 | I've always preferred logic symbols. They eliminate any risk of confusion. For example $x\in A=\{1,2,3\}$ or $x\in B=\{1,5,7\}$, students think $1$ doesn't satisfy the previous relations. For them or (in english) is exclusive. But when you use $\vee$ instead of "or", everything becomes clear. | |
| Jul 22, 2015 at 19:19 | comment | added | Gerhard Paseman | I challenge (what I think is an assertion of yours) the notion "not seeing the connection between s. l. expressions and meaningful statements in words is a grave impediment to learning mathematics". I agree it is challenging but some people don't process symbols as well as words. Everyone eventually needs the mini-logic course that includes distinguishing "For every apple there is a worm..." from "There is a worm so that for every apple...", but those ideas are needed before training them in notational (mis-)use. Gerhard "Thinks Parenthetical Use Is Underappreciated" Paseman, 2015.07.22. | |
| Jul 22, 2015 at 18:35 | history | asked | Joonas Ilmavirta | CC BY-SA 3.0 |