Timeline for Why are induction proofs so challenging for students?
Current License: CC BY-SA 3.0
36 events
| when toggle format | what | by | license | comment | |
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| Nov 12, 2020 at 22:55 | comment | added | LSpice | @Traubenfuchs, re, how would you use the inductive approach to disprove an assumption? | |
| Jul 21, 2019 at 10:21 | answer | added | guest1 | timeline score: 0 | |
| Oct 3, 2018 at 17:21 | answer | added | conveniencesample | timeline score: 6 | |
| Sep 12, 2018 at 23:50 | comment | added | guest | The biggest issue is not understanding what proof is, but just all the algebra to keep track of. It becomes challenging and daunting. Students nowadays lack manipulative muscles. | |
| Jul 13, 2017 at 3:51 | answer | added | Daniel R. Collins | timeline score: 9 | |
| Jul 13, 2017 at 3:12 | answer | added | Dan Christensen | timeline score: 10 | |
| Apr 13, 2017 at 12:50 | history | edited | CommunityBot |
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| Jan 29, 2016 at 22:06 | answer | added | Alan T | timeline score: 7 | |
| Jan 12, 2016 at 6:11 | answer | added | Douglas Silva | timeline score: 9 | |
| Nov 27, 2015 at 19:04 | answer | added | Chan-Ho Suh | timeline score: 11 | |
| Nov 24, 2015 at 16:31 | comment | added | user21820 | @JoshuaTaylor: That's correct for most concrete applications of induction, as I state in my CS-oriented answer, since the top-down viewpoint is always the best way to understand recursive structures (though bottom-up sometimes gets you lower space complexity). On the other hand, in my logic-oriented answer you will find that it is the apparently bottom-up generative procedure that is the core reason for believing the induction schema. This is much more powerful than the induction you need for concrete data structures in CS, and there's no convincing top-down justification for it. | |
| Nov 24, 2015 at 16:18 | comment | added | benblumsmith | Just a quick comment that I love this question (+1), and I am using all my willpower to resist the urge to read all the answers and add my own, for the sake of what I had planned to get done in the next 2 hours. One quick relevant anecdote: researchinpractice.wordpress.com/2011/05/09/induction | |
| Nov 24, 2015 at 14:26 | answer | added | David E Speyer | timeline score: 15 | |
| Nov 24, 2015 at 2:27 | vote | accept | Joseph O'Rourke | ||
| Nov 22, 2015 at 0:07 | answer | added | Joseph O'Rourke | timeline score: 13 | |
| Nov 21, 2015 at 21:22 | answer | added | user5935 | timeline score: 22 | |
| Nov 21, 2015 at 20:27 | answer | added | Ethan Bolker | timeline score: 22 | |
| Nov 21, 2015 at 18:13 | answer | added | Zelphir Kaltstahl | timeline score: 9 | |
| Nov 20, 2015 at 22:12 | comment | added | Joshua Taylor | I don't have any empirical evidence, so this is just a comment, but I've often felt that proof by induction is often presented as "prove a base case, then prove inductive case", which feels sort of backwards to me. If we look at the inductive case first, then we observe the relationship between successive cases. Then we finally have a motivation to follow it backward to some base case. | |
| Nov 20, 2015 at 13:40 | answer | added | DavidButlerUofA | timeline score: 89 | |
| Nov 20, 2015 at 9:30 | comment | added | ASA | Students (like me) are only taught the necessary steps to proof correct assumptions with induction and pass exams with it. Me, including most, if not all of my peers never understood how those scribbles depict proof of anything at all. We were never confronted with problems where the induction approach is used to disprove an assumption that seemed obvious at first glance. That would indeed make induction a useful tool. The way it I know it and used it it's a daunting (at best!) trip into theoretical math land. | |
| Nov 20, 2015 at 0:36 | answer | added | gnasher729 | timeline score: 5 | |
| Nov 19, 2015 at 23:26 | comment | added | alexw | Get a blank piece of paper. Write out P(n) at the top. Write out P(n+1) at the bottom. Their goal is to get P(n) to "turn into" P(n+1). Once they understand the algebra there, you can then explain that this means that P(n) -> P(n+1). Then you can get into the formal definitions and intuition. | |
| Nov 19, 2015 at 17:30 | answer | added | user21820 | timeline score: 25 | |
| Nov 19, 2015 at 17:03 | answer | added | user21820 | timeline score: 15 | |
| Nov 19, 2015 at 5:16 | comment | added | keshlam | Just an observation from the other side of the fence: It's hard to teach programmers recursion (and when it is or isn't appropriate) too, and that's almost a parallel with this question. It's a different decomposition of the problem than they're used to. [To really confuse them, go to nonprocedural rule-driven recursion, which "makes good programmers better and bad programmers obvious".] | |
| Nov 19, 2015 at 4:57 | answer | added | user52817 | timeline score: 11 | |
| Nov 19, 2015 at 1:04 | comment | added | Joseph O'Rourke | @BenCrowell: I have a range from 1st-yrs to seniors, computer science majors (and some math majors). Indeed for some this will be their first exposure to proofs. | |
| Nov 19, 2015 at 0:55 | comment | added | user507 | What level are these students at? For example, I do a little of this in my freshman calc course (mostly relegated to extra-credit problems), and at that level, many students are simply not up to speed on arithmetic and junior high school algebra. Another thing to think about with college freshmen is whether they have had a proof-based high school geometry class. If they haven't, then they probably haven't had any previous exposure to writing proofs of any kind. | |
| Nov 18, 2015 at 23:18 | answer | added | Cort Ammon | timeline score: 16 | |
| Nov 18, 2015 at 20:56 | comment | added | Drathier | As a student that learned about induction proofs a few years ago, the hardest part was that it didn't look like a proof. Most of my peers didn't think they'd actually proven anything, just simplified an expression. | |
| Nov 18, 2015 at 20:24 | answer | added | mweiss | timeline score: 31 | |
| Nov 18, 2015 at 19:56 | answer | added | Aeryk | timeline score: 10 | |
| Nov 18, 2015 at 17:28 | answer | added | Henry Towsner | timeline score: 39 | |
| Nov 18, 2015 at 16:36 | comment | added | celeriko | maybe you will be more successful the nth+1 time ;) | |
| Nov 18, 2015 at 16:32 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |