Timeline for Where can I inform me about experiences with exam tasks heading for deeper understanding?
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
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| Mar 30, 2014 at 17:55 | comment | added | Mark Fantini | @Toscho I certainly will not throw adapted IMO problems at him. This discussion has run its course, I will not reply further at the comments. Farewell. | |
| Mar 30, 2014 at 17:53 | comment | added | Toscho | @Fantini In course on linear algebra involving diagonalizing matrices, if a student is not able to do elementary calculations on fractions, you will fight for him to not leave him behind? He'll be very grateful to you, but don't ask the other students. | |
| Mar 30, 2014 at 17:45 | comment | added | Mark Fantini | So if your student doesn't have it, damn him? Reality has it that (way too many, yes) students don't have basic understanding. You shouldn't just leave them behind. | |
| Mar 30, 2014 at 17:18 | comment | added | Toscho | @Fantini Now, I understand, what you mean. That's, what I would call "basic understanding" and what's done in German curricula in grade 8 or 9. | |
| Mar 29, 2014 at 20:17 | comment | added | Chris Cunningham | I suspended judgment on this answer until I saw the example added, but now that it is added I have downvoted the answer. I don't think the IMO is actually a productive source of good conceptual questions. | |
| Mar 29, 2014 at 17:47 | comment | added | Mark Fantini | @Toscho "Solve this equation" or "solve this equation in 5 steps" do not test for understanding. What I'm trying to say is that your example doesn't seem (to me) to bring to the front conceptual difficulties someone encountering functions will have for the first time. A functional equation will be even harder to grasp than, for example, comprehending why $y=x^2$ defines a function in $x$ while $y^2 = x$ does not. | |
| Mar 29, 2014 at 15:17 | comment | added | Toscho | @Fantini For example, let them solve $f(ax)=a^2f(x)$. | |
| Mar 29, 2014 at 15:11 | comment | added | Toscho | @Fantini They shouldn't see some difference but solve the problem. What's the difference between "deeper understanding" and "elaborate exercise"? And this has nothing to do with quadratics. But you can create a problem of functional equations, that is solved by quadratics. | |
| Mar 29, 2014 at 14:27 | comment | added | Mark Fantini | @Toscho Are you sure students will see the difference? To me it looks like an elaborate exercise in manipulation. Would you recommend this to someone having trouble with quadratics? | |
| Mar 29, 2014 at 10:17 | comment | added | Toscho | @Fantini As long as you don't supply what "deeper understanding" is for you, I can't really answer. This example shows students the difference between arguments, function values for specific values and functional equations as well as the possibility to substitute $x$ in a functional equation $f(x)=$. | |
| Mar 29, 2014 at 2:18 | comment | added | Mark Fantini | I stand by my comment. How does your example test for a deeper understanding of functions? | |
| Mar 28, 2014 at 16:52 | comment | added | Toscho | @BrianRushton Added an example. | |
| Mar 28, 2014 at 16:52 | history | edited | Toscho | CC BY-SA 3.0 |
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| Mar 28, 2014 at 15:55 | comment | added | Mark Fantini | I have downvoted because I find it hard to believe IMO questions test for deeper understanding. Math olympiads in general do not strive for teaching conceptual clarity but for timeliness, techniques and having a huge question bank in your head. | |
| Mar 28, 2014 at 14:46 | comment | added | Brian Rushton | I'd be interested in seeing one or two examples; would you be able to take one of those questions and show how you would make it easier? | |
| Mar 28, 2014 at 14:39 | history | answered | Toscho | CC BY-SA 3.0 |