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Is it easier to remember something if it is expressed in a funny and/or fascinating way rather than by learning through repetitious exercises that hopefully instill the necessary understanding ?

The limit concept is very hard for novices, the concept of the infinitesimal was argued about for a long time by experts before it was finally included in textbooks. I don't think repetitious often uninspiring exercises could cover the 'subtleties' of limits or differentials or any related concepts that often require $very$ creative approaches to understanding them. Yet maybe a very creative even artistic approach could make such ideas 'reachable'.

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    $\begingroup$ Expression in a funny way may help memory, but not deep comprehension. Also, infinitesimals were used way longer before being put in rigorous footing, and people had no qualms about it. I agree, rote learning and/or repetitious exercises possibly does not help much covering subtleties of limits, but do you know of research that a creative/artistic approach does so more effectively? $\endgroup$ – Mark Fantini Jul 22 '14 at 21:10
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    $\begingroup$ Homework is necessary but it doesn't have to be drudgery, nor does it need to be a long list of repetitive exercises. That some repetition is beneficial is out of question. Just because students find it boring does not mean it is being done the wrong way. It might work, but your suggestion is still incredibly vague. $\endgroup$ – Mark Fantini Jul 22 '14 at 21:45
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    $\begingroup$ I did mention Edward DeBono's teaching methods of lateral thinking which are very creative and could be applied to learning subjects. Also Harry Loraine and Jerry Lukas (forgive spelling) wrote 'The Memory Book' about using very creative ways of remembering formulae ,dates in history ,all sorts of things that would make learning more creative and fun. Jerry Lukas said these methods made it alot easier to learn science and math. $\endgroup$ – user128932 Jul 22 '14 at 22:04
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    $\begingroup$ There has also been a lot of research showing the effectiveness of rote learning. See, for example, educationbythenumbers.org/content/… $\endgroup$ – Joel Reyes Noche Jul 23 '14 at 1:05
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    $\begingroup$ For remembering mathematical ideas, I recommend neither rote memorization nor funny/fascinating expressions but understanding. $\endgroup$ – Andreas Blass Jul 23 '14 at 4:30
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What you are referring to, I believe, is students who are actively engaged with, thinking about, and emotionally connected to the material rather than being told to passively absorb it. This distinction between Active and Passive learning modes is a hot topic in education research these days. I don't know about mathematics specifically, but physics departments are whole-heartedly embracing active strategies, lead by Eric Mazur at Harvard. You can check out his publications and videos for great examples of how to apply active strategies to traditionally "dry" material.

A quick google search shows that there is current research into active learning in mathematics:

Active learning increases student performance in science, engineering, and mathematics, 2014

Active Learning in the Mathematics Classroom, Grades 5-8, 2007

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    $\begingroup$ T.V.O. had a great series in the 70's (I think) called Eureka with really funny cartoon animations explaining basic principles of Physics ; the voices of the cartoon characters were done by Billy Van as well as the naration , I think. Also the concepts explained were not always easy. It may sound silly but couldn't many not-so-easy concepts be explained with 'funny' animation? $\endgroup$ – user128932 Sep 7 '14 at 3:30
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First of all, I am not happy with putting rote learning against fun, since one of them is more cognitive and the other more affective. Moreover, fun or not, there is something called "cognitive obstacle" which basically implies that it doesn't matter whether you enjoy learning what you are supposed to learn or not, there are certain fundamental obstacles that occur for you. Regarding the concept of your interest, the most famous obstacle is the gap between "potential infinity" and "actual infinity" .

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    $\begingroup$ I agree. Rote learning can be fun (just ask an athlete who enjoys doing exercises) and non-rote learning can be non-fun. $\endgroup$ – Joel Reyes Noche Jul 26 '14 at 4:01
  • $\begingroup$ Rote learning can also bore and irritate some students to the point of dropping out. Didn't Einstein compare some of his teachers to drill sergeants. One teacher famously said he wouldn't amount to anything ( I think). $\endgroup$ – user128932 Jul 27 '14 at 4:11
  • $\begingroup$ Mathematics is extremely fun and fascinating. Being able to figure out an important Theory with just pen and paper is like an intellectual treasure hunt in your mind. A lot of repetitive exercises will probably not instill a fascination with playing around with numbers. $\endgroup$ – user128932 Sep 8 '14 at 5:26
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    $\begingroup$ I didn't mean to defend "rote learning". I've just meant to say you are comparing two incomparable things. $\endgroup$ – Amir Asghari Sep 8 '14 at 19:08
  • $\begingroup$ Do you mean rote learning and creative learning are incomparable? Surely the effectiveness of both in terms of measuring 'long-term' understanding and the 'enjoyment' of continuing to learn can be assessed and compared? $\endgroup$ – user128932 Sep 10 '14 at 6:35

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