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67 Example Questions (1 closed)

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up vote 12 down vote

added by David Speyer Jan 24 '14 at 15:29

I think this general style of pedagogy question is the kind I would most like to see in this SE. – Mike Miller Jan 24 '14 at 15:44

This is an excellent question. I agree with Mike that it seems most representative of the kinds of questions that I would like to see. – Jim Belk Jan 25 '14 at 18:24

Newcomers: Please note that, during the site Definition phase, there is no purpose to upvoting a single question more than 10 times. Please look farther down the list for questions to upvote. – Jim Belk Jan 27 '14 at 4:49

@twirlobite I am as impatient as the next user and have reallocated votes before, but nagging others to do something potentially harmful out of impatience is really going too far. – Phira Feb 6 '14 at 0:09

<giant comment conversation removed> Please do not use comments like a chat room. If you have a question about how the process should work, please use the discussion forum. Thanks – Robert Cartaino Feb 9 '14 at 22:06

show 1 more improvement suggestion

up vote 12 down vote

added by Brian Rushton Jan 26 '14 at 2:13

up vote 10 down vote

added by Daniel Moskovich Jan 24 '14 at 5:43

What is a "threshold concept"? Do you mean "prerequisite concept"? – Jim Belk Jan 25 '14 at 18:26

No- I mean en.wikipedia.org/wiki/Threshold_knowledge So, "identify the key conceptual barriers to be crossed to achieve mastery of high-school trigonometry". – Daniel Moskovich Jan 26 '14 at 1:37

Ordinarily the question title on an SE site is followed by the question body expanding the scope of question. No doubt what you meant by threshold would ordinarily be expanded in that way and no-one would have to ask. That's the difficulty here: Trying not be too verbose and at the same time not be too obscure. So I'm learning from this that on area51 I stick to focussing on writing brief titles and I can add a comment to replace the usual SE question body. – Geoff Pointer Feb 9 '14 at 0:31

up vote 10 down vote

added by Frank Muer Jan 24 '14 at 10:29

up vote 10 down vote

added by Mike Miller Jan 24 '14 at 16:14

Duplicate of this MSE question – Mike Miller Jan 24 '14 at 16:15

Why did you post a question and then flag it as a duplicate 16 seconds later? – WChargin Jan 27 '14 at 4:26

The intent was to post an already posted, well-received question on MSE that would have been better served at the proposed site. – Mike Miller Jan 27 '14 at 4:54

up vote 10 down vote

added by Jim Belk Jan 25 '14 at 20:02

up vote 10 down vote

added by Jim Belk Jan 25 '14 at 20:31

up vote 10 down vote

added by Brian Rushton Jan 26 '14 at 1:29

Meta: How can I show intuitively that the new proposal will require MathJax? ;) – SF. Jan 30 '14 at 12:16

up vote 10 down vote

added by Brian Rushton Jan 26 '14 at 2:10

A useful answer to know. It may not be specific to math, however. And it may depend on what level we are talking about. – GEdgar Jan 27 '14 at 15:39

<comments removed> @John Please do not use comments to answer these questions. This proposal is not part of a Q&A site, and comments simply do not provide the vetting mechanisms for which we create Q&As. Right now, the task at hand is to help define what is on and off topic for a site. Comments are here to help improve the questions; not to answer them. See What is the rationale for deleting answers? Thank you. – Robert Cartaino Jan 30 '14 at 3:18

up vote 10 down vote

added by Joseph O'Rourke Jan 26 '14 at 14:56

up vote 10 down vote

added by David Speyer Jan 26 '14 at 15:59

up vote 10 down vote

added by Brian Rushton Jan 26 '14 at 21:17

up vote 10 down vote

added by brendansullivan07 Jan 26 '14 at 23:02

up vote 10 down vote

added by Wrzlprmft Jan 27 '14 at 14:46

up vote 10 down vote

added by elixenide Jan 27 '14 at 18:26

up vote 10 down vote

added by Brian Rushton Jan 27 '14 at 19:33

This is a very nice question on a specific technical problem in math teaching! (By the way, I changed the font of my handwriting many years ago for this precise purpose. See this image for my solution.) – Jim Belk Jan 31 '14 at 0:00

up vote 10 down vote

added by abatkai Jan 27 '14 at 21:10

I like how specific this question is. I imagine "what are some good examples to motivate [topic x]" will be a common and very useful type of question. – Jim Belk Jan 29 '14 at 19:14

up vote 10 down vote

added by crownjewel82 Jan 28 '14 at 16:11

up vote 10 down vote

added by Wrzlprmft Jan 30 '14 at 23:30

	My comment may appear strange because specificity is generally encouraged but I think this would be a good general discussion. The importance of pure maths is often underrated by applied maths students in general. Reiterating that it's important like a mantra is not enough, I spend a lot of time working on ways to explain various pure maths concepts that I believe are key to properly understanding a variety of applications. Pure maths isn't just for those that readily understand it. Terse texts may well be best for courses, but what about everyone else? – Geoff Pointer Feb 8 '14 at 0:00
	@GeoffPointer: As with many such issues, I think that the general question (e.e., “How do I motivate students of another discipline to learn abstract maths?”) as well as the specific one (e.g., this example question) are good questions. Since showing examples is an important part of the answer to the general queston, the specific question follows more or less automatically. – Wrzlprmft Feb 8 '14 at 10:27
	Absolutely, but there seemed an irony to me. I'm certainly not suggesting we need to write a more general version here and now. – Geoff Pointer Feb 8 '14 at 13:42

up vote 10 down vote

added by Jim Belk Jan 31 '14 at 2:51

	Who is "we"? I don't insist on this. (I think one should provide some context where this applies/for which context the question is meant.) – quid Jan 31 '14 at 15:38
	@quid I have changed the wording a bit. – Jim Belk Jan 31 '14 at 16:16

up vote 10 down vote

added by user89 Jan 31 '14 at 3:00

	What do you mean by "geometric algebra", exactly? Are you referring to Clifford algebras? – Jim Belk Feb 1 '14 at 23:47
	@JimBelk Yes, that is correct. – user89 Feb 2 '14 at 2:12

up vote 10 down vote

added by PLEASE DELETE ACCOUNT Jan 31 '14 at 22:13

up vote 10 down vote

added by HarMath Feb 1 '14 at 5:03

up vote 10 down vote

added by Wrzlprmft Feb 2 '14 at 10:14

Inspired by Is Euclid dead?. – Wrzlprmft Feb 2 '14 at 10:16

up vote 10 down vote

added by scaaahu Feb 10 '14 at 6:57

	This is a true story I personally encountered in the US. – scaaahu Feb 10 '14 at 7:15
	It is a good question. It involves culture-shock when instructors end up teaching students not as brilliant as they were back then. – GEdgar Feb 10 '14 at 15:23

up vote 9 down vote

added by JRN Jan 23 '14 at 11:02

up vote 9 down vote

added by JRN Jan 23 '14 at 13:17

up vote 9 down vote

added by Mike Miller Jan 24 '14 at 6:58

This question is too (actually, entirely) opinion-based. Any suggestions for improvements? "What studies have been done..." seems too close to Joel's question above. – Mike Miller Jan 24 '14 at 10:25

How about "has an emphasis on intuition been proven to be more pedagogically effective than an emphasis on proof"? – JRN Jan 24 '14 at 16:20

I like this question, although I agree the phrasing is a bit off. How about: "What role should proofs play in a first calculus course?" – Jim Belk Jan 25 '14 at 18:29

I've edited the title to Jim's suggestion. While the question perhaps hasn't fundamentally changed, I think it better focuses answers in this form. – Mike Miller Jan 25 '14 at 19:54

Mathematics education is simply a more opinion-based subject than mathematics: thinking in terms of "right" and "wrong" answers seems like a poor approach. I think that for a site like this to be successful, some leeway on the "no opinion-based questions" rule must be made. In fact there was a previous proposal for such a site made by my colleague Sybilla Beckmann; as this issue was a sticking point, and after the proposal did got through she created (with the help of Jacob Hicks) a different site which asks for "topics" and "comment" rather than "questions" and "answers". – Pete L. Clark Jan 28 '14 at 6:25

show 3 more improvement suggestions

up vote 9 down vote

added by Jim Belk Jan 25 '14 at 20:48

up vote 9 down vote

added by Jim Belk Jan 25 '14 at 21:05

up vote 9 down vote

added by Potato Jan 26 '14 at 8:27

up vote 9 down vote

added by Mike Miller Jan 27 '14 at 0:28

up vote 9 down vote

added by Guy Coder Jan 28 '14 at 14:06

I think this is a very interesting and practical question. I usually use more than one textbook when self-studying, and I'm curious whether having more than one textbook would help for students in a classroom. – Jim Belk Feb 1 '14 at 23:53

I too find that when self-studying it pays to have more than one textbook. I try to find complementary books by different authors offering different ways of presenting the information. If having only one textbook by one author doesn't work for you, then what is the point of having the textbook. – Guy Coder Feb 2 '14 at 2:08

I really like this question as well, if only because it is extremely well suited towards helping me in the situation that I am today. However, I wonder if there are any studies on this topic (think about how one would go about designing a study to test for this), and I wonder if this question is a heuristic most students and self-learners have already discovered and can attest to (hence leading to a lot of good-natured, but meaningless upvoting of the question). However, I was able to extract an idea for a question which I will post! – user89 Feb 2 '14 at 2:41

up vote 9 down vote

added by HarMath Feb 1 '14 at 5:15

up vote 9 down vote

added by PLEASE DELETE ACCOUNT Feb 1 '14 at 9:46

The way this is worded sounds like it will solicit opinions rather than facts. – starsplusplus Feb 18 '14 at 13:12

Out of curiosity what is the current divide between science fact and social opinion? Still quite wide? Teaching and learning are complex social processes. As such, theories about them are mostly social opinion, although some studies do have pretty clear results. One area of the process of learning involves the study of the human brain. This particular study is becoming more science based as we better understand the workings of the brain and has led to improved therapies in many brain damage cases for example. But, in the study of education we're still largely in the realm of social opinion. – Geoff Pointer Feb 19 '14 at 0:04

up vote 9 down vote

added by user89 Feb 2 '14 at 2:22

I worry that the answer to this question might well depend on the self-learner in question, but I also wonder if it is possible that we as a community can draw out interesting commonalities between texts that are widely accepted as being excellent self-learning resources. Perhaps we can come up with a set of heuristics in the process that is helpful to authors, instructors and students. – user89 Feb 2 '14 at 2:25

+1. I'm very interested as well and would find it very instructive. – LePressentiment Feb 2 '14 at 4:46

up vote 8 down vote

added by Robert Mastragostino Jan 26 '14 at 6:52

up vote 8 down vote

added by LePressentiment Jan 28 '14 at 2:33

up vote 6 down vote

added by LePressentiment Jan 25 '14 at 11:13

I asked a similar, but more general question just recently. I wonder how a set of similar questions suits Area51. Should I just delete the question I asked? See here: area51.stackexchange.com/proposals/64216/… – user89 Feb 2 '14 at 2:52

@twirlobite: Your other more general question interests me equally. I embrace both! – LePressentiment Feb 9 '14 at 12:44

up vote 6 down vote

added by LePressentiment Jan 25 '14 at 11:17

This is a helpful good question. Why does this question have a close vote? – Frank Muer Jan 27 '14 at 7:01

Totally appropriate question. Various countries/states have elements of maths history in secondary and tertiary curricula. Interesting stories about real mathematicians often add colour and brighten a lesson/tute/lecture. For example, Pascal and his involvement with that casino guy, whose name escapes me, and how the intuitive grasp of probability is often wrong. As a composer I've learnt a lot from studying famous composers why wouldn't that also apply to studying maths and mathematicians of note as well? We are talking about maths education here aren't we? – Geoff Pointer Feb 9 '14 at 0:17