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Need to refresh your math skills? From basic algebra to calculus and beyond.

khanacademy.org

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Re: Need to refresh your math skills? From basic algebra to calculus and beyond.

#51
My math skills were always bad. I mean, even though I had one of the best scores in school, I could never explain why it works, e.g. why 9^1/2 is the same as sqr(9).

Since I want to self-study the Quant Finance, I decided to refresh and develop my math skills up to the Calculus. This website is amazing! Not only it's a good refresher, it's the best source of knowledge created by one man.

Re: Need to refresh your math skills? From basic algebra to calculus and beyond.

#52
post #46

Earlier quoted context omitted.

Well, just to provide a single example, my wife is totally disinterested in games. Absolutely doesn't care, to the point where if someone tries to motivate topic X via games she ends up feeling that topic X cannot have any value to her at all. By contrast, she is very interested in math, and wishes that at school it had been presented as other than a collection of facts to memorize and processes to learn and apply. I…

How do you motivate basic maths, though? Not everything can be directly connected to drug couriers and what not. Ultimately I suspect the only way to succeed in maths early on is to consider it to be a kind of game. That is, puzzle solving for fun.

  > How do you motivate basic maths, though?
  > Not everything can be directly connected
  > to drug couriers and what not.
So far I've always succeeded, and I don't even think I'm especially gifted. On current experience, if you name a topic or technique, even in basic math, I can probably relate it to and motivate it by (comparatively) real world requirements at an appropriate level.

  > Ultimately I suspect the only way to succeed
  > in maths early on is to consider it to be a
  > kind of game. That is, puzzle solving for fun.
I agree entirely that people who are going to go and do science or math probably have an element of problem-solving enjoyment, and for them, such motivation not only will work, but is the most appropriate. Getting such people to puzzle over why something happens, and getting them curious about how it works is probably the best thing you can do for them.

When I'm talking to people I show them a couple of things and gauge their reactions. Here are two:

http://www.fieggen.com/shoelace/ianknot.htm

http://news.ycombinator.com/item?id=604347

Any given person will react in one of two ways. One is to half-shrug as if to say "who cares?" and then move on, the other is to look closer and say "Do that again." People in the former group are most likely to need motivating with things that matter to them which might (but might not!) include games. The others can just have their curiosity poked and you're off and running.

YMMV, personal opinions only, etc, etc.

Re: Need to refresh your math skills? From basic algebra to calculus and beyond.

#53

I make this comment every month: There needs to be a comprehensive site that aggregates all the educational videos on the net (lectures, conference talks, screen casts, simple instruction,etc.).

We took an initial stab at this and aggregated about 10K videos, and give tools to take notes and tests. Eventually we plan to extensively integrate text contents from Wikipedia, OpenCourseWare etc along with these videos.

We are a very young website and would love to get feedback on what are the other resources you guys looking for: http://www.nalandau.com/course/8/programming-(10)

regards, Balaji Viswanathan, Founder, NalandaU.com

Re: Need to refresh your math skills? From basic algebra to calculus and beyond.

#54

Earlier quoted context omitted.

"I found that the best way for me to internalize a particular subject in hard science is to follow its history by reading the original papers." I've often wondered why math programs (and books) aren't structured this way, explaining the historical context, reproducing the original papers (or explaining the arguments or proofs in the paper if the original happened to be in Latin or whatever), with a section on how the…

Knowing the price of 1Kg of Potatoes, the street-side vegetable seller in my home town in India only needs to know how much to charge me for 3/4 Kg. He doesn't really care how innovations in mathematics resulted in fractional multiplication. This can be extended to the teaching of basic maths. Students who show an interest or an aptitude for grasping the finer and more insightful details can go on to read up on it, o…

" He doesn't really care how innovations in mathematics resulted in fractional multiplication."

But I care.

In your world do only potato sellers need text books?

I wasn't talking about textbooks for potato sellers, so I fail to see how this is relevant. The implicit audience in my post is a reader of HN. Does your potato vendor post on HN? ;-)

I wasn't talking about elementary mathematics in case that wasn't clear from the context. So now you know.

As you no doubt know already, I was responding to a very specific comment that said "I found that the best way for me to internalize a particular subject in hard science is to follow its history by reading the original papers." and I just made an observation noting my surprise why (some) textbooks aren't structured to help people like the commenter , not your potato vendor whom I haven't had the honor of meeting.

"What we really need is professors knowledgeable enough to answer these questions or point the student to the right texts."

Another strawman?

(a)I was asking for some textbooks to be structured this way for people who like learning that way.

(b) there is no reason not to wish for good professors and textbooks of all kinds (NOT professors ExclusiveOr textbooks - where did you get that idea?) .

Since I wasn't advocating that potato sellers should be taught the history of additions and fractions, or that textbooks should be substitutes for good professors, I'll leave you be to hack at your favorite strawmen in peace ;-).

Re: Need to refresh your math skills? From basic algebra to calculus and beyond.

#55

I like the style and I appreciate the idea. In fact, I’ve been working on something in the same direction. So, here are a couple of things that I prefer to do differently. First, these are video lectures but without actual students present. As a result, he is essentially talking to himself. I noticed that this causes him to skip some details that students might be wondering about. I prefer to start with actual lectur…

One thing that video has that HTML doesn't: single-file archive ability. Sure you can have a single HTML file as long as you keep it text-only, but most of these topics are going to be diagram (and math figure) heavy. There's just no good way to archive the content for later perusal. (Granted YouTube doesn't want you to directly download the videos, but it's not like it's that hard to circumvent -- and once you have the video you can easily find a player for it on any platform)

[Note: I don't count .webarchive or .mht files as 'good enough'. .webarchive files are Safari-only, and I don't even know of a tool to be able to extract data from them. .mht files are 'sorta' supported (IE, Opera, Firefox w/ an extension), but I don't like the idea that the data is Base64/MIME-encoded. Personally I like .maff (Mozilla Archive File Format). It's only supported in Firefox with an extension (and nowhere else unfortunately), but it's basically a Zip file with the HTML/CSS/images inside of it.]

Re: Need to refresh your math skills? From basic algebra to calculus and beyond.

#56

Earlier quoted context omitted.

"I found that the best way for me to internalize a particular subject in hard science is to follow its history by reading the original papers." I've often wondered why math programs (and books) aren't structured this way, explaining the historical context, reproducing the original papers (or explaining the arguments or proofs in the paper if the original happened to be in Latin or whatever), with a section on how the…

Frequently the historically motivated path is too long or creates too much baggage. It's not always the case, granted, and sometimes the historical development does give you the motivation, but you're still asking for a gifted teacher, and that's rare. A gifted teacher can teach with or without the historical perspective, and in my experience a clean, direct presentation with appropriate motivation and context is usu…

I suspect there is a compromise between an extreme use of history and ignoring it.

In my physics class in high school, we discussed the progression of models of the atom. Each time, we learned what experiment led to the new thoughts, and how surprising it was. I thought this was a great way to learn the topic. We didn't, however, spend too much time on the history and never read any of the original papers.

Note: We did have a great teacher.

On the other hand, one difficulty with teaching topics historically is that it is hard to group things by topics. For example, in mathematics, the function is a relatively recent idea. Newton died before the function was thought up, but calculus is usually taught as "take the derivative of a function." This is not to say that history would be useless in this case, but it may require even more talent from the teacher.

Re: Need to refresh your math skills? From basic algebra to calculus and beyond.

#57

Buying good textbooks to learn from is a lot more cost effective than spending on the high-speed internet connections that is needed to download even a short video in any reasonable time. This "resource" is only useful to already have high-speed internet access.

In which country? (Just curious).

Re: Need to refresh your math skills? From basic algebra to calculus and beyond.

#58

Earlier quoted context omitted.

A month of high speed internet is cheaper than a single text book in many countries. Considering there's probably 40 textbooks worth of material on this one page alone, nevermind the rest of the internet, I'd say priorities should be on providing internet access.

OLPC + Khan Academny videos = win.

Only if they were in Spanish - here in Uruguay we have the OLPC deployed for all schoolchildren, but most students don't have the level of English required :)

Re: Need to refresh your math skills? From basic algebra to calculus and beyond.

#59
post #46

Earlier quoted context omitted.

How do you motivate basic maths, though? Not everything can be directly connected to drug couriers and what not. Ultimately I suspect the only way to succeed in maths early on is to consider it to be a kind of game. That is, puzzle solving for fun.

> How do you motivate basic maths, though? > Not everything can be directly connected > to drug couriers and what not. So far I've always succeeded, and I don't even think I'm especially gifted. On current experience, if you name a topic or technique, even in basic math, I can probably relate it to and motivate it by (comparatively) real world requirements at an appropriate level. > Ultimately I suspect the only way…

If you can make it happen, I am only glad for it. I think it is a shame that so many people miss out on maths. I haven't tried to teach it yet, so I can't really say. I've tried at times to come up with real world applications for the maths taught at school, but didn't come up with much.

I think one exercise I would give my pupils would be to determine the real prices of mobile phones.

Enjoyed the shoelace link, will try it the next time I tie my shoes.

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