Friday, March 5, 2010

IPL: Mathematics

Note: This is specially for maths students. Others may get lost!

Mathematics, and related subjects, are an immensely valuable area of application for procedural learning techniques. Through the method, one can build up a strong practical ability in solving mathematical problems. Whereas regular SuperMemo (i.e. declarative) will help you get good at recognising symbols, recognising which formula(s) to apply, recognising what the next step in the solution of a problem is, and so on, procedural items will encourage learning the other aspect to mathematics - dare I say the more useful aspect, inasmuch as it is the basis of problem solving and scoring marks in exams.

First, you need to start with specific problems you want to learn how to solve. This is much more effective than saying "I want to learn how to solve Ordinary Differential Equations". If you really want to be able to solve all types of ODEs, then you will just have to input several sufficiently different problems, in order to reinforce different skills. Now, taking a similar tack to the musical example in the last post, you can:

  1. Begin by specifying a specific mathematical problem. This could simply be a page reference to your textbook, which holds the whole solution. For example, you could add a new topic in your Pen & Paper collection that just says "ex3, pg92, Heinemann VCEyr11" (specifying the exercise number, book and page number).
  2. Attempt to solve the entire problem at once. Where there is difficulty, make a cut or variation. As an example of a variation, imagine an example from statistics, which requires first determining the standard deviation, then the variance, and then using these in another formula. As a variation, you could simply invent a value for the standard deviation, keeping all else the same. The result would be a smaller, easier exercise, which may be closer to your current level of ability. Once you can do this one, and independently calculate the standard deviation of a set, you could recombine these together (more on that later).
  3. Once you can solve any part, go through the process listed in the previous post in order to transform your topics into items
Personally, I have been less inclined to use IPL for this type of learning. That is, although I learn procedurally, I have not made a habit of studying these things incrementally. Instead, I generally learn how to solve a particular problem, and then import it into SuperMemo as a procedural item. Hence, although I use SuperMemo for the long term reinforcement of the procedural component of mathematics, I still often train my skill initially outside the context of SuperMemo.

Since this application is much quicker to the final result than IPL (though not necessarily more efficient) I expect to get replies on this topic a little sooner. Just choose a type of maths problem you are already familiar with and take a specific example. Then, import this into SuperMemo. This can be as simple as putting "ex3 pg 41" into the question, and "pg98" into the answer box. They key thing is that in answering such an item, you perform the calculations on paper, instead of just thinking "first multiply that, then divide... etc.".

Good luck, and I hope to hear back from you soon!

10 comments:

  1. Do you intent on continuing this way of procedural learning by supermemo any time soon?

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  2. I don't know if my time is wasted because no one subscribes to this blog, even though several have left interesting comments.

    Nevertheless, if I know there is an audience of at least a few people I will continue.

    Your comments are very encouraging!

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  3. Time is never wasted when we write. The initial point on writing a blog, IMHO is having enough patience so more people find its usefulness. On the other hand our own writing enhances they way we think and the way we analyze our current methods and strategies.

    I have used props to study semantically (e.a. factual knowledge), I just never though about needing to use the actual prop on procedural knowledge with supermemo at hand. Some of your ideas are very englighting in deed.

    I would like to make a review of your blog on mines, if you're ok? I've added this blog to my blogroll, you can check it out at TheSuperMemoBlog.

    Good luck!

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  4. Thanks for the support... I would certainly appreciate a review. I keep up with your site through RSS and I find it often sparks thoughts on new topics.

    As for your advice, I think you are right... I will get back to blog posting as soon as possible:) i am sure it will come in handy to some people once it is s bit more comprehensive.

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  5. thanks for the support, I will. I am currently writing the next post, but it is quite a hard one to cover so it is taking some time:) I may post it in several parts.

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  6. I found your blog very interesting. I subscribed to it with RSS and will be following.

    I have a guestion: Why do you fist add your procedural elements as topics and later convert them into items? Why don't add them as items from the beginning?

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  7. @Andrej This is only the case if studying procedural elements incrementally. Like in regular incremental reading (IR), you first begin with topics and only translate to items once they are processed into discrete bits of knowledge (or here, skills). Thus you start with topics and translate to items.

    If you use IPL as described, every topic will represent a slightly different version of the basic skill, and is hence worth memorising. Finally, in order to maximise redundancy (and hence stability), you should memorise all the topics (as items).

    On the other hand, as i said in the post, I don't normally study mathematics incrementally (though perhaps this is a bad thing), but rather formulate items outside of SuperMemo, in which case I directly add them as items.

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  8. I totally agree with what was said regarding the usefulness of writing one's thoughts. I see this blog as a very important document regarding a set of techniques that are usually disregarded when using an SRS. Very interesting stuff, in my opinion.

    I see you only write the exercise and solution page numbers. I usually write the problem and its solution in text or, when equations are involved, latex, but sometimes I just take a screenshot of the piece of information and paste it in the answer field. Advantage: no need to go around with my books or even open and close documents in my computer. Disadvantage: it takes a LOT longer to encode the information (your method is nearly instantaneous).

    I think I use the same strategy as yours: I usually pick a set of problems that more or less illustrate the subject I'm studying and encode those. It has been working very well to me, so far.

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  9. @Nuno

    thanks:)

    You're right - it is much better in the long term to write the entire solution (or a screenshot of it) it the answer field. This is also what I generally do. However, it is indeed time consuming, and can act as a bottleneck to the acquisition process. Therefore, if I am feeling lazy I just insert the page number. However, I always eventually import the information. In fact, I bought a tablet so that I can write the solutions directly to the computer by hand, rather than use an equation-writing program!

    ReplyDelete