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!