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CRAM Math method

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The basic CRAM Math method is:

  • learn something basic about algebra and then
  • use it.

If you learn something basic about algebra and DON'T use it, you lose it. It's as simple as that.

In the contents below, the method is contained in sections 1 through 3; sections 4 and beyond are additional reading and only necessary for understanding how the method came to be.

The importance of practice

By using it, you practice it on the homework exercises or by talking it out with your favorite algebra tutor. The more you practice, the better you get. Without any practice, only expect to experience brain flush.

Think about learning to tie your shoe laces. When you were real young, learning to tie your shoe laces was a real pain in the brain. After several days, weeks, or months, you finally learned to tie your shoes, and now, you do it without thinking. Doing algebra is just another skill, like tying your shoes or some other simple task that you do all the time without sweating about it. If you never practiced tying your shoes, you would have forgotten how to do it... or you discovered slippers with velcro straps.
A note on homework practice: Usually, the number of homework problems assigned in class is just enough to give you the feel of using whatever topic the instructor feels you should be learning at this point in time. It generally is NOT ENOUGH to give you enough practice to make you fully competent. SEEK OUT MORE OPPORTUNITIES TO PRACTICE!
One source is looking up old algebra books in your campus library; another is that some people may have posted old homework sets on the Internet.
From experience with my tutoring clients, just doing this on a regular basis (3 or more times a week) works out to a full grade improvement on completing the class. Not doing this means a lot more stress just before the final exam, leading to the other kind of cramming.

CRAM Math extensibility

The CRAM Math method can be extended to any degree:

  • learn something basic about algebra and then
  • use it.
  • learn something in addition to the above
  • use the new concepts in combination with what is already known
  • repeat the above last two steps over and over until you pass the course

It is the process of learning then doing and learning/doing more that is the heart of CRAM Math methodology. It is no harder than learning to dress yourself by doing it every day... unless you are a nudist!

Universal applicability

The CRAM Math method can be applied to any subject with enough tweaking and editing.

Method applied to biology

  • learn a basic biology concept or term and then
  • use it to describe something biological.
  • learn something in addition to the above
  • use the new concepts in combination with what is already known to explain something biological, then write out the new composite idea in a few short sentences
  • repeat the above last two steps over and over until you pass the course

Method applied to chemistry

  • learn a basic chemistry concept, term, or molecular formula and then
  • use it to explain some chemical property without blowing up something in the lab.
  • learn something in addition to the above
  • use the new concepts in combination with what is already known to explain something chemical, then write out the new composite idea in a few short sentences
  • repeat the above last two steps over and over until you pass the course

Method applied to the subject matter of X

  • learn a basic concept, term, or formula of X and then
  • use it to explain something about X.
  • learn something in addition to the above
  • use the new concepts in combination with what is already known to explain something X-traorinary, then write out the new composite idea in a few short sentences
  • repeat the above last two steps over and over until you pass the course

CRAM Math method source

The inspiration for CRAM Math came from reading Rene Descartes' Rules for the Direction of the Mind in the Britannica Great Books series many years ago.

Rules for the Direction of the Mind without Descartes' annotations

The following twelve Rules were translated by Elizabeth Anscombe and Peter Thomas Geach in 1954 for their work "Descartes Philosophical Writings", and their copyright was not renewed.

Rule I

The aim of our studies should be to direct the mind with a view to forming true and sound judgements about whatever comes before it.

Rule II

We should attend only to those objects of which our minds seem capable of having certain and indubitable cognition.

Rule III

Concerning objects proposed for study, we ought to investigate what we can clearly and evidently intuit or deduce with certainty, and not what other people have thought or what we ourselves conjecture. For knowledge can be attained in no other way.

Rule IV

We need a method if we are to investigate the truth of things.

Rule V

The whole method consists entirely in the ordering and arranging of the objects on which we must concentrate our mind's eye if we are to discover some truth. We shall be following this method exactly if we first reduce complicated and obscure propositions step by step to simpler ones, and then, starting with the intuition of the simplest ones of all, try to ascend through the same steps to a knowledge of all the rest.

Rule VI

In order to distinguish the simplest things from those that are complicated and to set them out in an orderly manner, we should attend to what is most simple in each series of things in which we have directly deduced some truths from others, and should observe how all the rest are more, or less, or equally removed from the simplest.

Rule VII

In order to make our knowledge complete, every single thing relating to our undertaking must be surveyed in a continuous and wholly uninterrupted sweep of thought, and be included in a sufficient and well-ordered enumeration.

Rule VIII

If in the series of things to be examined we come across something which our intellect is unable to intuit sufficiently well, we must stop at that point, and refrain from the superfluous task of examining the remaining items.

Rule IX

We must concentrate our mind's eye totally upon the most insignificant and easiest of matters, and dwell on them long enough to acquire the habit of intuiting the truth distinctly and clearly.

Rule X

In order to acquire discernment we should exercise our intelligence by investigating what others have already discovered, and methodically survey even the most insignificant products of human skill, especially those which display or presuppose order.

Rule XI

If, after intuiting a number of simple propositions, we deduce something else from them, it is useful to run through them in a continuous and completely uninterrupted train of thought, to reflect on their relations to one another, and to form a distinct and, as far as possible, simultaneous conception of several of them. For in this way our knowledge becomes much more certain, and our mental capacity is enormously increased.

Rule XII

Finally we must make use of all the aids which intellect, imagination, sense-perception, and memory afford in order, firstly, to intuit simple propositions distinctly; secondly, to combine correctly the matters under investigation with what we already know, so that they too may be known; and thirdly, to find out what things should be compared with each other so that we make the most thorough use of all our human powers.

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