Wednesday, July 20, 2005

Self-Directed Learning of Calculus - Part 3

While studying calculus, one quickly encounters the idea of a function. Although an equation is the most common procedure for describing a function, one might also use a table where one column contains the value of the independent variable and the second column the values of the dependent variable.

Tables are ubiquitous to Learning. I have previously indicated how I use tables to assist me in time management. This post will display four types of table that I use to make my notes about the content that I am Learning.

I have created the following table to guide me as I read and work my way through a chapter in a book.

The table was created using Dreamweaver for use on a web page, however any software program that creates tables (e.g. Word, Excel) could also be used.

This table acts like a template. Each time I begin a new chapter in a calculus book, I simply copy this table and modify the dates in the right-most two columns. Each row consists of one of the steps that I have identified as being important for developing a deep understanding of the content. The overall table acts like a checklist to ensure that I have not inadvertently missed a step. On the other hand I may place a n/a for "not applicable" in a cell to indicate that the step does not appear to be important for this particular chapter. I have used the idea of color (red) to indicate a step that I have not yet attended to, but plan to, in the near future.

The next table that I create is for actually making notes of the content. Here is a sample from one such table:

The first column contains either a direct quote or a summarizing statement in my own words of an important idea or point. The second column indicates the page number in the book in case I wish to refer back to this information at a later time. The third column contains my personal comments or reaction to the content. Once again, explicit reflection is an important component of my Learning strategy.

Here is a second example where I have embedded a table within a cell in order to make the steps in a mathematical proof as clear as possible.

One more table! The premise of this blog is that one is interested in Learning that is Self-Directed. In such cases one usually does not have an instructor who can state at the outset the goals for the lesson or unit. Thus the formation of a table that identifies the goals is the last step, rather than the first, that I engage in while Learning the material in a chapter. Here is an example:

This particular table utilizes 5 different types of knowledge outcome. Depending on the chapter there may be only a few, or very many, different entries for each category. When Learning other topics, one may want to create a different system. Reflecting on the type of knowledge that is important is itself an important aspect of Learning.

I also utilize color in the third column to emphasize the degree to which I believe that that understand the topic (green for "3" which symbolizes confidence, yellow for "2" which indicates partial understanding, and red for "1" which means substantial effort is still required. Reviewing this table at any time can be a guide as to where I should devote my energy. It may also be appropriate to change the rating and color to reflect a change in my understanding (i.e. forgetting!). Here is a table with such colors:

Clearly, I find tables to be useful for organizing my Learning in at least four distinct ways:
1) as a checklist for following the identified steps in my Learning,
2) as a way of structuring my notes to incorporate reflective comments,
3) as a way of structuring the format of mathematical proofs,
4) as a way of identifying and organizing the important ideas of the material.

Comments and suggestions are welcome!


At 4:35 a.m., Blogger AussieBoyd said...

Hello Dale.

I found your ideas very interesting as I too am updating myself again in things mathematical after a several decade 'layoff'. I have been producing summary documents in MSWord as I am going with sufficient detail (I hope) so that it can be used as a solid memory jogger next time in the future I read each topic. I am thinking of incorporating some of your ideas in the structure of my summaries.

Good luck with the continuation of your work.


P.S. I saw in your web-site that you were listening/watching the ashes cricket series earlier this year. What on earth is a canadian doing watching cricket? I am impressed.


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