A General Goal Orientation To Learning Mathematics
Instructor: William V. Thayer
You may wish to keep in mind SOME GENERAL GOALS that may help you focus YOUR THINKING ENERGY while you study a math course.
Learning in a mathematics course may be enhanced by your willingness to use and thereby improve:
1. your ability to define and skill at defining terms, expressions, processes, operations, and strategies;
2. your ability to listen, read, speak and write with vocabulary skills essential for progress in mathematics;
3. your understanding of the general application of definitions and concepts and your energy in applying definitions and concepts to your basic areas of interest;
4. your skill in computing accurately and efficiently with and without calculators or computers;
5. your ability to recognize mathematics as a way of thinking and speaking about quantities, qualities, measures, and qualitative and quantitative relationships and to extend beyond to a level where you model your applications;
6. your ability to use mathematics to gather data, to present and interpret this data, to read and understand mathematics reports, charts, graphs, and accounts with and without modern technology;
7. your ability to use a general problem solving technique and incorporate computer and graphing calculator technology to facilitate problem solving;
8. your understanding of the logical structure of a mathematical proof: both formal and informal and both deductive and inductive. Also, your understanding of the logical structure of subject areas within mathematics, and the logical structure of mathematics as a useful part of an individual's philosophy. Make these types of your logical structures meaningful;
9. your ability to demonstrate mental traits such as visualization, curiosity, imagination, creativity, and play related to each concept and strategy to promote understanding and problem solving;
10. your ability to develop attitudes that lead to appreciation, confidence, respect, initiative, and independence for yourself and foster the same for other individuals;
11. your "preparation for" and "ability to" work with others in group activities and problem solving situations with an understanding of group dynamics for innovative decision making as well as conditions of "groupthink" that lead group problem solving astray.
within your individual studies, during small group interaction, through all class activities and in your community.*
Consider the above list as you strive for excellence in understanding mathematical ideas and develop corresponding techniques. Add more activities or general goals by experimenting with new ones that may help you increase learning or make learning more meaningful and pleasant. Reorganize your methods and even style of learning for deeper understanding and interest. Pursue the lines of inquiry that you find your mind selects naturally while not diverging from the outline of course material too far. It is OK to spend large amounts of time studying just a few ideas, pages, or problems and as a matter of fact this is YOUR MAGIC for learning mathematics. Also give yourself personal permission for making lots of mistakes. Use the criterion of "when time seems to flow" as your gauge for individual development to realize a sense of accomplishment then personal complexity may change as well. Don't get stuck or stay stuck! Help yourself to be an expressive engaged learner, that is, "be all you can be".
* Keep pencil and a learning journal, log or just plain scratch paper next to you and actively fill in the details of ideas that lack continuity.
Copyright © 1982 through © 1999
with all rights reserved by
William V. Thayer,