Mathematics, part 1
by Dr. Carl H. Selzer
This is the first in a series of mathematics articles that I’ve agreed to write for “The Homeschooler”. I sincerely hope these articles will be of a significant resource to you as you contemplate the teaching of mathematics to your child (children).
Mathematics may be defined as the science of pattern and relationships. As a science, the “mathematics classroom” should be a scientific laboratory where children experiment, explore, observe, draw conclusions, and verify results. Problem solving should be the main focus of any mathematics program.
Having defined mathematics, the next question is why do we study mathematics? I believe that we’ve been incorrectly answering this question. Traditionally we’ve answered the question, why study mathematics, as follows:
1) You need it in later math courses.
2) You need it for college.
3) You need it to function in the real world.
4) You need it for specific careers.
These reasons are not convincing to me, nor are they convincing to children. Actually, these aren’t really the reasons at all. Rather, I’d like to suggest that we study mathematics because in mathematics we learn how to answer every important generic-type question. The skills obtained by answering these questions are applicable to almost every profession or career.
People need mathematics and mathematical skills and abilities when they encounter questions like:
1) How can this information be sorted, organized, grouped and visualized?
2) Does it follow? Can you verify that fact?
3) What are the possibilities?
4) What strategies are available?
5) What are the chances? What are the risks?
6) Can we simulate or model the situation?
7) A small part of the situation is visible, but what is “actually” there?
8) Why does this work?
9) Are these figures accurate? Do the books balance?
10) What’s missing? What’s extra?
11) Are these two things related? Does one factor influence the other?
12) What are the extremes? What is most likely? How much variation can we expect?
13) Is that reasonable? Do I have enough?
14) What are the ground rules? What limits do they impose?
15) Is there a different way to look at the situation?
16) What if? What are the possible consequences? Have we explored every possibility? Have we missed something?
17) How much is necessary to complete the task?
18) Does this problem behave like any other situation? What’s the same? What is different?
19) Can it fit in the available space?
20) How fast is the situation changing?
21) Have we reached the maximum or minimum? Can things get better or worse? What’s best?
22) Can the situation be visualized?
23) Can we create a scale model?
24) Will our proposed change really make a difference? How can we tell?
25) How do you know it’s true? How can you be sure?
26) What is the result of this series of actions? Are the steps reversible?
These are surely not the only questions studied in mathematics, but will give you a good idea of what our children need to learn.
Next issue topic–What kind of mathematics for our children’s future–a look at the REAL world.
