Saturday, April 19, 2008

Math Contents

Mathematics Content Areas for student

The committee identified four major content areas. The original statement from the committee was a bit more terse, but we now identify the four areas as follows:

  1. 1.Logic, Critical Thinking, and Problem Solving: Students should learn skills that will enable them to construct a logical argument based on rules of inference and to develop strategies for solving quantitative problems.
  2. 2.Number Sense and Estimation: Students should become "numerate," or able to make sense of the numbers that confront them in the modern world. For example, students should be able to give meaning to a billion dollars, and distinguish it from a million dollars or a trillion dollars. Part of developing such number sense involves making simple calculations or estimates to put numbers in perspective. As a simple example, a student should be able to quickly figure out that a star athlete earning $10 million per year earns about 400 times more than the average American.
  3. 3.Statistical Interpretation and Basic Probability: Reports about statistical research (for example, concerning diet or disease) are ubiquitous in the news. Students must have the stools needed to interpret this research. Note the emphasis on interpretation. While it is certainly useful to show students how to calculate a mean, a standard deviation, or a margin of error, our non-SEM students will rarely perform such calculations once they leave our course. But they will encounter such statistics in the news, and we must equip them to interpret these statistics critically. Because statistical interpretation involves inference from samples to populations, it also requires a basic understanding of probability. This study of probability can then be easily extended to relevant topics including lotteries, casino gambling, risk assessment, and disease and drug testing.
  4. 4.Interpreting Graphs and Models: Graphical displays of numbers abound in modern media, so learning how to create and interpret graphs is clearly important. Though it is a bit less obvious, an understanding of modeling is equally important, because many major issues today (such as economic or environmental issues) are studied through mathematical models. While we do not expect non-SEM students to create sophisticated mathematical models, we must teach them how to interpret what they read or hear about models. For example, they should know enough to question the assumptions of a model before accepting its predictions, and they should understand the difference between linear and exponential growth. We group graphing and modeling together because we have found that one of the easiest ways to teach students about modeling is by presenting graphs as simple mathematical models.

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