The Mathematics of the Social Conscience

A proposal for a High School Math Elective

Background:

Various observers have noted that Americans can compute (do arithmetic), but they can't use mathematics. In fact, some of us have observed that many people do not recognize the difference between computing and using mathematics. Most experts trace this problem to the way that we were taught mathematics. This has resulted in the NCTM Standards which promote problem-solving, reasoning, communication, and real-life applications, above basic computing. If you can't solve real-life problems and communicate your understanding and results, then your computing skills are of little value to you.

Developmental Psychologists have noted that people develop a strong moral conscience between the ages of 13 and 25. However, without good evaluation skills, people can easily be led into supporting institutions that are inconsistent with, and fail to support, their own value-systems.


Purpose

Students will learn, through experience, to research and evaluate issues that are of concern to them. Students will use methods of mathematics to build their understanding of their topic of concern. These methods may include creating and reading charts and graphs, using statistical models for comparisons, evaluating statistical reports to determine what things may be concluded, and, more important, what things may not be concluded from the available data. Students will judge the value of alternatives, and create their own alternatives based on the data they collect and organize.

Course Overview

This will be a research and analysis course. Students will pick issues that are of concern to themselves. They will be guided in asking questions critical to the topics they pick. They will research, and organize data according to their questions. Whenever possible, they will use their data to lead them to asking more questions. They will be guided in evaluation techniques that apply to their research. Students will publish before their class, the school, or on the web, the results of their research.


Examples

Taxes

Students with economic concerns may ask questions like, "Are the tax plans being proposed really fair and equitable?" This will lead to questions like "What is meant by 'fair and equitable?'" "Who pays the taxes now?" "Who really pays the indirect taxes?" "How much must be collected to cover the current budget?" To answer these questions students may look at IRS statistics of income. Then they will need to ask, "what are the flaws in the IRS statistics of income, and how can we work with those shortcomings?" In the end, students will propose what types of taxation they believe are most equitable, and what types they believe are least equitable. (eg: IRS stats)(IRS data)

Environment

Students concerned about the environment may pick topics that lead them to ask such questions as, "What are the strengths and weaknesses of the various measurement techniques used to understand the environment?" "What does this imply about what we really know, or don't know?" "How do we distinguish between a long-term trend, and short-term 'noise'?" "What is the economic cost, and consequential environmental impact of laws designed to help the environment, and laws designed to help people?" "What was the environmental impact of the green revolution?" Students may review past models, such as those discussed in "The Logic of Failure." Student will study feedback models, such as predator-prey relationships. In the end students may have to propose answers to questions such as,

Logic of Failure

"How long can we wait to act, when we have incomplete information?" "How long should we wait?" "What consequences should we expect from different 'solutions'?"

Prejudice & Social Injustice

Students concerned about prejudice and social injustice will ask questions like, "How do we measure social injustice?" "How do we consider the impact of different factors that affect people?" "How can we consistently define social injustice? They will consider how different world-views of 'fairness' lead to distinctly different outcomes (tax model). They will use statistical models (eg: gender models) to determine what should they things they should expect. Using these models they will describe what ideal and near-ideal systems might actually look like (income example). They may study cognitive theories of pattern recognition along with statistical judgment errors and simple algorithms for making choices with incomplete information. In the end they will report what consequences various approaches to dealing with inequity may have both good and bad. Other resources: Titanic data, even more Titanic data


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