Ethics Graphically

Mathematical reasoning can be used to organize other types of thinking. Ethical awareness can be used to motivate mathematical concepts such as abstract space with positives and negatives. We can use either system of thinking to reinforce the others. Here we present a few lessons to integrate ethics and mathematics.
The lessons below can be used to help guide students towards ethical thinking. They can be used by math teachers to validate diverse utility for Cartesian coordinate graphs which include negative numbers and logical diagrams. They can be used by elementary teachers to hint at the existence of negative numbers. And they can be used as an introduction to basic economic concepts.

Draft: January 2012


Lesson 1: Choices and Consequences

Our choices affect ourselves. Our choices affect others.
We start by creating a plot showing how our choices affect ourselves (x-axis) and how our choices affect others (y-axis.) We label our quadrants, as shown, and post our chart where students can view it. We start with a discussion of what the quadrants imply.
Quadrant 1 could be called the friendship or community quadrant. Here we represent all the choices that I can make that are good for both me and the others involved. These are the choices that help me make and keep friends.
Quadrant IV could be called the selfish quadrant. These are all the choices I can make that benefit me but harm others.

Quadrant III could be termed the spite or anger quadrant. This represents all the choices I can make that harm both myself and others. Typically, these types of choices are primarily in anger or spite. It is not unusual to see a child hurt himself when he is so angry he want to hurt someone else.
Quadrant II could either be the altruism quadrant or the fool's quadrant. These are all the choices that help others but harm me. Sometimes it is good for an individual to accept self-sacrifice for the good of the community. Young learners need to recognize this. But sometimes accepting self-sacrifice for others is a fool's choice. Unfortunately, learning to distinguish between altruism and foolishness is quite challenging.
Students should readily recognize that most choices should be first quadrant choices. They should be able to quickly reason that third quadrant choices are never good. With some guidance they should recognize that choices that seem unfair because they benefit others more than self are still better choices than choices that harm either others or self.

Once we have instructed students to understand the quadrants, we can use the plot to give students feedback on their decisions. When a student chooses a certain behavior we can ask him guided questions.

  • How did your choice or behavior affect you?
  • How did your choice or behavior affect others?
  • What quadrant represents your choice? Did your choice promote friendship?
  • If it was not a first quadrant choice, could you have made a first quadrant choice in this situation?
  • Can you help your peers to make more first quadrant choices?

With repetition and feedback students can learn to recognize and discuss the consequences of their choices.

Lesson 2: Moral vs. Ethical
Raising the young involves teaching right vs. wrong. However, we must not teach this dichotomy as mutually exclusive. Avoiding wrong choices is not the same as making good choices. Making mostly good choices does not negate the impact of the harmful choices one makes. The ultimate growth step will prove to be recognizing in ourselves what we dislike or like in others.

  Wrongs one should not do Good things one should do
How others impact me
What wrong things should other be prevented from doing?
What sins should others be judged for?
What good things should others do?
How do we reward them?
How I impact others
What wrong things should I avoid doing?
Ethics / Ideals
What good deeds should I do?
Who should I help?
How should I help them?

As we did in lesson 1 above, we can make a chart in 2 dimensions. But, unlike above, the regions in this chart represent logical sets, not positive and negative. We develop our sets by looking at both good vs. wrong, and other vs. self.
Although are chart exists in two dimensions it hints at a somewhat linear sequence in stages of ethical development. The young child is dependent and very sensitive to that which harms him. He sees the world in terms of moralism - the wrong and unfair things that others do tome. From this it becomes easier for us to teach children morality - the wrong that they should not do. He yearns for others to treat him fairly and do what will be good for him and his team - idealism. Ultimately, he must learn to be ethical - he must learn to do what is good for others.
Again, we can use the chart to help students reflect on their decision, and their judgments of others.

  • Did your actions hurt or help others?
  • Did the actions of the others help or hurt you? If you were them what different choices would you have made?
  • Consider the consequences of your choices? Are you making choices that impact others the way that you would want to be affected?
  • Are you willing to make the same choices that you expect others to make?

Lesson 3: Short-term vs Long-term Consequences
The two discussions above leave out a critical component in developing ethical thinking. Our choices always have short-term easy to see consequences, and long-term harder to see consequences. We can chart these also.

Costs & Risks
Short term
Long term

In this case, students will need guidance filling in the blanks. But the chart can be applied to many situations. Many boys want to make the big play and be seen as the star. But their choices could cost the game or undermine the team. The class clown wants to be funny now. He does not see what this might cost him or his friends in the long run. The young child wants to play and avoid work. He does not see that he will still have the work to do later, when it might be even harder. Students may be guided to reason about long term costs by filling in the chart follow their decisions.
Unfortunately adults can be just as weak as children when it comes to examine long term consequences of short term choices. Think of how many adults smoke or have found themselves deeply in debt.
Again, this lesson takes much repetition.

  • Why are you making this choice now?
  • How will it affect you in the long term?
  • If you go for the benefits now will it make you any more able to face the costs later?

Mathematical reasoning may be applied to any aspect of experience - some much more successfully than others. Experience can motivate students to understand new concepts such as negatives or abstract spaces. These lessons may be used either to use charting and graphing to motivate ethical reasoning, or to use ethical reasoning to motivate understanding of quadrants and negatives. The lessons give one example of how math crosses over into other aspects of experience.

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