Not enough attention is paid to the stages of adult development as described, for instance, by Robert Kegan. (See The Evolving Self or this terse summary) For instance, how we answer the question “Why take math?” depends on the developmental stage of our interlocutor.
Kegan’s conception of the development of the self has six stages: Stage 0 – Incorporative, Stage 1 – Impulsive, Stage 2 – Imperial, Stage 3 – Interpersonal, Stage 4 – Institutional, and Stage 5 – Interindividual. As a person progresses through the stages (not all reach the last stage) various “subjects” get incorporated into the self and become “objects”. I now think of the objects as those concepts we can manipulate and make judgements about and the subjects as the immediate unconscious concerns that are we are currently using to maneuver through the world. [This is a change from the original post.] I am not sure if Kegan would agree but I think that the objects accumulate so that the subjects of all the previous stages become the totality of the objects in the current stage.
This is fairly abstruse stuff for one such as I who is not versed in the psychological view of humanity. Here are the “hooks” I use to keep the stages straight.
Stage 0: Incorporative – concerned with immediate physical needs – a young child.
Stage 1: Impulsive – concerned with physical satisfaction – a child.
Stage 2: Imperial – concerned with finding the parts of the world that align with one’s interests.
Stage 3: Interpersonal – concerned with interpersonal interactions as necessary to achieving one’s interests.
Stage 4: Institutional – concerned with social norms and one’s place in society.
Stage 5: Inter-individual – concerned one’s own principles as they relate to social norms.
These descriptions are very rough and probably wrong but the idea a developing self moving through a series of stages is compelling. Say your fifteen year old son got home at midnight a hour past curfew. Which parental response would he “hear”? “We were very worried when you didn’t call. Please have some consideration” versus “You broke your promise. You can go nowhere after school unless one of us accompanies you.” The second response works for someone in stage 1 or 2 and the second for someone in stage 3.
So in random order to make things less predictable, here are possible responses to “Why take math?” and the stage (highest) of development where I think they would work best.
Why take math?
- Because I (the authority figure) say so. This would work with a stage 1 personality if accompanied by a hint of punishment and with a stage 2 person if stated matter-of-factly as “It’s part of the world. Deal with it.”
- Because society says so. This would work with a stage 4 individual who is finding his/her role in the world and thinking about job and family.
- Because that’s what everybody does. This is a stage 3 response. Math as a normal rite of passage experienced by all educated people.
- Because that’s what people have been doing since the 1600’s. Stage 4 – Studying mathematics is part of civil (civilizing) society and we teachers and students of mathematics are simply instruments of historical progress.
- Because it is good for your soul. Stage 5 – In the context of human development math transcends the personal, interpersonal and the societal. It uplifts us.
- Because you will be keeping up with your peers. Stage 3 – direct reference to peers. Assumes the person does not want to stand out and be different.
- Because college requires it. Stage 2 – This is the world as it is, so get with it. An appeal to authority.
- Because part of being an educated person is knowing mathematics. Stage 4 – if “educated” is defined by social norms and Stage 5 if “educated” is understood as a choice made by the best and the brightest in history.
- Because it will help you in your future/ present job. Stage 2 if the voice of authority is speaking. Stage 4 if the connections with vocational aspirations and mathematics have been made explicit.
- Because it will help you understand your major’s curriculum. Stage 5 – A commitment has been made to a major course of study and the need for various prerequisites are becoming clear.
- Because the Chinese are learning it. Stage 4 – Our society is competing with their society. Your responsibility to our way of life requires you to take math.
- Because your child will need your help with his/her homework. Stage 3 and 4 – With thoughts of love, marriage and family come a vague sense of responsibility (Stage 3) or specific plans for one’s future include marriage and children.
- Because the mathematical approach to problem solving is useful and enlightening. Stage 5 – Studying math helps us navigate our modern complex society and understand the machinery of social interactions
- Because it’s fun. Stage 2 if one is living for pleasure. Stage 5 if one is searching for one’s self in the midst of all our social roles. If Stage 2 and studying mathematics becomes no longer fun, the person will quit and must wait to be revitalized somewhere else in his/her psychological development.
- Because it is satisfying. See because it’s fun.
- Because it is an important human achievement. Stage 5 – Mathematics has an important position in the panoply of human endeavors and part of being a whole human being is knowing mathematics and its history.
- Because it is the way we will communicate with aliens. Stage 5 – Math is intrinsic to the universe and thus has value.
- Because it has a certain purity and aesthetic. Stage 5 – Math for math’s sake. Studying mathematics is the study of truth and beauty. Need I say more.
Again, the stages as I described are sketchy at best. However the principle remains that how we answer students’ questions, how we phrase assignments and test items, and how we build our syllabi must depend on the psychological developmental stage of our particular students.