Goals for a Curriculum on Thinking and Learning
Created: August 24, 1998. Last Modified: April 8, 2002.
I have four goals for this course on problem solving and real-life thinking and learning:
Recognize the importance of asking (and answering) questions
Young children are naturally inquisitive, but their curiosity is rarely satisfied, and they eventually lose interest for a number of reasons. Many of these "basic" questions would stump most adults. For example, what makes the sky blue? Why is the ocean salty? How do birds/planes fly? How does water get to the top of trees?
These types of questions extend beyond the scientific. How does the stock market work? What determines the value of a company or the price of a product? Or even more ambiguous, what makes a good leader? Or a great violinist?
The process of answering these questions can lead to important discoveries. For example, two scientists were drinking coffee one day, and wondered why coffee stained in a ring rather than as an even circle. Researching this problem led to important discoveries in capillary action and surface friction.
Trying to answer questions that may not have a right or wrong answer builds analytical skills and helps identify and develop value systems.
Demolish the fear factor
Often, the main thing that prevents one from learning a new topic -- especially math and computers -- is fear. People are afraid of breaking a machine, or they are intimidated by the sight of equations. Ultimately, it's a fear of the unknown or the unfamiliar.
The primary goal here is to dash this fear factor, to show people that they are capable of conquering new areas and skills, and that once they do conquer these fears, they are exposed to a whole new realm of thinking and knowledge.
Defeating this fear factor means posing unfamiliar problems and teaching students skills to effectively navigate through these problems.
Think out of the box
Hard problems have non-obvious solutions, and require non-traditional ways of thinking. The goal here is to teach the students to exhaust the obvious possibilities, and then explore the non-obvious possibilities.
Another way to phrase this is approaching problems from different perspectives. There is the classic joke about a mathematician, an economist, and an engineer stuck on an island with a can but no can opener. Each see the problem in different ways, and come up with solutions of varying quality.
Alexander Calandra told an anecdote in the Saturday Review about a physics exam entitled, "Angels on a Pin: A Modern Parable." True or not, I found it a very revealing anecdote on real-life problem solving versus institutional problem solving.
A fun way to practice these techniques is through lateral thinking puzzles, where someone presents a scenario and a simply-stated mystery, and the others try to solve the mystery by asking yes/no questions. On this note, Martin Gardner has written many articles on the educational value of solving puzzles.
Trying to explain a concept to others forces you to formulate the concept in your head, allowing you to identify both the strengths and the gaps of understanding. If you can explain a concept fluidly and answer related questions easily, you very likely have a strong understanding of the concept. If you cannot, then there are clearly things you do not understand.
In his book, Genius: The Life and Science of Richard Feynman, James Gleick tells a story of a physicist approaching Feynman with a question about quantum mechanics. Feynman promised to prepare a freshman lecture on the topic, failed, and later explained, "I couldn't reduce it to the freshman level. That means we really don't understand it."
Having students explain a concept to a group of students and the teacher, followed by a Socratic dialog, is a very worthwhile exercise. Once convinced of the value of this technique, students will hopefully learn both the value of formulating problems on their own in order to clarify their own understanding, and of the value of collaborating with others, if only because it forces you to think about problems in different ways.
Calandra, Alexander. "Angels on a Pin: A Modern Parable." Saturday Review. December 21, 1968.
Gleick, James. Genius: The Life and Science of Richard Feynman. New York, NY: Pantheon Books, 1992.