John Dewey, the eminent philosopher of education, examines pure inquiry in
Logic, the Theory of Inquiry.
It is a fascinating and exhaustive dissection of the components of the process of forming questions. He describes the ecology of thought, stimulus, questioning and knowledge. He says that doubt leads to questions and calls doubt a result of "the disturbed relation of organism-environment". In his view, doubt is never fully removed, instead the inquiry process, "institutes new environing conditions that occasion new problems. What the organism learns during this process produces new powers that make demands upon the environment. In short, as special problems are resolved, new ones tend to emerge."
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Dewey sees the process of inquiry as an organism's natural search to achieve balance when presented with a stimulus. He also sees the inquiry process as growing and changing with a person as they adapt and learn. Finally, he does not expect a complete removal of doubt, but a forward moving process where new questions emerge as older questions are refined or resolved.
Now, cut to the classroom setting. What sort of "disturbed relation of organism-environment" will cause a student to react with productive questions necessary to stimulate learning and further the process of inquiry? As a teacher I have prepared many lessons that I was convinced would fascinate my students, and prompt engagement and questions, only to have students be mentally checked-out. At other times students have shown unexpected persistence in working through problems driving themselves forward to find an answer. The topic itself is not what engages students, it is the framework each student builds in order to examine the topic.
The importance of framing the topic is to formulate an interest. It takes time and an amount of directed looking to begin to perceive patterns and take interest. Author Chris Barnard writes in
Asking Questions in Biology:
"Unfamiliar systems are often boring. The details may not reveal patterns and may seem to change at will and without direction and nothing 'significant' or worthy of mention may arise."
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Without patterns, everything becomes monotonous or overwhelming.
So, even "culturally responsive" or "student-centered" content can be met with resistance. Even seemingly exciting topics take some time to lure us in, and to stimulate our individual interest. A classroom of twenty-seven individuals will frame the topic in equally different ways. It requires patience and process and a culture of the classroom to allow students to find the patterns that stimulate their interest and provoke the questions that promote seeking answers. So while almost any subject can feel boring at first, almost any subject can engage as one begins to see patterns in a piece of that subject.
How do we help students to make sense of problems in Math in order to begin finding solutions? The traditional expectations of a Math class are to learn the necessary skills within that subject, whether Algebra, Geometry or Statistics. The focus on skill alone removes the math from its application, and makes it more difficult for students to frame a problem for themselves. Yet, a focus on applications alone can be problematic, if the applications require skills and practices that students do not yet know. A working Mathematical process, like a Scientific Method can enable students to follow a consistent process to make sense of and persist in solving problems.
George Polya, in his influential book, "How to Solve it" published in 1945 and still widely referenced today, lists four phases to problem solving; understanding the problem, making a plan, carrying out the plan and reviewing the completed solution.
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Actually solving, or carrying out the plan is only one component of a rather lengthy process. In his scheme, understanding the problem requires the same attention as solving the problem. Understanding the problem also means framing the problem to provide access and interest. Understanding the problem could involve "Google-ing" it, but as teachers we need to emphasize that reading about a topic, naming a topic or being able to look up a topic does not mean we understand the topic.