I have a constructivist teaching philosophy. During my Senior Seminar Math class, we discovered the constructivist philosophy and saw many examples of math teachers applying the philosophy to their classroom. I was extremely impressed with the results, as well as the research behind the constructivist philosophy, showing students concept knowledge increasing.
The constructivist theory states that knowledge is not universal. It is personal to each individual person, because each person uses their prior knowledge to “construct” the knowledge in their schema. It is much like how two people can walk through a haunted house together, and come away with very different memories of their experience. Because this is the core belief of the constructivist theory, those who wish to implement it into their classroom, use an interactive, problem-based, inquiry model for teaching their students. The teacher is still the director of the classroom, but asks students to discover the solutions with each other’s cooperation. The teacher facilitates discussions, and teaches students concrete knowledge based upon their discoveries.
For example, a teacher may give the students a cylinder, and ask them to find the volume of it. The students, at this point, do not know the generic formula for the volume of a cylinder, but instead have to use their prior knowledge to make a conjecture. The teacher would have them work individually, in small groups, and then discuss their findings together as a class. In the end, the teacher will point out the generic formula, after the students are close to finding it themselves. This way, the students will understand the CONCEPT behind the formula, and will be able to generate the formula later in life. It is when students are simply given the formula, and asked to practice it that adults no longer remember it when they are older. Do you remember the formula of a cylinder? If you do, is it because you understand WHY that formula works?
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