The process of inquiry-based learning motivates students to learn new mathematical concepts. Teaching is most engaging for students when their own thoughts, opinions, and curiosities are addressed in the subject at hand. The best way to ensure that students feel they have a stake in their own learning is to create a classroom that values exploration, where teacher and students alike can support, discuss, and evaluate ways of thinking in an open and ongoing way.
In a traditional classroom, students first learn about discrete concepts and procedures, such as the perimeter and area of a rectangle. They would then learn how to use the formula "A = L x W" to find the area of a rectangle, given its length and width. Later, students would learn about the area of a triangle and how to find the area using a formula. Eventually, students apply this knowledge to determine the area of a figure composed of a rectangle and triangle.
When a teacher uses inquiry-based learning, the process is reversed. The teacher presents a problem first, such as, "If you want to paint the front of a house, how much area must you paint?" Students then explore the problem and-with the teacher's guidance-discover that they need to understand how to cover an area with a standard-size unit. After solving the problem, students look for efficient procedures for finding the area and then develop formulas accordingly.
For another example of how to use inquiry-based learning, see the Reflections lesson plan on page 113.
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