Traditional Verses Inquiry-based Learning
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 an example of how to use inquiry-based learning, see the Reflections lesson plan.