Mathematics Miseducation

1. Stolp, Derek (2005). Mathematics Miseducation: The Case Against a Tired Tradition. Maryland: The Rowand and Littlefield publishing group.

Stolp shows that what we believe about the needs of children and what motivates them to lean promote practices that are counterproductive and ultimately corrupt students' own healthy motivations.

Mathematics Miseducation is a refreshing opposition to how mathematics is traditionally taught in kindergarten through college. He states a compelling case to revamp the way we teach mathematics through the use of real world and open ended mathematical problems. Stolp refers to the way we teach students enables them to be map followers rather than explores and discoverers.

Stolp suggests that we make a few changes to our approach:

Principle 1: Begin every unit of study, if possible, with a real-world problem. The ideal is to use a real world situation to develop the mathematical tools needed to solve the problem. This gives purpose to the learning and will help the students think as a mathematician would.

Principle 2: Design an attack on the problem together. Teacher creates a plan with the student not for the student. This allows student to be participants in the journey. They discover along the way instead of mimicking what the teacher has already shown them.

Principle 3: Whenever possible answer a question with another question. Declarative statements are the death of inquiry. You should resist the temptation to be the revealer of truth.

Principle 4: At the end of the unit once the problem is solved, to go back and to reexamine the path taken. This allows the students to summarize the important ideas. It also enables connections between previous units.

Principle 5: To examine the problem's background as well as historical record. Why did these problems first arise? Who were its creators and solvers? This gives depth and meaning behind what we do.

Principle 6: Aim for depth not breadth. This allows time for thoughtful investigations and discoveries.

Principle 7. Do not teach from a text book. Textbooks are poorly designed and often lack real-world applications.

Relevant Quotes:

On Motivation :
"Rewards and punishments can be used to get many kids to learn what we want them to learn, but it is clear that many more are not learning effectively. Moreover, for those who do learn, the cost is that their own healty motivations are corrupted. Instead of learning out of curiosity and desire to make sense of some facet of their world, they learn in order to please the teacher or parent, to get into the most prestigious college, to prove that they are better and smarter than their peers, to win a prize or public recognition. Under these circumstances, learning itself has been relegated to the second-class status of "means to an end", and when those ends are no longer available, there is no reason to pursue the means. "