Math Class
Living Wisdom School math teacher Theodore Timpson describes a problem-solving session.
Today in math students continued working on a problematic question: How far does the earth turn in one hour? They have already spent two sessions studying the question, and they made many discoveries along the way. This kind of process creates a rich environment for them to develop mathematical knowledge and useful strategies.
We first divided the question into two parts: (1) How much does the earth turn in an hour, measuring at the center, and (2) How much land passes beneath the sun in an hour, at the surface. With some guidance, the children realized that the first question would have an angular answer, and the second a linear one.
The first part required them to reason about the number of degrees in a complete circle and the number of hours in a full rotation of the earth. This they did, and both problem solving groups were able to arrive at the idea that the globe turns 15º in an hour. The second part required more information, they realized. How far is it around the earth? They examined the globe, and discovered a scale diagram on the surface. They then proceeded to measure in centimeters the distance around the globe at the equator. It was particularly difficult to translate the number of centimeters to the number of miles using the scale (3 cm = 500 miles). But they did it through their own reasoning. From there they could divide the number to find the distance passed in an hour.
Each group came up with different answers, since they used different methods. We then discussed whether both answers were reasonably close. We also had to interpret what "21,333.333" on the calculator means - is it 21 million? We confronted ideas of accuracy, margin of error, estimates, and sources of information. The students also had to listen very carefully to each other, since each of them was expected to be ready to explain the group's answer. The whole experience was a very good example of what can happen when children are given the opportunity to reason, discuss, and explore mathematics with only subtle encouragement and guidance from the teacher.
