The Horse Problem!
A man buys a horse for 50 dollars. Decides he wants to sell his horse later and gets 60 dollars. He then decides to buy it back again and paid 70 dollars. However, he could no longer keep it and he sold it for 80 dollars.
Did he make money? lose money? or break even? Explain why.
I was watching a Marilyn Burns video titles 'About Teaching Mathematics'. In this video, this particular question was taken to the 'street'. There were as many answers as there are strategies to solve it! Why is this problem such a problem for so many?
Answer When presenting problems like this one to students or individuals, let them devise a plan for solving the problem. Some students will need to act out the problem, others will need to draw charts or graphs and then some individuals will work it out using various computations. Thinking skills are skills needed for a lifetime, by letting students devise their own plans and strategies in problem solving, they are improving their thinking skills.
Good problems are tasks that allow students to devise their own methods to solve them. They should not be presented with the strategy to solve them nor should they be told that there is a specific strategy to solve the problem. The problem should allow the students to use various strategies to solve it, they should be required to explain their reasoning and logic once they believe they have solved the problem. You want students to stretch their thinking and move toward understanding. Math should be problematic. After all, the single most important principle for improving the teaching of math is to allow math to be proglematic for students. (According to Hiebert et al., 1996.)
Students should be provided with good problems in mathematics, problems that are at their level and support a variety of strategies for solving are the best types.