I read one of the National Council of Teachers of Mathematics (NCTM) Math Teacher
articles. I was looking for some motivation to move forward with my agenda on diversity and Mathematics for all. In the past, I have recommended that math teachers engage in personal problem-solving as part of their ongoing professional development. The premise is that by continuously placing ourselves in math problem-solving modes, we may be better equipped to support our students as they engage in the same process. These personal problem-solving activities such as, reading mathematics education articles, experimenting with math problems or puzzles, making sense of the history of mathematics, exploring art and mathematics, or investigating realistic, applied math problems.
I chose the November 23, 2017, monthly calendar problem from the Math Teacher to pursue my professional development around experimenting with math problems.
The number puzzle is from an 1852 algebra textbook: “A certain number consists of three digits, which are in arithmetical progression; and the number divided by the sum of the digits is equal to 26, but if 198 be added to it, the digits will be inverted. What is the number?”
After feeling scared that I might not be able to solve the problem, I wrote the problem down and tried to understand the problem. I then made sense of the problem by writing some examples of my understandings. I thought, since this is from an algebra textbook, I decided to try to use some algebra. After about 5 minutes of setting up some equations, I decided that it would be easier for me to follow my instincts and just try out some example cases of solutions to the problem. I then gave up a little bit and wrote some arithmetic progressions using the digits 1, through 9. I worked for about 30 minutes until I was successful.
Finding the solution was empowering. The selected problem has very little to do with an applied problem, often recommended for a performance task in math and often recommended so that student witness the value of a real-world problem. The answer is not obvious; there is more than one way to arrive at the answer or perhaps the problem has more than one answer; there is a perplexing situation that is understood; the solver is interested in finding a solution; one is unable to proceed directly to a solution; and the solution requires the use of mathematical ideas. (Find the reference.)
I felt stress and anxiety. I wondered why I was doing this. I believe it is essential for pre-service and in-service teachers to engage in problem-solving because it puts you in the shoes of the student. I had forgotten what it felt like to not know exactly how to approach any math problem. I had forgotten about the tension involved in solving a problem. If we expect students to do this, solve problems, then we have to engage the process ourselves, and students must be taught how to engage in this process.
The process of solving the problem may mirror the process mathematicians engage when discovering a solution to a theoretical question. I only felt a sense of courage and confidence about solving the problem once I solved the problem myself. The steps, the feelings, the success, the stress, and finding the answer, all might be transferable to problem-solving in general. If we expect citizens in our democracy to make decisions and solve essential life problems, then how do we use the curriculum to engage students in problems that provide them with the experiences we want them to have for the classroom and life.