In another course I am currently taking Action Research, I am working with two other teachers to discover the meaning behind critical thinking in the math classroom. As a math teacher, I have noticed that one of the main issues that I face every year involves the lack of understanding when it comes to problem solving. Every year, without delay, I have at least (and trust me it's more) one student that refuses to even try word problems. The students leave them blank on homework, classwork, even tests! It has been a goal of mine to try to help students to become more comfortable with solving word problems and to replace negative feelings with positive ones. This is not an easy task. In the classroom I would present multiple problems and go through the steps to solve them, with the class as a whole. The results are always the same. The students who understood the problems did them, those that refused to try didn't complete them, and others tried and gave up half way through.
It was only through collecting data for my research project was I able to see the relevance between critical thinking and problems solving. According to some of my colleagues, critical thinking is being able to see various viewpoints of a problem. In fact, it is the responsibility of the teacher to look at the students answers and the process they took to get the answers and share the various ways with the whole class. The teacher must be willing themselves to accept various viewpoints to a solution, even when the solution is not conventional. After all, mathematicians used various methods to obtain answers and various methods to prove their answers. To quote one of my colleagues "if I leave a trail of cheese for the mice to follow, they will follow the path and will be successful, but if I take the cheese away I doubt they will follow the trail laid out for them."
This really hit home fr me as a teacher. If I stick to the traditional way of teaching mathematics I am simply creating robots or mice. If I continue to give my students the answers and show them MY way of answering a problem, I am not encouraging them to think through the problem themselves. It is up to me to give them those essential questions to muddle through to find their own answers. While my way is correct and may be easy, I cannot continue to lure them with cheese. Ultimately, it is up to the students to find the right path and hopefully get to the end of the maze. By researching the questions of critical thinking in the math classroom and curriculum development I know what I have to do in my teaching to make mathematics more meaningful to my students. As a bonus, I will be finally matching my philosophy with the reality in my classroom.
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I totally know where you are coming from in terms of dealing with alternate responses to problems that you pose to your students. I think that one of the hardest things as teachers is that we need to understand that not everyone learns the same way that we learn. This idea often leads to mental tug of war when you are trying to assess students in the classroom. It's great that through action research you were able to come to some of these conclusions. I learned a lot through my action research project too although mine focussed on special education. Nice post!
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