· Mathematics is about learning to ask questions, formulating interesting and relevant questions leads to the drive to find solutions. It is impossible to get a meaningful answer if you have a meaningless question. So many times all students care about is getting the “right” answer, however, if the questions was pointless or not interesting then the answer does not matter. When searching for a solution to a problem, students should be taught to ask many questions and then evaluate those questions to determine which answers are most likely to lead to a solution to the problem.
· Mistakes are not only acceptable but are to be celebrated; the only way to advance mathematical understanding is by making mistakes. This includes struggling with concepts and ideas, looking at a problem from one direction and not making any progress and having to start again from another side. Too often students are given the impression that there is always a fast answer, or that there is always a formula ready at hand to use to solve any problem. When the reality is that many problems don’t fit into a tidy mold with a quick solution. The more students are able to see that mistakes in math lead to better solutions the more likely they will be to stick with difficult problems and persevere in solving them.
· Explaining concepts to others helps students better understand their own ideas. Having to clearly state why a particular method works or how an answer was derived ensures that students have a firm understanding of their ideas. By describing the method used to arrive at an answer students must examine their own thinking and are likely to catch their own mistakes or find areas of misunderstanding. A dialog back and forth between students provides students the opportunity to learn to question not only their own answers but also the thinking of other students. Students should know it’s ok to questions someone else’s answer and continue looking for clarification until they are convinced.
· The mathematics classroom should extend beyond the classroom walls, not simply by providing “real-world” problems in a textbook, but by providing students problems from other areas of their lives. Although, there is a beauty in solving a mathematical puzzle just for the sake of finding a solution, there are opportunities throughout the other disciplines that lend themselves to being solved with math. In particular, I think that math and science should be closely linked in the curriculum and
· All students have something they can contribute in a mathematical conversation. Students will approach problems from different places due to differing background knowledge. Because math learning builds on previous knowledge many students will be at different places in their understanding of math at any given time. However, at any level of understanding, each student will have something unique to offer to the conversation.
This is a living document, over the course of my final semester of coursework at UNI I will continue to examine and refine this belief statement.