“Mathematical power is the ability to explore, to conjecture, to reason logically and to use a variety of mathematical methods effectively to solve problems. The ultimate goal of mathematics education is for all students to develop mathematical power to participate fully as a citizen and worker in our contemporary world.”
- from Michigan Curriculum Framework Vision Statement for Math
I love this statement! I used it with our practicum students this summer, I use it when I give presentations or workshops and I use it with my students, particularly because it is usually so in contrast with how they define math. We look at defining math at the beginning of each school year. Last year, each of my middle school students interviewed at least five people about math and how they used it in their lives. We categorized and graphed the results. Not one matched the vision statement above. If I remember correctly, we had a lot of responses similar to "math is addition and subtraction" or "math is manipulating numbers". . . we also had a few "math is torture" and "math is a bunch of stuff you don't have to understand, but it will help you with your checkbook".
What was more amazing was that when asked, many people, particularly adults and/or high school upperclassmen, said they did not really use math in their daily lives. Right around this point is when we start looking at the vision statement above. "Mathematical power". Wow! Many of my students are very knowledgeable about video games (in fact, I almost banned conversation about getting a wee, until I was tutored in video-game-ology) so the concept of mathematical power grabbed their attention right away! Nowhere in the definition of math, at least from the State of Michigan, does it state that to be participate fully as a citizen do you need to memorize your times tables or be able to answer 50 problems in 3 minutes. You need to be able to "explore" - awesome! You need to be able to "conjecture" - ooooh, estimate and hypothesize, you mean math is like science....? You need to be able to "reason logically" - well, there are steps and formulas that can help with that. . . . You also need to be able to "use a variety of mathematical methods effectively to solve problems" - wow, good thing they teach you that stuff in school!
I'm not advocating that fluency with operations and procedures isn't necessary, because it certainly helps a person apply methods more effectively and can help keep memory skills sharpened. What I am saying is that nowhere, within this vision of mathematics, does it say that you have to be fast all the time, or that you should complete these actions automatically or without thinking about what you are doing. In fact, the verbs that are used in this vision are active verbs: explore, conjecture, reason, use effectively and solve.
I frequently read editorials or other articles about how US students are performing poorly in math and have seen statements such as "how can schools improve math instruction". Though it may be over-simplifying what is a very complex issue, my response would be: add a verb not a worksheet or timer.