Is our goal to have students performing better on standardized tests or to be prepared for what they are going to encounter in college and life? The ideal would be that they would be prepared for both. So the questions become, what do we want to leave the students with? How are we going to prepare them for the real world? What do we want them to learn about themselves? And how do we do it? To clear the air, I don’t believe that students are taking my calculus class because they need help doubling a recipe or balancing their checkbook. I believe it is because we want to expose students to the poetry of numbers, to have a new outlook on how to solve problems, to be able to think outside of the box, and to see how the unbreakable human spirit has conquered problems that once mystified the greatest of thinkers. Like any great symphony, mathematics represents a pinnacle of human creativity. We teach math to enrich the lives of our students in a way akin to reading poetry or composing music. This is the story of a student-created exhibit showcasing the beauty, humanity and intrigue behind math in history, philosophy and the applied arts.

In these examples student have to first ask the question – what information do I need to solve this problem? The textbook usually gives you that information. But here students build the problem and decide what matters. The question that’s usually buried at the bottom – it’s the last thing in the textbook problem – now becomes the first thing in the student’s mind. I want to make that question “irresistible” to the student, so they have to know the answer.

Let’s see how the Duncan sidesteps the issue of testing and innovation – while US students spend endless hours honing their test taking skills, the demand for routine skills has disappeared from the workplace. Anyone know of a meaningful and rewarding career that looks like filling out a worksheet? Maybe Friedman will be willing to tackle the stifling impact of testing on creativity thinking among our students.

I recently saw this video clip from an old Abbott and Costello film. It reminds us that math isn’t simply about learning a computational process, or getting the right answer. It’s pretty clear that Lou Costello has learned the wrong algorithm, and he defends his approach it with great determination. We learn math skills so that we can apply mathematical thinking to the problem solving we will need in our lives. Thus, much can be learned from the procedures we use to generate both the “correct” and the “incorrect” answer. Sharing our thinking with others allows us to negotiate a deeper understanding of algorithms and their application in the real world.