“Don’t teach kids mathematics, teach them to be mathematicians.” (I believe it was Seymour Papert)
It was in the scoping phase of a new project where this came to mind, and I realized that, depending on your definition of ‘mathematician’, I don’t want them to be mathematicians either, but I want them to be mathematical problem solvers. That is, I don’t necessarily want them to be able to create mathematical theories any more than I want them to be able to recite math formulas; I want them to be able to solve problems with mathematics. And, as Jonassen tells us, the problems we give kids to solve in schools bear little resemblance to those they need to face in the real world.
My thoughts wandered further, however. I wondered if we could create rubrics around what a good math problem-solver looks like, and have students evaluate each other and assist one another in becoming good problem-solvers. Like Brown and Palincsar’s Reciprocal Teaching, they could take turns solving problems and looking at how they do it.
Of course, I want to generalize it, and find rubrics that define meaningful skills like searching, design, research, problem-solving, etc, even for adults (ala work literacy) that individual can use for self-evaluation, but also peer or guide evaluation (360; level 3, etc) and mentoring. Particularly for digital literacy.
What do you think; would you like a set of such metrics and a social support infrastructure to self-develop in the use of new technologies and skills for accomplishing your goals?
The problem with metrics is that it “forces” processes and limits creativity. In math, for example, proofs that are memorized give a “standard” understanding, but don’t take into consideration the different ways someone can come to the same answer. My son’s teacher makes them take apart the proofs, explain each step, and then put it back together in their own words, explaining it to partners. While they may not get the exact wording, they definitely learn the logic behind the proofs.
Likewise, I was shocked when a coworker from Hong Kong approached a math problem in a totally different way than I did. What was shocking was that we came up with exactly the same answer (different processes). New technologies allow us to come up with different strategies based on our own understanding and experience, yet develop common understanding. What I think needs to be focused on is how that common understanding is developed (in the case of my son by dissecting the proofs and putting them back together, in my case by looking at another approach to problem solving and understanding how two approaches can come up with the same answer). I think you mentioned before about the importance of communication. I think meaning making skills are more important (perspective taking, creating shared cognition, collaborative and cooperative learning, listening skills) than determining a numeric measure for “how to accomplish your goals”.
Virginia, you’re right and I misspoke. When I asked whether you want metrics, I didn’t mean measures so much as qualitative guidelines (e.g. “did you try re-representing the problem in different ways”). I did indeed intend the type of meaning-making activities you discuss, and thanks for calling me on it.
This post brings up many questions in my mind, the biggest being: Can we really teach the majority of people to be thinkers and problem solvers? My 46 years of life experience has shown me that the majority of people prefer to do rather than create. So much of education is connected to motivation and if the majority of students do not have a natural curiosity to understand “why” it is important that we continue to teach “how.” Let’s consider new technology. Only one person needs to have the vision and understanding to design a new technology. Then someone (a good Instructional Designer) needs to translate that design into a process that a large number of people can learn. Finally, hundreds of people need to learn how to produce it and use it.
I realize that I have a very different view of education than most, but I believe that public K-8 education should be focused on “how.” High School should begin to offer a mix of how and why. Higher education, however, needs to refocus itself on “why.” You see, I believe that when you offer a young child open ended situations and too many choices/solutions, they become frustrated and discouraged. If you teach them only one way, they naturally begin to question your knowledge and authority as they mature. The trick at that point is to encourage them to discover a better way, rather than insisting that your way is the only way. I stand by this theory whether you’re teaching math, history, religion or life skills.
Donna, interesting question. I’d argue that as Dan Pink says in his “Whole New Mind”, that the differentiator going forward will be the ability to not just execute, but innovate. Of course, there will always (?) be those who do, but I probably have a bias towards the so-called ‘knowledge worker’. However, I think we can do a better job of motivation, too.
I’ll also argue that the ‘why’ can begin to be addressed early. I like the notion of the spiral curriculum, where we revisit things in greater breadth, depth, and integration. I agree it’s got to be adapted to the developmental level. Also that you can’t just insist it’s your own way, you have to guide their discovery. Thanks for the contribution; great discussion!