As an adult, a parent, and a teacher, I believe in self-directed learning. I fully understand how kids can be self-taught readers and writers. In fact, as a kindergarten teacher, I saw it first hand and it was beautiful! And yet, I still have days that leave me wondering...yes but "what about math?" I truly have a math hang-up in the context of self-directed learning and self-willed curriculum. That's OK. It just means that I have done a lot of thinking about it and I'm happy to share my conclusions with you.
Changing Education Paradigms. To relate this back to math, people who like following the steps to get a nice neat answer are just not sought after in today's economy.
Math, as we learned it, is not really all that useful anymore. In fact, even our public schools understand that (at least in the province of Ontario); they are teaching "new math" to students. The focus is on problem-solving and discussion based learning that highlight the multiple solution paths to get the answer (and sometimes even multiple solutions!) Do you remember your math homework as a kid? Completing the textbook problems and then working on the assigned word problem questions at the end? Well, kids today are spending much of their time in discovery mode; working on those difficult math word problems, but in groups. As someone who loved math the old way, it took me a while to get my head around this "new math". Once I understood it, I realized how it was actually far superior to the ways in which we had been taught. The rote memorization was replaced by depth of understanding.
Taking it back to Sir Ken Robinson's Changing Education Paradigms, I think we can all agree that today's world doesn't need human calculators. We have an app for that. What we need are people who understand math at a deeper level. People who can create the apps or solve other big problems in our world. Hmmm...Now that is an interesting concept to me. Not everyone needs to have the same math exposure to be useful or successful in our world. In fact, the ones who pursue math the most are probably the ones that are most interested in math anyway and those kids need depth of understanding of the key concepts that interest them most, not following memorized steps. Humph. My math education is obsolete.
Despite the positive changes, I think there is still room for improvement in the way students are learning math in the public system and the only way to address it, from my perspective, is to actually make it more self-directed. By allowing children to follow their interests and natural skill sets, the kids who are naturally curious about math will spend more time contemplating those big math questions and the kids better suited to other lines of work will be free to pursue that learning. All kids will pick up the necessary math they need to function in the world, and they will have a better chance of picking up what they need and retaining it if they pursue it naturally as opposed to having the concepts artificially placed in front of them. In fact, Benezet's work with Math Training indicates that allowing students to develop their brain in areas that are more interesting to them appears to have better results than teaching math to students, at least from grade 1-5. If you are curious, check out this blog by Peter Gray Peter Gray does a nice job of describing how giving kids space to discover how to learn effectively instead of telling them what to learn has better results for achieving success.
I'd like to end with a personal reflection. When I look at my kids learning, I am inspired to stay on this path. Never having been taught a stitch of math, my two year old has started counting to 20. Rote counting at first, but now she is understanding that there is meaning behind each number name. Counting to 10 has never been so exciting. My five year old regularly adds and subtracts, creative sorting by attributes, and he has started playing with the beginning concepts of multiplication and division. He's a math guy in the making I think. He is currently obsessed with Lego Mixels and that has lead to him counting money and working to understand the fractions involved in coins so that he can buy more of these creatures with his allowance. My kids are absorbing math because the world they live in is simply more interesting when you understand the numbers. I just show them the world and give them opportunities to explore in the directions they are most interested in, and then they just learn what they need to learn to get them where they want to go.
I have a math hang-up because it is scary to let go of old paradigms! We think that covering all the bases with traditional instruction will help kids get to where *we think* they should go. But if you can let go, and I hope you can, they will go so much further. They will be spending their time doing the things that matter most to them. Oh, and one more tidbit; for those of you who disliked math growing up, self-directed kids don't really have those hang-ups. When they have freely taken charge of their own learning, kids are naturally confident in what they can achieve. How beautiful is that? No matter the task or it's perceived difficulty, they are resourceful and bright and use their strengths and skills to get the job done.
So I'm going to try my best to not give my kids any of my hang-ups. They can pursue whatever captures their mind, on their own timeline. Whether they choose to spend their day focused on reading, writing, math, or catching a seagull, I'm going to trust them.
Yes, this kid actually caught a seagull after his mom dared him. I think this is hilarious.