I’m preparing to teach a class on sustainability and mathematics this January–it’s one of my favorite topics because it’s so personally meaningful and the math is really interesting.
I get to teach my kids Geometry this summer, and yesterday we did circumcenter, incenter, centroid, and orthocenter constructions. I’ve never done those before, and I was captivated by the beauty of the constructions. I decided to turn a few into watercolors. It was a lot of fun. Here’s another:
In this one I also constructed the orthocenter and the centroid, athought it’s hard to see (they’re pretty close to each other.) Highlighting the construction marks makes it clear that the circumcenter is constructed from the perpendicular bisectors of the lines. It’s not as easy to see that the incenter is constructed from the angle bisectors–I’d love to find a way to show that. This is my favorite way to integrate art and math–using art and design to illustrate mathematical concepts. In many cases a picture is worth a thousand words.
A friend of mine sent me an article about STEAM–the education movement to integrate the arts into STEM (science, technology, engineering, and math) classrooms. I think this is hugely important, although I think it has to go beyond just setting up more discovery learning opportunities. I also think teachers need to realize that engaging in art can be really scary for some kids (just as scary as math is for others!) I advise going slowly. And primary to the whole equation is the relationship between the teacher and her students. When that’s in a good place, you can accomplish just about anything!
There is a trend emerging in our local elementary and high schools to use Kahn Academy and other online learning resources to supplement or replace classroom instruction in math. I understand the attraction. At the small schools in the region where I live you tend to see a wide range of abilities in students. There are simply not enough resources to create different classes for kids who learn at different speeds. By using an online curriculum, kids are free to work at their own pace. The faster students can barrel ahead, while the slower ones can re-play a lecture to reinforce a concept that didn’t come through the first time. There is the potential to minimize classroom management issues and maximize everyone’s productivity–sounds like a win-win.
However, what teachers and administrators who jump to embrace this new way of teaching need to realize is the importance of the real time teacher-student relationship in learning. Relationship is another important way to make information sticky. A teacher, teaching in real time, can intuit moments of confusion, enlightenment, or boredom in a way that a computer never can. A good teacher can leverage those moments to propel or pause a lesson, to engage or disengage students from on another, in order to broaden the education of the whole class. I’m not saying it’s easy, but I believe it’s an art worth striving to master–and that is lost when we rely upon online learning.
Most of the students I’ve talked to emphatically do not like learning from Kahn Academy or other video lectures, whether they find math inherently easy or difficult. The online lectures are good as a back up or reinforcement, but as the primary source for content they are disorienting. Most teenagers (especially the ones who struggle with math) are not good at knowing whether or not they have mastered a concept, and what they need to learn next. The computer algorithms that attempt to figure that out from them are flawed and impersonal. There’s also the HUGE problem that when a student doesn’t understand something in a lecture, he or she can’t ask the video a question. Most teachers know that when your student doesn’t understand what you said, repeating it word for word is generally not going to help. There are also a million other factors that affect how receptive someone is to learning–human relationships are all about meeting and welcoming the ineffable. And that’s all part of education.
I think that Kahn Academy and other online learning tools are a great resource as long as you see them for what they are: distance learning. They can be really helpful if you’re in a situation where you don’t have access to a classroom and a live teacher: studying while working full time, recovering from an illness, or traveling. But if you have a choice, it makes much more sense to choose live human teachers as the means for teaching math and all other subjects. In addition to classrooms, textbooks, and instruction, I believe human contact is critical to quality learning.