After nearly a year of creative hiatus, I am excited to share the first images of my new project.
Since last August I have been focusing on improving my craft as a middle and high school Algebra teacher. I am inspired by my students to create a new series of prints weaving together math, art, and history.
The images above are illustrations of the Greek method for approximating the circumference of a circle by inscribing a series of polygons with ever increasing number of sides. The more sides a polygon has, the closer its perimeter is to the circumference of the circle. Ancient Greek mathematicians worked on calculating perimeters of polygons with more and more sides in an attempt to arrive at a definitive whole number ratio of the circumference of a circle to its diameter (or pi.)
The top image above is a circumscribed and an inscribed polygon (representing upper and lower bounds for calculating pi.) The lower image is an inscribed triangle and hexagon (a nod to Eudoxus’ “method of exhaustion.”)
These two mini prints are just me getting my feet wet–I’m also working on a larger print that I’ll share more about later . . .
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.