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My Math Education Interview (Lesson)
The Education Wars Part XII
Last month I put out an offer to walk through some math problems with a student. Now I'm going to explain the purpose behind that lesson. Currently, the lesson is only on YouTube, here:
Please subscribe to our YouTube channel to…um…influence the machine.
This was my first time running Streamyard, and Liam wasn't with me, so I wanted to keep the number of new variables in my experience low so that it did not affect the lesson.
My sincere thanks to Iris and her father, who is a Rounding the Earth subscriber, for their participation and permission to share the experience. Iris was great. Her father told me that she was a good student, particularly with languages. She is a rising seventh grader without any sort of advanced math training, but obviously keeping up with her lessons through the sixth grade.
Those interested in my history and philosophy as an educator can start here.
Now, let's talk about what this lesson is about.
The Need for an Interview
After I helped build an online school and mathematics community, wrote a couple of textbooks, and designed a dozen or so courses at Art of Problem Solving, I felt that the problem of advanced students not having an outlet was solved, and that the largest problem in education was the lack of cohesive community cultures. I felt this way for many reasons. Recently, it has been highlighted in various literature (Mertz et al, 2008) that girls in the U.S. achieve highly in math when they grow up in communities with a strong math focus (there are already enough boys working in advanced math programs that it's socially easier for the girls?), but almost nowhere else. I felt the problem was even broader—that everyone is at a dramatic disadvantage anywhere there is not a healthy culture of learning math.
I decided to experiment with a learning center model in Central Alabama, where there is not currently a particularly strong culture of math education. The school wound up with almost half girls, learning topics such as number theory, combinatorics, complex geometry, and other tools not usually seen in regular classrooms, though I'll talk more about that another time. For now, I want to talk about the largest hurdle I faced in getting started.
When I moved to the Birmingham area, my old math team coach and several parents got a group of families together to see who might be interested in classes. I wound up with something like 16 students in two classes. In the larger class of 12 students, there were three students there who just weren't interested in being there. These three boys were not simply disinterested, but would tear down the class at times with bad behavior, which was even one of the boy's stated intentions.
In truth, I felt bad for him and the others, but my primary goal was to build a highly functional and enjoyable classroom. At the end of that ten week season, I scheduled new classes. All but those three students re-enrolled, and some new students showed up. But I stopped taking students unless I'd interviewed them first. What I realized is that many of the more advanced math children (the boys in particular) were resistant to essentially all teachers and schooling, which they regarded as a waste of time. Given my own experiences in school, I can't blame them, but that was exactly my point in building a school—to provide a different model and atmosphere. My next task was to gain trust.
The interview I began to follow is mostly easily described, but you really need to watch the video in order to understand it. I would,
Have a basic introduction with the student that focused on them (not the parent).
Find out a little bit about the student. Let them talk if they wanted to. When there is something that you need to understand about somebody, they often just let you know. They also let you know details about their lives that you can weave into lessons, which helps connect lessons to life or help regulate the waves of energetic focus so that students don't get overly drained during a two hour class.
I chose to work through counting problems with students in particular because this area of math (combinatorics, which is foundational to probability, statistics, and other subjects) is both undercovered and poorly covered in the traditional curriculum. I found that out of around 1,000 students interviewed this way, I was able to successfully navigate to a place of learning in all but one single case.
The goal was to start simple, keep track of the connection of the lessons and strategies (starting simple, using a model, etc.), and reach a point that challenged each student to do something they'd never done. With the older or particularly advanced students I would often challenge them with a variant of the classic Fibonacci recursion:
At the end of the interview, almost invariably, the student asked their parents to enroll them in class. They could see how much they would learn, and they would see that I could guide them. And we got to know one another.
Out of the next thousand or so students, I had just one or two behavior problems to sort out. The school wound up with a 97% quarter-to-quarter re-enrollment rate, and two years later there were consistently 150-200 enrollments at a time. Students would often say they learned more in a ten week, twenty hour course than during a whole year of school. And for the record, the per class-hour cost was right in line with national averages of spending in public schools.
A New Era of Education
There are more opportunities for students than ever. The internet has substantially broadened access to better teachers and more opportunities. Who doesn't ever use videos to learn something?
But the challenge now is to regulate the minds of children, and reform healthy communities. Young people need guidance by people physically in their communities. The online experience is imperfect, and perhaps unhealthy in more than limited doses—at least until children have grown into both healthy relationships and personal control over their education.
On top of that, millions of Americans and others are homeschooling for the first time over the past year. A lot of local homeschooling coops and unschooling or autonomous learning families or groups are finding their way through the fog to reach an understanding of how to make it all work. My hope is that this interview will be helpful for some people to watch and think about with respect to that process.
I will say that I was probably better at conducting the interview 14 years ago. I haven't taught much in the past (almost) six years since I shut down my last school, and heavy work weeks leave me with less rest than I'd like. Perhaps younger, more dynamic people can see this and make it work even better. I hope so. But I'm happy for anyone to get anything good out of it, whether that's observing practiced patience of what is mundane (for somebody who has walked through it over a thousand times; and learning about the student can be the part that isn't mundane) or the Socratic methodology of asking the student questions until they put the pieces together themselves. Because as we all know, we learn everything better by our own efforts.