After five (5!) pages, I will give it my highest recommendations.

Point the first: David Foster Wallace is an amazing author. If he wrote something, you should read it.

Point the second: Infinity is a concept that should and does confuse everyone in the world. “A big number” is nowhere near enough of an explanation to describe how to conceptualize an idea as complex and beautiful as infinity. There is no reference that makes it simpler, only more well-defined.

Point the third: David Foster Wallace sticks up for mathematicians in the first pages. He notes that he isn’t a math guy himself, and then puts up this aggressively respectful tone that made me paw through the pages.

The book is filled with IYI, or “If you’re interested,” for those that want to learn more about the mathematics behind the ideas. Which I am. I feel like this book may have been written for me, with all of the ideas and concepts and beauty and amazingness.

Two things I have trouble describing are infinity and the writing of DFW. Having them both together is excellent. Do yourself a favor and read this book.

]]>**That’s a dirty, dirty lie. I have not considered *lesson plans* for weeks. I have watched documentaries on math. I have attempted to calculate ridiculous birthday problems. I have helped people with their own math problems. I have pages of notes on linear algebra as I attempt to recall the nuances of the Invertible Matrix Theorem. And I have had long talks with myself in my head about how best to teach people abstract algebra if they never got past high school algebra. I can’t help but think about math. Silly brain.

Having the option to start my class with a question that relates to students’ lives is so powerful. Just by being aware of the world they inhabit, I have moved from an authority figure to an approachable mentor. Especially with mathematics, this shift will drastically change the ability of marginal students to find their way, as well as see you as a human being and not a math robot.

As an example, my students want to find the area of different parts of the Deathly Hallow symbol and work out how the circle has to be in relation to the line for the circumscribing circle to be equilateral. We aren’t even to that point in my curriculum, so now it’s something I need to hold on for later in the year! And they were sad about it! I was completely amazed at the enthusiasm in the room over finding area.

So, if you want to be a teacher and you want to spend your time reading math books, that’s fine. By all means, read more math books. But make sure you see some of the latest movies. Watch a TV show. Read some fun YA fiction. If students can relate to you, then they will come talk to you about their lives, which will lead to them coming to talk to you about math. Just being good at math is intimidating. Be more.

]]>Take today, for example.

On Monday, we studied the Exterior Angle Theorem. This theorem is one of many, many, many simple ways to take a diagram and end up applying algebra to solve problems, which is one of the primary goals of the course. But even more important is to use triangles to develop some important theorems with parallel lines. For students, this is when the class becomes a crap shoot. Half the time, they see the connection instantly, and half of the time they stare at the board for the rest of the class.

As a teacher, this is the worst moment of the day.

For the students who get it, further instruction is almost meaningless. I can provide some new and interesting tangents on the concept, but it’s hardly ever needed. They can solve any problem I can throw at them until I introduce some new and harder ideas. If I continue to discuss the same topic, they will be bored before class ends, and will become disruptive as they demand new material.

For the students who don’t get it, they are angry and frustrated at this point. A concept that other students clearly understand is beyond their grasp, which means they are now the intellectual inferiors in the class. Some get upset and try harder to get it, drawing darker and darker circles in the desktops. Others check out, claiming their inferiority and refusing to attempt understanding, instead spending their time drawing in the margins. No matter what I discuss for the remainder of class, they will be disruptive as they wait impatiently for the end of the hour.

If I choose to teach the former group, I lose the latter, and vice versa. If I instead attempt to teach to the middle, I lose both groups.

In many other classes, everyone can read the passage and come up with their own opinion, or write an essay, or memorize lines. But math, and particularly geometry, is a binary game: you get it or you don’t. I have adapted Dan Meyer’s skill-based assessment plans, and this is getting me a better idea of where my students are on this scale, but I still don’t have the faintest idea about how to get everyone in the class from 0 to 1.

There must be a better way to teach Geometry to a group of students. I really wish I could figure out what it is.

]]>Wait, I can’t do it. Winter Break.

Once upon a time, I loved the holidays. Even now, I can respect the need for a break when all seems dark and bleak. But the idea that my classes have to sit back for two weeks of forgetfulness is crazy. If there is any sort of LEGO building block style of lesson planning, then I will have to review for at least a week when we return, as well as devote next week to wrapping up an incomplete lesson before the break ruins everything. To add even more agony, in another four weeks, the semester will end. Students will soon move on to new classes, and I will find myself teaching Linear Algebra instead, using my wasted regression plans for tinder as I attempt to use fire to keep the darkness at bay.

It isn’t that I regret the happy time people will spend away from school. I just regret that my course will be so choppy as a result. Someday, I’ll plan this thing out right. Maybe the fifth time is the charm…

]]>I am motivated by a constant need to change things.

At a recent open house, I was asked if I taught any AP classes. I’m not sure if I believe that Calculus should even be taught at the high school level, so the question of whether we had AP Calc took me a little off guard. College Calculus is a traditional benchmark class, which is purposefully difficult in order to keep people who are not ready at arm’s length. The experience of coming into your freshman year with a fast-paced, academically challenging class chock full of homework is not an experience that any dedicated student should escape. Since I feel students need to be challenged, let me leave aside the validity of a gateway course, and just say that I believe it is more important to take Calculus in college than to skip it.

What is the purpose of AP courses? Would a college rather accept a student with a 3 on an AP test, or would they rather see a wide span of academic pursuits? At a school where I have implemented two full years of elective, advanced math courses, it is clear to me that I am focused on allowing students to entertain their curiosity, more than their need to start college a year early. I think my students understand this. My Calculus class is a springboard, which attempts to prepare them for the inevitable horrors they will face freshman year. Knowing that a student already has college credit in a benchmark class like Calculus means they should be prepared to move into higher mathematics, right? We have allowed a test to take the place of a year of experience in the purposeful factory-of-failure known as college Calculus.

So when I am asked by a parent about AP courses, I fall into a motivational trap. In broad terms, the question can be translated as “I want you to do what is best for my child.” Based on my experience, I think that what is ‘best’ is to give them a wide selection of possible academic courses that will entice them into developing an amazing work sample that will impress colleges into bringing them into their programs. I believe that what is ‘best’ for students is to push them in cycles of challenge and contemplation, to build their critical thinking skills and teach them how to solve problems on their own. I act as though the ‘best’ student is one who has owned their education. None of this has anything to do with standardized tests, or anything to do with skipping out on fundamental challenges in college.

Of course, I capitulate. I explain my program, but add that I can fill in the gaps that would allow a student to take an AP test. I give in to personal weakness, because I know that my explanation sounds like an excuse. If institutions of education across the country find the AP test to be the highest form of academic achievement, then who am I to say otherwise? A teacher in a small school with a BS and a dream?

Like I said at the start, my motivations here are entirely selfish. The system of education in the US is in dire need of some changing, and I want my voice to be added to the chorus of educators trying to fix it. That’s why I plan to write. That’s how I hope to teach.

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