It is Week 3 of the New Blogger Initiative, school is about to start on Thursday, and I will begin teaching Algebra II soon after . Since it’s already something that’s been waking me up at night (once literally, often figuratively), hopefully trying to write out some unifying concepts of the swampland of more-advanced-but-still-high-school math counts as still doing work, right?

The big reason those courses feel like a hodgepodge of ideas is that…they are! All the higher degree polynomials, trigonometry, piecewise functions, conics, etc are thrown together into four semesters or so in order to prep students to take calculus and be able to differentiate and integrate as many well-behaved functions as possible. Not a single American friend of mine in college seemed to have the same sequencing of ideas as I in high school, while most international students wondered why we had spent so much time learning about cubics and trig identities instead of number theory, combinatorics, inequalities, and proof.

Another issue is that advanced high school mathematics, even more than Algebra I, is like an underwater mountain range in that on the surface it appears disconnected. Some of the deep ideas that connect the topics in the space between linear equations in two variables and calculus are very deep indeed (e.g. the Fundamental Theorem of Algebra, insolvability of the quintic).

A view from the Cubics to the Island of Imaginary Numbers

All that said, here are three big themes that I want to emphasize in my Algebra II class, in other words, themes that are accessible to my students on an everyday basis, not deep, deep results that I hope to give them a glimpse at.

1. Modifying the behavior of functions by changing different parameters. These classes can be a place for “mathematics as tinkering.”
2. Detecting what answers make sense. I suppose there is some throwing out of extraneous solutions in Algebra I, but Algebra II is where you really need to have your guard up re: answers given you by formulas and algorithms.
3. Translating between different written forms of a function and its graph. To me, this is the largest. Two expressions that are equivalent may reveal completely different information about a function. For example, it is hard to see a parabola’s axis of symmetry if the function is written $f(x) = ax^2 + bx +c$. The process of first figuring out what quantity is important and then illuminating that quantity with algebraic techniques is probably more useful than any of those quantities themselves.

Now I suppose I have some talking points when we decide what to cut from Algebra II tomorrow!

For the second week of New Blogger Initiation, a response to:

It took me a long time to realize how lucky I’ve been in terms of my own math education in the following ways:

1. I cannot remember a time when I could read and there were not math and puzzle books in my house.
2. In elementary, middle, and high school, my parents and my school worked together to make sure I had a math class that was challenging and interesting for me.
3. I got to go to Math Camp!
4. College. Lots of math there.

However, it’s only over the past year or so I’ve become more aware of another (and perhaps) the largest advantage; I LOOK LIKE a math nerd. While my teenage self considered it the WORST THING EVAR that I was skinny, pimply, white, and male, no one ever thought it was weird I was on the math team in high school. Even now, when I tell barbers/bouncers/parents’ friends about what I do, a knowing nod is often the response. I figured this might make sense in the gun-slinging, okra-popping part of the world I’m from, but it seems to be about the same everywhere I’ve lived (Texas, Chicago, NYC).

Let’s call the male character in the comic is emblematic of a type of (often young) male that I will call a “math jerk.” Especially if you were a math major in college you know the type: vainglorious, sees math as his high and lonely Hemingway-esque destiny, and often kind of smelly.

A math jerk need not actually come out and say things like “girls suck at math” to qualify as a math jerk. There are a few reasons I think I (even narrowly) avoided becoming a math jerk.

1. Luck again: I always went to schools where, even though I was high-achieving, there were always other students with similar interests and abilities. This definitely cut down on the nerd resentment feelings I had to watch many of my college friends slowly shed.
2. Female math role models; two out of four of my math camp counselors were girls. My favorite professors in college and grad school were both women, both of whom are now the ones I am in closest contact with. Especially as someone who could never really see himself in a stereotypical male-male, avuncular master-eager apprentice, Jedi-Padawan relationship, my relationships with both of these awesome women and what I learned from them really carried me through much of my post-high school math career, both mathematically and personally.

One aspect of my new school that I’m excited about is that it usually swings about 60/40 girls to boys. It seems that this way there might be some of the benefits of an all-girls school and some of the benefits of a traditional mixed gender school. I’m looking forward to how it will play out!

Thank god for this New Blogger Initiation. Otherwise this would never get off the ground. Hopefully participating in this will achieve two goals:

1. Get me to write more.

2. Encourage me to publish more posts that are just drafts now. Many of the organizers of this have expressed surprise how many of us are “nervous/scared.” I might not go that far, but it’s definitely a little intimidating (even when invited and welcomed so warmly) to be around so many people who are clearly awesome.

Anyway, in response to:

Meetings are starting up. School is revving up. You are teeming with ideas (which is why we’re doing this Blogging Initiation now). What is one goal you have for the first week of school?

I am about to start at what seems like a great school. Everyone I’ve met who works there seems amazing and all reports are that kids (for the most part) are treated as adults and thus act as adults. One concern is that, somewhat in the interest of space, somewhat in the interest of simulating college, teachers have offices but no fixed rooms.  This leads to my:

Goal: Start to figure out what “mobile solutions” I can use to make my classes run more smoothly and create the classroom culture I want.

Maybe this is my own nerdiness shining through, but I feel a little sad when I see all the amazing #Made4Math projects filling my reader. Who wouldn’t want a painting of Felix Klein in their room? It’s also stressing me out a little because I feel I can’t really start figuring this stuff out until the year really gets going; at least in my school we have a week-long advisory workshop before regular classes start. Here are some of the aspects of my classroom for which  I want to figure out “mobile solutions” in the first week of school:

1. Norms, rules, and regulations in the classroom. If I had four walls of space, I would want everything from mathematical habits of mind to the bathroom policy clearly posted. That’s just the way my brain worked as a student. I am attempting to jump in the SBG deep end and want a way for that policy to always be accessible.
2. A space (real or figurative) for student work. I don’t know what the hallway situation is yet at my school re: student work on bulletin boards and the like. While that would be nice, even better would be a way of showcasing good mathematical work in the space of the classroom during normal class time. I want evaluation of past work to be part of the regular rhythm of class.
3. Little stuff: I really don’t want to deal with a pencil-less student in the middle of a college-level statistics class (apparently this can be an issue especially with the younger students). How do I not waste the relatively short math periods at my school having students rearrange the desks?

Some of this can be solved digitally; I am (incredibly) lucky that most of my students have computers at home, and they all have access to a SWEET lab at school, so things like my grading policy can go up to my site. That said, one of my biggest weaknesses teaching right now is focusing on what I’m saying at the expense of how (often) I’m saying it, so I’d like to figure out something that feels more “immediate” for students. If I were a student in my class feeling down about a C average, I might not feel very motivated to take time out of lunch to schlep to the 7th floor computer lab and check up on the grading policy.

My school will be open later this week, so hopefully I can go in and poke around. One reason this is one of my primary goals is that if I don’t make it a priority, I’m someone who will easily lapse into disorganization. Hope it works!