# I’m teaching math!

I just found out yesterday that part of my teaching load will consist of two sections of Algebra II Honors. I’ll also be teaching two sections of Honors Physics with Kelly O’Shea, which I’m super excited about, but right now, my head is spinning a bit from the newness of teaching math.

Here’s a little background on the Algebra II Honors course at my new (old) school. Algebra II Honors is a course taken mostly by sophomores, after they’ve completed a Exeter-style problem solving course that focuses mostly of geometry in the 9th grade. Students in this course go on to take Precalculus Honors in the 11th grade, which is mostly differential calculus.

The description from the school website reads:

Honors Algebra 2 / Trigonometry

This course covers all of the topics from Algebra 2 in addition to a full treatment of trigonometry. While students consider the properties and applications of each of the major function families in isolation, significant time is also dedicated to the study of function composition and transformations. Prerequisites: Algebra 1 and Geometry, and departmental approval. Text: Larson et al., Algebra and Trigonometry.

One other good thing about teaching this math course is that its that most of our Honors Physics students are enrolled in it, so I’ll likely be teaching a number of my students in both math and physics, which will be a new and exciting experience.

I’m still gathering background information, but as I understand it, this course has historically been a pretty grueling and fast-paced race through functions and trig— a “tools” course, if you will. I’m also still finding out exactly how much leeway I’ll have in terms of approach to this course since I’ll be teaching it with one other teacher who is completely new to the school.

Finally, I’m most excited to be teaching this course so that I can feel like a more legitimate member of the math blogging/twitter community, and feel a bigger payoff for reading so many math blogs. Here are a few thoughts and questions flowing through my head at the moment:

**Standards Based Grading**: I really want to do SBG with this class, and I think it will work well since many students will already be enrolled in Honors Physics which will be SBG. I’m wondering if any Algebra II teachers out there have a good collection of standards you’ve used with Algebra II?**Developing a Theme**: Back in the beginning of the year, Dan Goldner asked a question that struck me even when I had nothing to do with math teaching: what’s the theme of Algebra II? The comments on this post are excellent, and Dan followed it up an excellent first stab: Relationships. Another interesting theme is MBP’s, How can we predict the future?**Writing**: I loved Sam’s post on including more writing in Math (and the ugliness that brings). I want to do this, and I’m wondering how to do it with SBG. Should writing be a separate skill for each topic/unit, or should it be folded into the standards so that you haven’t mastered a skill until you can answer problems that ask you to write about it instead of just doing computational work?**Pitfalls**: I imagine a course like Algebra II, is filled with pitfalls. My experience teaching physics has helped me to find many of the misconceptions students have about various physics concepts, and I now find myself not just trying to get students to avoid these, but instead, actively engage and build upon them. Where can I go for similar help in Algebra II?**Teaching for understanding**: Sue Van Hattum recently shared an excellent essay by Richard Skemp on the difference between relational and instrumental understanding. This article clearly articulates that learners can often operate with two completely different ideas of what it means to understand. Too often, students teachers can get into the trap of teaching procedural understanding how to manipulate a particular equation or follow an algorithm (instrumental understanding), and completely neglect any deeper understanding of why a particular algorithm works or its place in a larger framework of understanding (relational understanding). I see this all the time in physics, and am pretty well attuned to how to identify instrumental understanding in my students, but I imagine it’s going to take much more work on my part to do this as easily in mathematics.**Preparing for the future**: In a little more than a year after my students enter my classroom, they’ll be taking derivatives and powering their ways through related rates problems. What things can I do in my class to help make sure my students are best prepared for success in this curriculum?**Instilling a love for math**: As Kelly mentions below, Algebra II in general, and this course in particular are often seen as “weed-out” courses where students decide (or are told) that they are not “math people” and leave the class with a feeling math isn’t for them, or worse, that they can’t do it. This is something I want to avoid at all costs. I can certainly see SBG and coherent theme helping with this goal, as well as a bunch of other outside the class ideas like MArTH Maddness or even having the class start up a Saturday Math circle for local kids, but I think this is something that needs to be woven deeply into the structure of the curriculum as well.

That’s it for now. I’m sure I’m going to have many more posts as I begin to dive into preparing for this course, and I appreciate any wisdom you might be able to share to help guide me on this new adventure.

Another goal of the course might be to keep all of the students learning and loving math. From across the hall, it has looked like a weed out course for the honors track in recent years. For example: it is very rare for an Honors Physics student to have to take regular Chemistry the next year. It is not at all rare for an HAlgII student to have to take regular Precalculus (which is almost entirely the exact same course in terms of topics covered) the next year.

Thanks Kelly. You are right, and I modified my post to state this goal explicitly, and hope that we’ll be able to have conversations about this in the coming year.

Hihi, MATH! Exciting! Welcome!

Just two quick things! First, for the writing / connecting processes with understanding (I see them as the same thing), I made SBG skills that talked about understanding and explaining. So one way to do it is to fold them into the skills. I didn’t label them as “writing” questions, because sometimes I’d have some writing and something else to get at the concept. But mainly, it would be writing.

As for SBG skill lists, there are a few out there for Alg II. I didn’t do SBG for Alg II, so I don’t have one. But I thought since you’re starting from scratch, you might find our curriculum outlines (which can be made into SBG lists) useful:

Alg II: http://fc.packer.edu/~ljoseph/index_files/Algebra%20II%20Curriculum%20Outline.pdf

Alg II Advanced: http://fc.packer.edu/~ljoseph/index_files/Algebra%20II%20A%20Curriculum%20Outline.pdf

Precalc: http://fc.packer.edu/~ljoseph/index_files/Precalculus%20A%20Curriculum%20Outline.pdf

Precalc Advanced: http://fc.packer.edu/~ljoseph/index_files/Precalculus%20Curriculum%20Outline.pdf

Always,

Sam

Sam,

Thank you so much—this is a huge help.

As you’ve pointed out, one of the biggest problems with algebra 2 (and precalculus, for that matter) is coherence. I’ve taught algebra 2 with trigonometry for several years, and I’ve come to believe that there are at least three possible approaches to the course:

1) The traditional one, where you run the kids through a laundry list of different function types, perhaps tying them together with the concept of transformations.

2) The modeling approach, where you use data collection, experiments, whatever, to motivate the existence and utility of different function families.

3) The algebra approach, which I’m only beginning to work out, but where you focus on common strategies for solving problems that may involve different types of functions. A simple example of this is to consider the similarities and differences between the solutions to 2x^2 + 5x – 3 = 0, 2(sin x)^2 + 5(sin x) – 3 = 0, and 2e^2x + 5e^x – 3 = 0. This approach would incorporate not just analytical methods of solution (factoring, rational root theorem, etc.), but also matrix methods of solving systems (which could lead nicely into a deeper discussion with honors students of vectors & vector spaces), as well as computer-based methods of solution (e.g.,Mathematica, Sage, Octave) and their benefits & downsides.

The first approach above doesn’t lend itself well to a theme; I’d argue that the last two are more thematically coherent and more likely to “teach for understanding” than the first. I think putting writing into your students’ work will be valuable, but (like you say) difficult to pull off. With your teaching physics and mathematics, you’ll have a great opportunity to incorporate plenty of modeling (and therefore writing) into your algebra 2 class if you wish.

I’m not knowledgeable enough about SBG to weigh in, but I’m curious to hear how it works for you!

Thanks Mike. You’ve pointed out a very interesting connection for me connecting modeling of function families and algebra strategies seems like a lofty, but very worthwhile goal.

Excellent! Welcome to the club — I’ll be teaching Alg. 2 next year as well, so my colleagues and I will be planning in earnest this summer. I’m jealous that your students have already had a problem solving course. My calc students this year had trouble modeling with the A2 functions and they had problems solving A2 equations as an intermediate step in a larger pursuit. So we’ll probably focus on covering fewer tools and giving more opportunities to use them.

Oh: here’s our live course outline. We’re just starting but it will evolve over the summer: Alg2

I’ve got two sections of Alg2 next year, so I’m looking forward to seeing what you come up with.

By the way, have you taken a close look at the Park School’s Math curriculum? There’s some wonderful stuff there.

Thanks Michael. I have seen Park’s math curriculum, and blogged about it with effusive praise, but I haven’t done a deep dive into it to really explore it. I know if I were starting a 9-12 math curriculum from scratch, it would be my starting point, and I’m very curious as how much the habits approach can be brought into our pre-existing curriculum and structure.

I also think the theme idea is really important. I had a student this past year (one of my absolute top Honors Physics kids this past year, but one of the bottom Honors Alg II kids) who often talked to me about the differences between what we were doing in physics class vs math class. She noted that we always started with an experiment or observation in physics, then built our understanding around it. She couldn’t find the same touchstones in her math class. She also said that she knew she was doing poorly in math because she kept getting bad grades on tests and homework, but that she didn’t know what she was doing poorly, so she didn’t know what to do next to fix it.

One of the most troubling things she said to me this year was (something similar to), “I don’t know how I’m going to make through two more years of math if I’m going to be lectured to every day.”

This is very interesting, and great food for thought as I start to envision this course. I’m also putting a link to your outstanding comment on my question on your post here as well for my future reference.

Could you “combine” sections and teach a problem-based learning course that integrates the content of Honors Physics with the content of Algebra II? Seems the real-world contexts combine the two “distinct disciplines” anyway – school might be only place they live separated.

Seems St. Gregory may have experimented with something similar in combined courses.

I’ve been asked to teach math a few times, and so far I’ve steered away from it. I can’t imagine bringing in the same passion. But recently I’ve been thinking of what can be done, if they let you *lol*. Since it seems that most your students will be in the honors physics classes as well, I’d propose creating a strong link between them. In my view of the world, mathematicians solve equations, physicists interpret them (starting with giving them units!). There has to be a middle ground, doing both! Sorta like Bo Adams points out above. Also, a great opportunity to use the same symbols in both classes.

This is the one math course that I’ve ever been allowed to teach (hah!), and I can say that creating yearlong coherence will probably be your biggest challenge. For me, my motto would be (paraphrasing Bill Clinton), “It’s the functions, stupid.” Maybe it’s because I’m a CS teacher at heart and the concept of functions just makes sense, but I feel like Algebra II can be couched in terms of what happens when you apply a certain function to a given domain of data. What would this quadratic function do? How about this exponential function? Finding real-world applications also seems to be an essential component of the course.

For me, Algebra II always seemed to be like that second movie in a trilogy — you knew it was the weakest of the three, but it had a bunch of important plot points that you had to get through in order for the end (calculus) to make sense. I’m sure you’ll be able to put a better spin on it, though. Why not try to incorporate some of your awesome physics stuff?