I didn’t get to do as much with this one as I would’ve liked, but I chose:

1.

Read another blogger’s post for the Math Blogging Initiation. Write a comment on their post.

Back in round 3, I almost responded to:

5. Statement: “Algebra 2 and Precalculus are a hodgepodge of ideas.” If you agree, what are some unifying and fundamental themes/ideas/concepts that can frame these courses so they can designed to be less of a mess and be something more coherent.

I’ve read a few of the responses to this one in my reader (but I’m getting hopelessly behind so I’m sure I’ve missed many more) and particularly like the responses by Bowditch’s Apprentice and Compact Spaces. I feel like the prompt is a reference to A Mathematician’s Lament by Paul Lockhart. I mostly agree with Lockhart’s main ideas and plan to share the opening analogy, a nightmarish method to teach music and painting, with pretty much all of my math classes in the future despite the fairly harsh criticism of the average/typical math education.

Here’s the table of contents for an Algebra 2 book from a major publisher (you won’t be able to tell which one; they’re all about the same):

- Expressions, Equations, and Inequalities
- Functions, Equations, and Graphs
- Linear Systems (includes a little bit of matrices despite the chapter title not mentioning it)
- Quadratic Functions and Equations
- Polynomials and Polynomial Functions
- Radical Functions and Rational Exponents (also includes some advanced function concepts: composition and inverses)
- Exponential and Logarithmic Functions
- Rational Functions
- Sequences and Series
- Quadratic Relations and Conic Sections
- Probability and Statistics
- Matrices (why isn’t the lone section of matrices from Ch. 3 included in here?)
- Periodic Functions and Trigonometry
- Trigonometric Identities and Equations

After chapter six, you may prefer some other shuffling of the chapters (I’d probably go something like 1-7, 9, 13, 11 as ‘musts’ for Common Core Algebra 2 … then use any remaining time on 10 {even though I don’t care much for conics for some reason}, 8, 12, 14 (harder trigonometry is definitely more ‘Pre-Calculus’ than ‘Algebra 2’ at that point in my opinion) in that order, but I would love to have this book as I’m currently book-less. I basically refuse to use our Algebra 2 book; it’s a ‘classic edition’ that was adopted like 7 years ago and was already old then – a teacher who was new to the district got to pick and chose what they knew they liked and then left two years later. He wanted ‘no tree frogs’ (his version of dogs in bandannas) but left us with a book that was completely visually unappealing (no color in the book except grayscale and lesson objectives in blue text) to use with students who are digital natives.

Every chapter title is a reference to the underlying theme of **sets, structures, relationships, and functions** in my opinion. Maybe I’m cheating and just being too broad with my unifying or fundamental ideas though. Obvious and not-as-obvious explanations (by the way, obvious is an extremely dangerous word in mathematics – I personally detest it almost as much as variations upon “the proof is left as an exercise for the reader” – thanks scumbag mathematics PhD):

- Chapter 1: the “algebra 1” they’ve probably forgotten – emphasize solution sets
- Chapter 2-8, 10, 13: basically have graph or function in the title … I’m only worrying about a lot of the conic section stuff because I’m theoretically legally obligated to include it in Algebra 2 – I really don’t feel like I ever really learned about ellipses and hyperbolas as the high school teachers never got to it and the college professors assumed I knew it (sad as it might be to admit that). I can complete the square but don’t know all the forms and focus business by heart.
- Chapter 9: A sequence is a function from the natural numbers to the terms of the sequence (in case you’ve forgotten)
- Chapter 11: Probability is a function of a random variable (the notation P(event) made so much more sense after I started teaching this stuff), and statistics is concerned with sets of data.
- Chapter 12: Matrices and vectors are probably the easiest algebraic structure for students to consider besides the real numbers (or subsets of the real numbers)
- Chapter 13: Trigonometric relationships abound … this is the chapter I personally would always run out of time before ever getting to in Algebra 2; too easy to put off until Pre-Calculus.

By the way, now that I’m basically finished with the post – I can merge my themes …. sets are a type of structure, and I was only including relationships to get at non-function conics. Thus, **Algebra is the study of structures and relationships. **Now I just need to check my work against a few more of the other newbie blog posts that I haven’t gotten to read yet …