Julie (@jreulbach) is awesome, but I’m pretty sure anyone reading this was already well aware of that fact, and has gathered all of the Algebra 2 teachers of the internet to join together in a blogging initiative. While I’m not teaching Algebra 2 this year (I had to give it up in order to get a first period planning in order to have a little more flexibility in the mornings with getting my 6 month old daughter to daycare), I am teaching Advanced Functions and Modeling. A course which is currently Algebra 2 version 2.0 for most portions of the curriculum. There is little to no new information presented to students, and most of the current design has a computational focus instead of an interpreting and analyzing focus. As the course is designed AFM is meant for those students who need a math beyond Algebra 2, in order to be college competitive, but who aren’t ready for the rigor of PreCalculus.
AFM’s current course description:
Advanced Functions and Modeling is designed to further strengthen algebraic manipulation and graphing skills while introducing a selection of other topics and application. Additional topics may include trigonometric functions, sequences and series, and probability. Concepts will be applied to real-world situations and technology will be used regularly. Prerequisite: Algebra II
I inherited this course description and a problem set/note packet for the course from my coworkers. While I am not a huge fan of the layout, mostly because it follows the Alg 2 curriculum very closely, I have just now had time/energy to try a re-write.
The old curriculum mapping went:
- Introduction to Statistics (measures of center, spread, comparing data, and normal curves)
- Linear Functions
- Quadratic Functions
- Exponential and Logarithmic Properties and Functions
- Sequences and Series
- Trigonometry (Triangles and Functions)
Given that students I teach in AFM are the same students who struggled with Algebra 2, this ordering has never felt 100% right to me. If they struggled with Algebra 2 material when it was in Algebra 2 is it really effective to just re-package the same content in a new course and call it AFM? I understand the need for students developing an actual understanding of key material from Algebra 2, especially if we want them to go on and be successful in any math classes they may take in college, but I wasn’t okay with presenting the material in the same way they had seen it before. As compartmentalized chunks of math that are always taught in the “here’s the rule”, “now here’s the practice”,”now here’s the ‘real world’ applications” structure. After much #MTBoS lurking during the first 6 months of my daughter’s life/my stent as a Stay at Home Mom, I think I’ve found a sequencing that I can finally support. Shout outs to Mary Bourassa’s blog for giving me the spiraling content idea.
- Unit 1: Introductions to Functions— functions vs relations, function notation, domain and range, family or functions.
- Unit 2: Introduction to Modeling— a mixture of Linear, Quadratic, and Exponential functions. The focus will be on justifying the choice of a function as a model for a given situation (from a table, graph of points, or verbal description)
- Unit 3: Introduction to Statistics–Reading tables (%s), Measures of Center, 1 Variable statistics and data visuals, Normal Curves and z-scores, and for the first spiral: Regression (linear, quadratic, and exponential).
- Unit 4: Transformations of Functions— Spiral from Unit 1 with a lot of Domain and Range descriptions. I know I’ll do a few Marbleslides in here.
- Unit 5: Sequences and Series— I will start of with Visual Patterns as an informal “find the pattern that works and prove it” exercise, and then move into a more formal definitions of arithmetic and geometric sequences (spiral from Unit 2 with Linear an Exponential)
- Unit 6: Geometry— I’m still in the brainstorming mode for this one, but I know I want right triangle trig in addition to some review from their Geometry course. I have been told by the SAT prep teacher that the geometry sections of the SAT are more rigorous than in the past and that my kiddos will need the refresher. I would like to bring in some of the IB Math problems I did at my old school, they were really good for getting students to think outside of the box and talk about the math.
- Unit 7: Trig Functions— Focus on using information about a situation to create a function to model the situation (max/min values and period), spiral with the transformations unit.
- Unit 8: Financial Math— A good portion of my students are seniors who go straight to a dance company, music chamber/conservatory, or the work force, instead of college. So they need a crash course in how to ‘Adult.’ I have talked about credit cards, monthly budgeting, leasing-vs-buying a car among other ‘adulting’ topics.
So far I’ve only made it through actually planning half of the first unit. I’m trying my best to move away from the “I do, we do, you do” style of teaching of the materials I inherited. Last year I didn’t change them because I knew I’d be out for half the year on maternity leave, I didn’t want to rock the boat and cause a headache for my maternity leave sub.So, I fell into the habit of drill and kill style instruction. I hated it. The students hated it. I don’t think they had any ‘ah-hah’ moments with the curriculum, and most importantly, I don’t think I changed their mind on math. Math was still hard. Math was still boring. And Math is nothing more than a combination of formulas you’re supposed to remember.
That is not the math classroom I want. In the past I have taken great pride in taking the students who hate math, and through modeling and problem solving activities, I slowly changed their hatred to mild distaste. Which for the time span of one school year, I’ll consider a victory. I, for selfish reasons, shifted my focus in my classroom and I need to get back on track. So I promised myself I’d do better by my students this year. I’d make worksheets/kill and drill practice a dirty word in my instructional vocabulary. I need to get back to my instructional happy zone: using math to ponder our world, model things we see happening, and answer questions we have about our surroundings.
My goal for this year is to have one day of instruction, some of which will be self guided, discovery style learning, and other parts will have to be direct instruction because I haven’t found a better alternative yet (let me know if you have one, until then part of my instruction will have to be the well timed curse word in my dirty word worksheet world). The instructional day will be followed by hands on practice, some sort of combination of Desmos activities, group activities, and 3-act problems/labs. I’ve found a bunch of interesting problems thanks to #MTBoS that I plan on using and/or altering to suit my needs to achieve this goal. Fingers crossed I can help improve my potty mouth. Both figuratively speaking with the change in instructional practices, and literally. I’m not cut out to be a stay at home mom, and my boredom did lend to a rediscovery of my love for colorful language…I need to work on that s*@#t before my daughter starts to pick up words…