How I Teach Calculus: A Comedy (Logistics)
This post is a part a larger series documenting the changes I am making to my calculus course. My goals are to implement standards-based grading and to introduce genuine applications of the concepts being taught. I’m not suffering any delusions that any of this is all that ground-breaking, I just want to log the comedy that ensues:
Direct instruction in calculus takes a long time to do well, but assessing quickly and un-damningly really does a lot more.
- Homework is practice. It never counts towards grades. My class should be rigorous (and engaging) enough that the necessity of practice is self-evident to students.
- Do whatever it takes to make sure the kids own their learning. Even if that means resorting to direct instruction.
- Standards-Based Grading is necessary and difficult (but it replaces checking homework!)
- Do not obfuscate the beauty of math with fluff, but use as much context generation as is effective. (real-world examples, applications, whatever you call it in your neck of the woods.)
- Summative assessments occur rarely and are to get a final snap-shot a student’s abilities. They also serve as management tools and college-prep.
I wanted to explain what my course looks like. I realized that I’ve been giving you all a rose-colored-glasses view of my room by only writing about my most interesting lessons. So here’s the big picture. Here’s a pie chart detailing the amount of time spent on each instructional strategy/activity. This is based on average behaviors over several months:
From most time to least:
- Direct Instruction: That’s me at the board doing examples, having Socratic dialogue, and explaining stuff. We call it “Playing Notebook.”
- Investigations: Kids doing things that I feel generate context or further understanding. i.e.: What I’ve been writing about.
- Guided Practice: Kids doing problems assigned by me, generated by activites from 2, or from the book. Generally this consists of a lot of one-on-one time for me and students who are having difficulties with mechanics.
- Standards-Based Assessment: Quizzes, and other formative-y type things that tell me where kids are.
- Summative Assessments: Basically a midterm and final. These are spaced far apart, and the time in between these tests has really become much more productive due to formative behavior and SBG.
Are you shocked I spend so much time at the board? I am too, but it works for the kids, and they are getting it; it must be done!
The real meat and potatoes of what I do is in the standards-based assessment. Direct instruction in calculus takes a long time to do well, but assessing quickly and un-damningly really does a lot more. Here’s what my gradebook looks like to date (We’re on semesters, so we’re about half way through the spring semester, and just starting integration by substitution). Each grade is out of ten for each students, and can change depending on demonstration of knowledge:
|1 – Limit Definition|
|2 – Limits Algebra|
|3 – Graph of Derivative|
|4 – Quotient Rule|
|5 – Product Rule|
|6 – Chain Rule|
|7 – Power Rule|
|8 – Implicit Differentiation – find derivative|
|9 – Implicit Differentiation – rates of change|
|10 – Optimization Algebra|
|11 – Optimization|
|12 – Mixed Diff. Rules|
|13 – Critical Points|
|14 – Mean-Value Theorem|
|15 – Abs/Rel Min/Max|
|16 – Algebra Skills|
|17 – Increasing/Decreasing|
|18 – Concave Up/Down|
|Midterm – Differentiation|
|19 – Area by Limit-sum|