Welcome to The Joy of Teaching... Algebra. Now that I'm back from visiting family over summer break, it's time to get serious about getting ready for next semester. In addition to a research project or two and prepping my tenure application, I'm working on redesigning my College Algebra course.
Picking a textbook
The first step of the redesign was picking a new textbook. That book is College Algebra: Real Mathematics, Real People, 6th Edition by Ron Larson. My previous text was College Algebra by Barnett, Ziegler, and Byleen. The Barnett text is good to prepare students for trigonometry and calculus, which completely missed the typical student in my class.
At Peru State College, students who do not test out of the math requirement in general education usually end up taking either College Algebra or Intermediate Algebra. Which means my College Algebra course is the only non-statistics course that many of our students take in college. And the Barnett text almost completely misses what I want my students to take out of college-level mathematics.
The ten-year test
One of the first questions I ask myself when designing a course is the Ten-Year Test[TM] question. Specifically, what do I hope students remember about my course in ten years? Now that I've finished my last degree about 8 years past, here are the results of some ten-year tests I've given myself.
Writing I - Pluralization (they vs. he and/or she)
Speech - Informative speech outline (Introduction, 3 main points, conclusion), indifferent feedback
Engineering Economics (Finance for you business types) - The time value of money, depreciation
Topology - Urysohn metrization theorem, open and closed sets
Human Factors - Radial and ulnar deviation, ischial tuberosity
In College Algebra, I want students to remember functions and mathematical modeling. But the Barnett text doesn't explicitly introduce functions until Chapter 3-- halfway into the semester. It is as though the ins and outs of operations on complex numbers are more important than actually establishing the intuition of a well-defined function. You won't win any contests guessing where I stand on that debate.
Planning the semester
As I've progressed in my career (this is year 8 of full-time college work, by the way), I've decided that I like having a somewhat detailed plan at the outset and deviating from it as needed. Kind of like the Miles Davis Quartet instead of Ornette Coleman-- except that those guys have actual talent.
At any rate, my first order of business was to draft the following weekly plan for the semester. Features include a non-standard amount of time between exams, two variable linear systems immediately after linear functions (mostly so I don't run out of time at the end), and a decision to hit only the bare bones of algebraic analysis of polynomials. The biggest weakness I see is the possibility of running up against the end of the semester right in the middle of logarithms which seem to require more sink-time than they might get. On the other hand, testing so soon after introducing the concept might help with that.
| Week | Sections | Notes |
| 1 | Chapter P | Group work at board, work through review exercises, p. 68 |
| 2 | 1.1-1.3 | Graphs, lines, functions |
| 3 | 1.4, 1.5 | Graphs of functions, transformations |
| 4 | 1.6, 1.7 | Operations on functions and inverses (may take more time) |
| 5 | Exam 1 | |
| 6 | 2.1-2.4 | Linear equations, graphical methods and complex numbers (All but 2.3 are simple, 2.2 and 2.3 will be done quickly). Quadratics (2.4) will probably not be done by next week |
| 7 | 2.5-2.7 | Maybe skip or abbreviate 2.5 Solve other functions algebraically, 2.6 is inequalities, 2.7 is linear models and scatterplots |
| 8 | 5.1, 5.2 | 2D linear equations |
| 9 | Exam 2 | |
| 10 | 3.1-3.3 | Polynomials and the Fundamental Theorem of Algebra |
| 11 | 3.4-3.6 | Rational functions, asymptotes and graphs |
| 12 | 4.1 | Exponential functions |
| 13 | Exam 3 | |
| 14 | 4.2, 4.3 | Logarithmic functions and properties of logs |
| 15 | 4.4, 4.5 | Solving exp and log equations, exp and log models |
| Final | Exam 4 |
Conclusion - Just like Speech class
So that's the starting point for the All-New College Algebra at Peru State College. As I add to my blog, I'll report on my own efforts and the results of working with Profs. Reed and Young whom I met at the Mathematics Inquiry Based Learning Workshop at Ann Arbor last May.
Thanks for reading, and remember the summer weather when you get snowed in in a few months.
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