Over half-way done my first time teaching Algebra 2 in over 8 years (under block scheduling), and it’s amazing how much technology has changed many of my former approaches. Nearing a chapter on polynomial functions, I was somewhat dreading the experience. This is a pretty dry chapter…synthetic division, rational root theorem, complex conjugate roots…there’s a lot of rules and regulations here, and not much room for engagement. Here’s what I settled upon to avoid dry lectures, promote student ownership, and encourage a serious review of resources:
DIGITAL NOTEBOOKS FOR POLYNOMIALS
On day 1 of the unit, I gave students their assignment for the chapter, which you are welcome to download: Polynomial Notebooks. The link describes the assignment:
This chapter contains many landmark theorems and ideas for analyzing polynomial functions. Your job is to create a digital notebook of the ideas below, using a Google Document to house your information, and eventually share with the class. You may use online resources, or examples you create, to serve as examples for each idea. The goal of this document is to serve as a resource which demonstrates an understanding of the ideas, and which helps you study their meaning and usage.
To be honest, this did not start off as I expected, as my students were simply not accustomed to not being fed material. The idea of seeking outside resources, being able to weigh their merits, and summarize them for use was foreign. But our second day in the computer lab was fruitful, as students had great questions about the Intermediate Value Theorem and Descartes’ Rule of Signs; what was really fasicnating were the student attempts to think about the ideas in language which made sense to them: “Does this mean that…?”, “Does this example work here…”.
Not all class time was spent doing research. We started class with sythetic division problems done on boards around the room. Also, I developed 3 “food for thought” questions each day during the unit, which helped drive discussions.
- Name a polynomial with roots 2i and -3 (multiplicity 2).
- How many possible negative real zeroes does the following polynomial have?
- Show that polynomial given must have a real zero between 2 and 3.
Enjoy all of these Food for Thought questions: food_for_thought_daily_qs2
It’s also interesting how different groups have chosen to format their notebooks. While some are going through my list in a linear fashion, others have developed connections and examples to help make sense of the rules. One ambitious young man has developed an outline of the topics, rearranging the ideas, providing examples, and organizing links.
Tomorrow we will have a group quiz on the material, and I feel like this experience has helped students personalize their needs, and think about their gaps. I also feel more confident in the aiblity of the class to think about these polynomial rules as a whole, rathern than as a set of disconnected ideas. Hoping for a good day!