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!
After the activity, a whole-class discussion is held to talk about Hallway Bowling as an experiment. What are we trying to prove? How does our activity provide data for the experiment? Where is the randomization? What could be done to improve the design? Here, we are looking to encourage “matched-pairs thinking”; where all subjects are exposed to both treatments (rolling with dominant and non-dominant hands), and we are interested in those differences. We can also consider blocking here if we feel that males and females may be effected diffferently by the treatments. We can also revisit the data later when we look at hypothesis testing procedures.
This week’s assignment in the 8-week Explore the MathTwitterBlogosphere project is to provide “A Day in The Life” of a math teacher. It’s Monday morning, and here is my day….
I had a conversation with a homeroom student who was excited to travel into the city to visit the Philly-famous Reading Terminal Market. I encouraged her to visit the Amish people and their fine foods, but the student admitted an irrational fear of the Amish folks. This led to an assignment from me: have a meaningful conversation with an Amish person, and report out to the homeroom. I’m happy to share that Kianna talked to a few Amish people, found them “fun”, and is no longer scared of them. A good start to the morning.
9:00, Algebra 2 – Today is test review day for exponential and log functions. What I like to do on days like these is to post problems through the room, let students wander, have conversations, work through problems, and ask questions. What I don’t want to have happen is to have students working quietly and isolated. Many students have the same needs and misconceptions; I strive to create an environment where those questions bubble to the surface, and it is OK to need help. At the end of class, we did a quick review of polynomial division as a table-setter for the next unit. I love having students write on desks, as I can wander around the class and assess work. It’s a great strategy for facilitating group discussion; just have a bottle of Formula 409 handy.
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