I start student teaching this coming semester, starting January 3, 2010. I remain anxious about classroom management issues and whether I can translate my inner light into thoughtful and fun learning experiences for high school students.

I’ve started thinking about the curriculum for the Geometry and Algebra 2 classes that I will be teaching. I’ve found many good resources on the blogosphere, including stunning treatments of logarithms by Kate Nowak (Log Laws , Introducing Logs) and Dan Greene (Intro to Logarithms , Big L). I’ve integrated this into my own treatment using the idea of relations/relationships.

I’ve also pondered over the last few months the many ways to teach factoring. With a general quadratic trinomial , the *ac*-method usually results in numbers that are unnecessarily big. Instead, I start from separate prime factorizations of *a* and *c*. This builds on the idea of natural numbers being “bags” of prime numbers (the “Bag Model”). Just like the guess-and-check method, this one takes practice. It’s similar to the X-method but different. I haven’t settled on one form yet and have developed a filtering-based approach (only using prime factors indirectly to generate factor pairs and much like the X-method) and a “spin” approach that is visually appealing but not helpful. This got me into a digression on the combinatorics of “possible” factorizations based on the first and last terms, which turned out to be more complicated than I thought.

I’ve also been working on ways to make geometry relational (filled with relations between objects) to give students cognitive tools to attach geometry problems and proofs. On top of this, I am making Glenn Doman-style flashcards in reading and math for my young daughter and preparing to take the Praxis PLT (blech!).