## Student Teaching

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 LogarithmsBig 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 $ax^2+bx+c$, 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!).