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!).

software facilities for teaching mathematics

Two stories caught my imagination today.  One is a geometry program akin to something like Geometer’s Sketchpad, KIG (for KDE Interactive Geometry), described by an article in Linux Journal.  The KDE EDU project has a number of great programs available for education.

The other is an idea for talking about averages, expectation, and probability.  It uses the TV show “Deal or no Deal” as backdrop, trying to evaluate whether or not to accept the Banker’s deal.  I got the idea while reading an issue of Linux Journal with an article by Dave Taylor (subscription required).  To my taste the implementation in shell script is a might obscure.  I would probably use Python to craft the solution while students described how to calculate the various quantities, as the notation appears (or could be made to appear with a few prior function definitions) more mathematical.  The program would ask which boxes we opened and progressively give updated statistics on the likelihood of winning it big.

Published in: on 2009.06.23 at 12:48  Comments (1)  
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