Thursday, January 26, 2006

The Future of Algebra II...

Well, the youngin's are all done their exams. Algebra II - as I expected, a class average of approximately a D. This will not happen next term. Many more phone calls to parents - to the point where the parents will (hopefully) start getting the kids to do their work if for no other reason than to keep me from calling.

Also, in the Do Nothing section, only 5 out of 20 kids have an average above 70. I wonder if the poor grades will have any effect on their future performance?

So far as lesson plans go, here's the deal:

  • I am ending Baker's Choice. We have not gone through the whole unit, though next year I would like to. We have covered through systems of inequalities, which is usually as far as level three gets. Tuesday we will have a wrap up and review, and Thursday we will have the test.
  • Next I will briefly cover systems of equations. They covered this ad nauseum in Alg I. I would like to present it as an application - give them a real world situation that they can attempt to solve any way they want, discuss the results, hope it leads us to one of the methods for solving systems of linear equations. The main methods we cover are graphing, substitution, and elimination (aka linear combination). I may cover Cramer's Rule, but then I would have to get into matrices, and I think I'd rather move on to functions.
  • So we will do functions after systems. I am having a little bit of a problem thinking of a way to present the concept of a function in a concrete manner. I like to introduce new concepts with this class by discussing actual concrete things, and so I need to come up with many examples for the kids to fool around with. After that, we'll talk about function notation and why function notation is important and/or useful.
  • Next, I am not certain if I will do quadratic functions or polynomial functions. I think I'd like to start with quadratic and then expand to polynomial. Again, I need to come up with concrete examples and real world applications. I want them to be as adept with quadratic functions as they are with linear. Factoring is going to be the major problem - they simply memorize (which they really aren't very good at) without understanding why. I think I am going to possibly do the quadratic functions unit using algebra tiles. If nothing else, we'll have fun with scissors.
  • I have also noticed, and may have already mentioned it here, that a big block of their misunderstanding things is actually a reading comprehension problem. They do not really understand the mathematical vocabulary, or directions. For example, on the midterm, many students attempted to solve an algebraic expression. Only equations and inequalities can be solved - expressions are simplified. I may do a mini unit on "The Language of Math", or may decide to make it a weekly feature, interspersing it within other units. One idea I have for them is to brainstorm all the mathematical terms they can think of, write them all on the board, define them in their own words, write an example of how they are used, relate them to the "non-math" definitions, make flashcards, etc. I would also like to do a lot more writing assignments - a lot of my students are terrible at expressing their ideas on paper. I believe they will have a much better understanding if they have to clearly write out their thoughts and ideas. I can also better see where the misunderstandings occur with open ended questions.

This is the rough plan -I'll have to see how it goes.


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