State Framework vs CSET

1.  Examine the State Framework and CSET Overview.  Are there discrepancies?  If so, where?  In your teaching experience, how closely have you aligned to the standards?  Deviations?

As I'm comparing the State Framework and the CSET Overview for Mathematics, I see a couple of discrepancies in Algebra and Geometry.  On the Algebra portion of the CSET, we are expected to "know why the real and complex numbers are each a field, and that particular rings are not fields".  This topic is focused in college when you take 'Discrete Mathematics'.  On the Geometry part of the CSET, we must "know the variants of the Parallel Postulate produce non-Euclidean geometries".  In a high school Geometry course, we only cover the Euclidean Geometry aspect.  Non-Euclidean Geometry is more advanced and is addressed in college should you decide to be a math major.  Neither of these expectations are in the standards of the State Framework.  


I've taught Algebra 2 and Geometry for the past six years and I cover most of the standards that are addressed in the State Framework.  The only thing I don't get to cover in Algebra 2 is mathematical induction. In Geometry, some of the standards indicate that students need to prove statements/relationships, such as congruent triangles or Pythagorean Theorem. I don't necessarily derive the Pythagorean Theorem as I dive straight into concrete examples.  If numbers cannot be incorporated into the discussion, then I do spend the time proving the concept (i.e. congruent triangles).     


On the CSET, there is a section where we need to master Number Theory and the History of Mathematics.  Neither of these topics are really addressed in High School Math courses since these are considered college courses.  Therefore, these deviate from the State Framework.

2.  Using the State Framework and CSET Overview, you will examine three increments (Hint:  You have already examined one of the three years) and detail your gaps in subject knowledge.  Choose one or two and SPECIFICALLY state how you plan to bridge the gap.


I have already listed my gaps for Algebra 2 (see hard copy).  I mentioned that I wanted to have a deeper understanding on those topics.  By having that new found knowledge, I can explain those concepts better with ease and confidence.  


In Geometry, I want to expand my knowledge on circles.  For instance, why is pi 3.14?  I could do an activity on pi day (March 14th), in which the students will investigate the ratio of the diameter and circumference using a string and a circular object (i.e. pie).  If they have shown me that their result is in fact the constant 3.14, then they can eat the pie.  :)  


In Pre-calculus, I have some difficulties with the Trigonometric Formulas and Identities.  The main problem is retaining the set-up and where they came from.  If I can derive them or come up with a mnemonic device (preferably a song or a meaningful phrase), then I will learn and not forget it the next day.  Visual aids may be helpful as well.