So, long story short, here I am sitting in Lawrenceville, NJ, which houses the Klingenstein program. The first few days were pretty hectic, but I think it's calming down. Thought I'd take a few minutes to jot down some of the things I've been learning/thinking about since my arrival at the institute.
1. Math-specific stuff: The old way of organizing topics around content chapters needs to be replaced by organization around themes, to facilitate the development of effective schema in the students' minds (which increases retention and all that good stuff). I am obviously a newbie at this, but I'll try to organize Geometry units to illustrate these. I'm not quite fleshing out everything.
- BIG IDEA: Measurement
--> Dimensions and quantities
--> Measurement methods
--> Indirect measurements such as Pyth Theorem and similarity ratios
- BIG IDEA: Conjecturing
--> Layered math formalism (definitions --> postulates --> theorems)
--> Making conjectures about circles and triangles and angles inside parallel lines
--> Multi-step solving of diagrams using various known pieces of info
- BIG IDEA: Multiple Representations
--> Coordinate plane concepts and skills
- BIG IDEA: Transformations
--> Both inside/outside of coordinate plane
--> On objects as well as "functions"
- BIG IDEA: Proofs
--> Basic postulates
--> How do we prioritize info?
--> Formal Geometric proofs (both algebraic and geometric)
--> Meta-cognition: How do we assess a proof/argument?
- BIG IDEA: Spatial Visualization
--> Proportional reasoning
--> 3-D to 2-D, or 2-D to 3-D
--> irregular area/perimeter/volume/surface area
Thoughts? That's my first stab at re-organizing the topics of a course based on this idea.
2. Small changes in the classroom can make big impacts on student learning. Things I am going to try this fall: slowing it down (wait time/questioning) and being positive/encouraging/empathetic. I'm going to ask a colleague to observe/evaluate me on my goals and to hold me accountable.
3. We do (individually) have the power to substantially affect school culture. One Klingenstein alum once started the first Gay-Straight Alliance (I forget the name) as his year-long project. Now there are GSAs all over the country, in private and public schools, and they help to foster awareness and compassion. I need to believe in the power I have to change the things that I think are problematic in the school.
Ok - dinner time. :) Ciao!