## Sunday, August 26, 2012

### That didn't take long.

I'm already toying with a tweak to the sequence.

My fear is that the unit on linear equations (slope, graphing, solving, etc) is going to be the hardest to implement with a true modeling approach. If that's the case, I don't want to disrupt any momentum I build in the first unit by deviating from the discover & discuss method before returning to it when we finish linear equations. So why not just switch Units 1 & 2 and make linear equations first?

It should serve as a (hopefully) easy introduction to my class as it's mostly a review of 9th grade algebra. It will give me time to get to know my class and set expectations for discussion and I can already see bridging from lines -> segments/angles (where I couldn't see a natural transition for the reverse).

On that note, does anyone teach slope / linear equations from a student centered perspective?

## Saturday, August 25, 2012

### The (tentative) sequence

I think it goes without saying that when you create a new curriculum from scratch by yourself, it's probably going to be a rough draft through June.

The overarching theme: start with a the most specific idea and build upwards toward the general - kinda like how physics starts with constant velocity and builds towards acceleration. I feel that the traditional geometry curriculum does exactly the opposite; it starts with the very general (and simple) and eventually leads toward the specific. I don't know if there's evidence that one approach is better than the other, but I'm personally a bigger fan of specific -> general.

In any event, here goes - I'll try to update links to unit overviews as they're completed. I've also tried to prepare by writing necessary worksheets for the first few units and list the standards that will be covered in each unit.

1. Linear Equations
• Types of slope
• Slope-intercept form of a line
• Parallel, Perpendicular, & Oblique lines
• Solving equations algebraically & graphically
2. Segments & Angles (the basics)
• Definitions of measure (length & area)
• Ruler & Angle postulates
• Segment & Angle Addition postulates
• Angle classification
• Angle pairs
3. Squares
• Relationship between sides & diagonals/area/perimeter
• Midpoint
• Angle bisectors
4. Right Triangles
• Isosceles right triangles (from squares)
• Triangle Sum Theorem
• Area & perimeter
• Pythagorean Theorem / distance formula
• 30/60/90 right triangles
5. Ratios & Proportions
• Similar triangles
• Trigonometric ratios
6. Rectangles
• Area & perimeter
• Angles formed by parallel lines & transversal
• Triangle congruence & corresponding pieces
• Parallelograms
• Rhombus
• Trapezoid
• Kites
8. Polygons
• Interior & exterior angles
• Area & perimeter of regular polygons
9. Circles
10. Surface Area & Volume
11. Symmetry & Transformations
12. Special Segments in Triangles
With the traditional (lecture based) approach, I covered these same topics, just in a different order (based on the textbook). Based on past pacing, I've never been able to cover Symmetry & Transformations (so I wasn't terribly sure where it should fit), and I'm not a big fan of Special Segments in Triangles, which is why I threw it in at the bottom.

### My big idea

2012 will be my 5th year teaching physics, astronomy, and geometry, my 2nd year utilizing the modeling curriculum in physics, and my 2nd year implementing Standards-Based Grading in both physics and geometry.

I attended the Modeling: Mechanics workshop in MI in the summer of 2011 and immediately fell in love. One of the first thoughts I had was "how could I implement this in my other classes?" Modeling is all about student discovery and geometry struck me as perfectly suited for such an approach, but I got bogged down in learning modeling and dealing with SBG, so I tabled that thought for the year.

This summer I went to ASU and attended the Modeling: E&M workshop which was incredible (huge thanks to instructor Michael Crofton for his hard work as well as the entire ASU staff). The only downside was that I was stuck in the desert with no car for 3 weeks, which means I had a lot of downtime. So I revisited the idea of Modeling: Geometry and jotted down some thoughts and outlined a basic framework. I've done a fair bit of Googling, and I've talked to a lot of people, but I can't find anyone who's already tried to merge the modeling curriculum with math of any kind (please correct me if I'm wrong - I'd love some help on this).

Basic premise: Most topics in a high school geometry course can be learned through discovery and discussion without much guidance from teachers in much the same way that Modeling: Physics is set up.

I've spent the summer of 2012 formalizing my plan and putting in enough of the foundation to force me to jump in. I plan on posting my plans, thoughts, and reflections here so that hopefully others will find some merit in the idea and help carry it forward.