- I'm teaching at a private school so technically, we don't have to do the Regents but our parents want us to offer Regents prep courses.
- The private school has its own curriculum imported from its California model that isn't correlated either to New York State or to the Common Core.
- We are restricted to 50 total sessions with the students per year rather than the 150 classroom hours you normally get at public school. If we need to go over 50, the parents have to pay more so we try very hard not to do that.
- I love all the ideas the blogging community has for geometry, but everyone seems to be pushing Common Core and the geometry Regents exam doesn't seem to be there yet.
- I have my own inclinations for teaching geometry that I'm having trouble shoving to the side to adhere to any standards.
- Two months ago my boss asked me to look at our boxed curriculum from California and compare it to the New York State Standards and the Regents exam and make sure they were aligned. I discovered that they couldn't be more different and she has asked me to come up with a Regents friendly curriculum map.

I LOVE the way Drawing on Math has organized her geometry class, but I'm really torn. I was also very inclined to do parallel lines and transverals right at the beginning but a Regents aligned textbook, AMSCO-Geometry, puts it more than half-way through the course. Why did they make this decision? Is there some profound reason students should do congruent triangles and transformations first? They've split up all the points of concurrency in triangles into different chapters too, whereas I was inclined to put them all together. Which way is best? A lot of the organization seems strange to me, but I've only learned geometry through teaching it over the past two years (I was skipped through it in High School and my college didn't offer any college level geometry courses) and I'm unsure whether or not to trust myself on what seems logical to me vs. how the book organizes material.

In the same Drawing on Math post, she also mentions scrapping most of the logic unit and only teaching converses. But the NYS standards have LOTS of logic material including converses, negations, contrapositives, direct and indirect proofs, truth tables and Law of Detachment. BUT, combing through old Regents exams reveals that they only ever seem to ask questions about negations, and the Common Core doesn't have much logic at all... Yet I love teaching it and when I got to college and took college level math courses, the fact that I'd been skipped through geometry became a real handicap in the more advanced proof based classes because I'd never been exposed to logic before. So I'm inclined to teach logic because knowing just high school level geo-logic would have really helped me.

*BUT*we only have 50 sessions and I can't waste time on material not on the Regents exam.*BUT*everyone's saying the Common Core is better anyway so shouldn't I align our curriculum to the Common core and not to a standardized test?*BUT*our kids*need*to pass the Regents because our parents care about it so much.
My heart tells me that I should just teach it in a way that feels right to me and if the kids really internalize the material they will pass the Regents. Yet the Regents has

[12/20/12 edited to add the following paragraph] I'm still struggling with the geo curriculum and I decided to trust the book and do triangles before parallel lines and transverals but I'm running into difficulties. If you don't do parallel lines and transversals first, then you can't do the proof that there are 180 degrees in a triangle (or at least you can't do my favorite one) and trying to do all the triangle stuff without this is pretty crippling. In fact talking about angles at all becomes a little sticky. We're supposed to do exterior angles in the triangle unit, but how do you prove any of the exterior angle theorems without knowing there are 180 degrees in a triangle? And what about AAS triangle congruence? They've thrown that in much later in the course 3 units after doing all the other triangle congruence theorems. I wish textbooks provided a justification for how they organize their content because I always start by trying to follow a book (they know best right? Tons of experts and trials in classrooms and thousands of dollars.) and then

*such*specific types of questions covering specific topics that I'm worried if I don't teach them with the Regents in mind, they'll get to the exam and it will use vocabulary they're not used to and ask types of questions we haven't covered. I wish the State would just trust me a little. I can help the students navigate this material but I want to let them enjoy it and I want to let them explore and I feel like I can't do that with this ticking bomb hanging over my head. I guess I just have to try something and hope. Teaching is about experimenting however nervous this makes me. I hate the idea of an experiment failing at the detriment to a student's enjoyment of math. But we learn by making mistakes right?[12/20/12 edited to add the following paragraph] I'm still struggling with the geo curriculum and I decided to trust the book and do triangles before parallel lines and transverals but I'm running into difficulties. If you don't do parallel lines and transversals first, then you can't do the proof that there are 180 degrees in a triangle (or at least you can't do my favorite one) and trying to do all the triangle stuff without this is pretty crippling. In fact talking about angles at all becomes a little sticky. We're supposed to do exterior angles in the triangle unit, but how do you prove any of the exterior angle theorems without knowing there are 180 degrees in a triangle? And what about AAS triangle congruence? They've thrown that in much later in the course 3 units after doing all the other triangle congruence theorems. I wish textbooks provided a justification for how they organize their content because I always start by trying to follow a book (they know best right? Tons of experts and trials in classrooms and thousands of dollars.) and then

*always*scrap the book a quarter of the way in because their sequencing just doesn't make sense to me. I wish I could squelch my internal sense of logic and just trust a textbook... my life would be so much easier.
I'm glad you like what I've been working on! Luckily MA standards weren't radically different from CCSS, but this transition period is rough since we are all changing at every level. Two years of teaching geometry is all I have as well (plus I don't like geometry in high school), trust yourself. As long as you touch upon everything on the regents and teach reasoning skills your kids will be good to go.

ReplyDeleteThank you for the encouragement! I've been so inspired by your geometry program, but I don't feel like I have the freedom to implement something similar. I agree with you though, I need to stay focused on reasoning and hopefully the kids will then have the skills they need to tackle problems they've never seen before. I can't teach them cookie cutter techniques for every type of problem. I need to help them develop tools that are flexible and they can use creatively. I know this and this is how I've always taught algebra but geometry has such a huge wealth of content knowledge that I feel a little overwhelmed. I'm worried that no matter how good they are at reasoning, if they can't remember what an incenter is they can't do that problem and so many of the problems rely on knowing a key piece of knowledge or a key vocab word.

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