Sunday, June 25, 2006

Summer Geometry

Tomorrow starts our very first summer Geometry course.

All of our incoming students take Algebra 1 as freshmen (even though many have "passed" already in 8th grade, the majority don't know anything about Algebra). For our students who are better or more interested in math, this poses a problem, as it does not give them enough time to get to Calculus by their senior year.

Our original sequence was the standard Algebra 1, Geometry, Algebra 2, Precalculus. To get to Calculus as seniors, motivated students were able to take Algebra 2 as an intensive, 5-week course after their sophomore year, and Precalculus as juniors. I taught the Calculus class for the first two years, and it was extremely difficult, because the students were definitely underprepared in their algebra skills, and much of our time was spent relearning Algebra concepts.

This year, we have switched the sequence to (what we think is a more logical) Algebra 1, Algebra 2, Geometry, Precalculus. The summer class then becomes Geometry. This gives students an entire year to work on their Algebra 2 skills instead of a ridiculously short 5 weeks. Of course, the same thing will happen in Geometry, but our feeling is that there are significantly fewer skills in Geometry that are needed to be successful at higher level math. It's hard to make these sacrifices, but we have to do so all the time.

So, that being said, tomorrow I will start teaching the summer Geometry class. I've never taught Geometry at all, and I have to figure out how to boil down the essentials into 5 weeks of daily 5-hour classes. (Whatever else happens, I must say I'm impressed with the students who have elected to spend their vacation taking this class! We talk about ganas a lot at DCP, and these kids really exemplify that ideal!)

What successes / failures have you had (or heard of) in trying to bring low skilled, underserved, or underachieving students to higher levels of math?


Robert said...

"Our feeling is that there are significantly fewer skills in Geometry that are needed to be successful at higher level math."

I'd say you're right about that. It's not that the skills coming out of geometry are less *important*, but geometry tends to be more about the repeated application of a few central skills (mainly logic and structured problem solving) to a lot of different contexts. It goes deep on a few very big skills versus going only somewhat deep on a whole lot of skills.

I've taught geometry (on the college junior/senior level) for 8 years now and it's consistently one of the most fun courses I teach. I think it's because it's very uncomplicated and students can jump right in to very interesting problems. Enjoy!

Dan Greene said...

Robert, thanks for your response. I am right now gearing up on the use of Sketchpad, which seems to be quite an amazing program, though some of the more advanced features are hard to figure out. We just got a site license, and I am excited to start working with it. Can you recommend any sites that have good sample .gsp files (especially more high school stuff - what I have seen has mainly been college level) or lesson activities? How much do you use software in your Geometry courses?

Anonymous said...

This may be an off-the-wall idea,but the Quilt Museum in downtown San Jose might make a good field trip, if you have the time. My sister is a quilter and says there's lots of geometry involved in quilt design. If it's not doable in the summer, given your schedule, it might work during the school year. I forget where the museum is located, but it's right downtown, near the art museum, I think.

-- Joanne Jacobs

Darren said...

Judging from the comments of the geometry teachers at my school, that course (one I'd *never* want to teach) creates as many failures as Algebra I does. Then again, we teach it as a very "proof-intensive" course.

There's merit to your schedule juggling. Algebra I and II lend themselves to higher math, whereas Geometry is--well, it's not a dead-end, but it certainly isn't as directly related to trig and calculus as Algebra I and II are.

I hope you'll post an update at the end of the summer.

Robert said...

I am a big fan of sketchpad and I use it VERY heavily in my Geometry class, and in other classes as well like Calculus. In fact, this coming fall, the geometry class will consist exclusively of student-driven Sketchpad projects. I ran an independent study with a math education major who wanted to do more geometry, so I basically gave him 14 Sketchpad projects and had him do one per week. He ended up doing about 20 of them, some of which he invented, just out of sheer fun and curiosity. He was student-teaching at the time too and got to wow his kids and supervisors with his Sketchpad skills. AND... he learned a ton of really good geometry in the process of solving the project problems. So I am redoing the entire course to replicate his experience. No textbooks (maybe... see my blog tomorrow about that), just Sketchpad and laptops.

As for resources, I'd say go to and to a search on "geometry" or "Sketchpad" and see what comes up. I've been meaning to add a bunch of bookmarks for geometry stuff to my own folder, so I can make those public if you want.

Be sure to check out the website of the (now-defunct) Geometry Center at the University of Minnesota:

Robert said...

Just to follow up, I'm keeping my geometry links at the folder:

Right now there are a measley three links in the folder, but I expect that to increase rapidly this week as I am taking the next week to start prepping for fall courses. So check back regularly or sign up for the RSS feed.

There are more math and teaching related links there too; replace "geometry" in teh URL with "teaching" or "math" or "mathematics". Or just go to for the whole sordid list.

Mike G said...

Great blog thus far!

Dan Greene said...

Thanks, Mike. Keep checking in, and if you know anyone who would be intersted in discussing these issues, please foward the link!

Also, if anyone has a specific topic that they want me to post on, just let me know.

Cal Lanier said...

If you've got kids who don't know Algebra in 9th grade, why so much focus on stuffing Calculus down their throats before college? You're making the same mistake that got them into this situation. They need Geometry on their report card, so by god, you'll put geometry on their report card. Never mind whether they actually know geometry.

Why not just teach them Algebra again, and then go through the sequence that has them in Trig as seniors? This is by no means uncommon and doesn't doom kids to inferior colleges. If you have any extraordinarily gifted kids, you can explore legitimate summer courses, rather than ones you cobbled together to fill a mark on their transcripts.

College admissions tests focus heavily on geometry. So if you're bent on doing this, then do be sure to give them the material they need to do well on the SAT or ACT.

Dan Greene said...

If you've got kids who don't know Algebra in 9th grade, why so much focus on stuffing Calculus down their throats before college? You're making the same mistake that got them into this situation. They need Geometry on their report card, so by god, you'll put geometry on their report card. Never mind whether they actually know geometry.

I should be more clear. The students who are taking the summer Geometry course are doing so because they wanted to, not because we are forcing them to. They have committed themselves to the idea of pushing themselves in math as hard as they can, to make up for all the wasted time in their earlier education (for whatever the reason). Also, these students only represent about 15 - 20 % of our student body, and they are primarily the ones who are coming in with higher math skills than the rest (and passed Algebra 1 as freshmen the first time around). The majority of our students don't even make it to precalculus - most have to repeat at least one class - usually Algebra 1, because their skills are so poor. The typical DCP freshman takes Numeracy and Algebra 1. Of those, about 50-60% fail Algebra 1 and need to take it over the summer. Of those, about 50% fail again. So we have many sophomores in Algebra 1, who also take a second year of Numeracy (if their foundation skills is what is holding them back, rather than effort and motivation). We hold the line quite rigidly - if they don't pass by the end of sophomore summer, they must repeat the year. This is because all of our students must pass Algebra 1, Algebra 2, and Geometry to graduate (as these are part of the CSU/UC A-G entrance requirements). We definitely don't pass students in a class just to get it on their report card. Ask any of our unhappy repeaters!

Finally, the reason I think a summer Geometry class is good (for the situation these kids are in) is because it allows them to spend more class time on developing their Algebra 1, 2, and Precalc skills, which will help them in higher levels of math more than Geometry will. This is not ideal, but it is a choice that we had to make here.

Anonymous said...

Another good place to get sketchpad ideas is:

I know that there are some good books out there that connect up directly with curriculum objectives.

(Sorry I'm so late to join the conversation!)


Dan Greene said...


Thanks for the suggestion. You're not late - I've only been blogging for a week now! Please keep checking back and comment whenever you can. The more people commenting, the more useful this site will be for everyone.

Anonymous said...

Why not give the 8th graders an assessment test to test whether they're ready for geometry instead of making them all repeat it?

Dan Greene said...

One of the criticisms of charter schools is that they take the cream of the crop and leave the public schools worse off. The mission of DCP is to serve the lowest achieving students, and we don't want it to become a "free private school".

Students who are truly done with algebra and ready for geometry in 9th grade are doing really well overall, and don't belong at DCP. We don't have entrance requirements (as it is a public school) but this is a disincentive for those students to choose DCP, where their needs will not be served very well.