I am two classes into a one-unit trial of the CPM geometry curriculum. I convinced the other teacher of the “standard level” geometry class to try it out with me; the next section of our usual textbook being similarity, we decided to implement CPM’s chapter 3, as close as we can without yet having copies of the textbook for the students. We are distributing the problems digitally using OneNote (we have 1:1 tablet PCs), which is actually working very well.1
It. Is. Awesome.
I know I’m just echoing Brett Gilland (and if you click that link and somehow don’t get stuck reading for at least an hour, you are not me), but the fact is that even if you are completely sold on the students-need-to-think-not-just-reproduce-procedures train, teaching that way is FREAKING HARD without good curricular support. The internet is amazing, and I work hard to come up with good activities that will work for my students, but the fact is I’m not prepared for it. I need to follow the basic order of our book, which has almost nothing in terms of engaging activities, so I supplement; but my supplements are taken from my head (inexperienced) or the internet (disconnected) and I have just as many miserable failures as I do successes, if not more. I feel like I spend 70-80% of my planning time thinking about ways to make my book more interesting, which is exhausting, and since I do not have people to back me up and edit my work or exhaustively examine it for reasonable flow, I spend a fair bit of class time fixing my mistakes. Or, just as often, giving up and going chalk-and-talk so I can catch up with my colleagues.
CPM provides a well-organized and connected series of problems that students work on in teams (with strategies on team roles and team strategies PROVIDED) to help them stay engaged in the concepts and understand the reasons behind procedures. It provides homework problems that are intentionally and cleverly spiraled and scaffolded. It provides a link giving hints (also scaffolded) for every single homework problem. It provides incredibly detailed teacher notes for every single lesson, in addition to a webcast giving teacher ideas for each lesson.
Here is a problem from the first lesson in this unit:
3-2. In problem 3-1, you created designs that were similar, meaning that they have the same shape. But how can you determine if two figures are similar? What do similar shapes have in common? To find out, your team will need to create similar shapes that you can measure and compare.
- Obtain a paper copy of the Lesson 3.1.1 Resource Page from your teacher. On it, find the quadrilateral shown in Diagram #1 at right.Dilate (stretch) the quadrilateral from the origin by a factor of 2, 3, 4, or 5 to form A′B′C′D′. Each team member should pick a different enlargement factor. You may want to imagine that your rubber band chain is stretched from the origin so that the knot traces the perimeter of the original figure (don’t actually use the rubber band, though).
For example, if your job is to stretch ABCD by a factor of 3, then A′ would be located
as shown in Diagram #2 at right.
- Carefully cut out your enlarged figure and compare it to your teammates’ figures. How are the four enlargements different? How are they the same? As you investigate, make sure you compare both angles and side lengths of the similar figures. Be ready to report your conclusions to the class.
Is this the most amazingly creative or challenging or fascinating problem ever designed? No. Would I write a blog post about it so that other people could find it, if I had come up with it myself? Again, no. It’s not sexy. It is a meat-and-potatoes kind of problem. But it is a meat-and-potatoes problem that cares about problem-solving (because I don’t instruct them in the dilation procedure directly first), teamwork (because I don’t give direct instruction help until it’s clear a student has exhausted the resources in their team), explanation (because they have to justify why they know, say, the angles are congruent), and broader connections (because we just tried this, physically, with rubber bands and we are now connecting that to the pencil-world and, oh, did you notice the coordinate plane and how easy this will be to connect to slope triangles, which they haven’t thought about in nearly a year at this point?)
This is what I need. I am currently in a world where I’m allergic to my meat-and-potatoes. It makes me ill. So I try to survive by eating as little of it as I can get away with, and supplementing with things that don’t make me ill: spinach and candy and caviar. But I can’t live off of spinach and candy and caviar, especially since the caviar is hard to get and the spinach is sometimes rotten. I will continue to seek out caviar and high quality candy, but what I really need in life is meat-and-potatoes that doesn’t make me ill. And THAT is what CPM provides. When Brett talks about making good teaching easier, this is what he means. Once I get the hang of this, it will free up HOURS of thinking and typing time for me to a) find better caviar and b) do other useful educational things, like get better at standards-based-grading.
I know there are other curricula that can do this, even if CPM isn’t exactly your cup of tea. CME. CMP (at the middle school level.) (why do they all have such similar acronyms?) They are rare, but they exist. If you are struggling with teaching the way you want, and you have ANY power to influence textbook materials, do some research and consider, seriously consider, getting one that will work for you. Especially if you are making your curriculum up yourself; that’s so very hard! Other teachers who agree with you really HAVE written textbooks! You can find one, and it will make your life easier.
I just wish CPM made a curriculum for AP Statistics.
- CPM tells me (very gently) that I’m technically breaking copyright law by doing things this way. Oops! They’re working with me to make the rest of my trial all legal and correct, which is awesome – if you decide to try out the curriculum, they’ll make it possible and you should avoid my mistake by asking them!