Let me start by giving credit where it is due. Alex and Bruce McLaurin (@BDMcLaurin) started spiraling at their school 5 years ago. They are the experts on it now and are sharing the experience with teachers far and wide. I got involved this past school year when I spiraled my grade 10 applied math class, second semester. Alex wanted to collaborate on this with me and Sheri Walker so we met 3 times during the semester to figure out what we wanted to do, try some things out and plan each cycle. We took the lead from Alex on which activities to look at and added a few things of our own. This was truly jumping in the deep end of the pool, but I firmly believe it is the only way to do this successfully. At the end of our session Alex said that if you try to do it slowly and incrementally, the kids will drag you back down and you will go there because that is your comfort zone. I agree, so jump on in!
A bit about grade 10 applied math. The students in this course have generally been unsuccessful at some point in math and most do not like math. There are a lot of behavioural issues and I would guess that in the average class, over half of the students have an IEP. Asking these kids to sit and take notes then do homework is a recipe for frustration all around. Instead, we tried to get them up and moving, doing math in context, even if it was a contrived context, and assigned no homework. There was no point assigning homework - those who would do it are the ones who didn't need to and the ones who needed to wouldn't do it. So no homework, no textbook; we created worksheets for practice which some students finished and others didn't. They did what they could in 75 minutes each day, which was different for each student.
Here is how it was structured. Over the course of the semester we did 4 full cycles and a bit extra at the end. This means no more units. Each cycle covered each of the overall course expectations (they start on page 53) and we tested all of these at the end of each cycle.
We uncovered the material through activities. Hands-on as much as possible, with manipulatives, graphing technology and whatever "stuff" we needed - spaghetti, pennies, linking cubes, algebra tiles, cups, etc. The activities started out very scaffolded and become more open-ended and richer as the course progresses. I blogged about it all starting here and I will link to Alex's blog posts below.
The first cycle started with the 26 Squares activity which took about 3 weeks. We hit all 3 strands of our curriculum. Next we did some toothpick activities to work on linear modeling and equations. We did Andrew Stadel's File Cabinet 3-act next to hit on some of the measurement strand. We used Smarties, Jujubes and pennies to solve systems of equations. That is where we ended cycle 1.
Please note that these are Smarties:
These are actually called rockets:
During the 2nd cycle we did Spaghetti Bridges for linear modeling/solving, a series of activities including High Fives and Frogs for linear and quadratics, found inaccessible heights for similar triangles and trig along with a roof truss task for the same expectations, then I did some work with surface area/volume of prisms and pyramids (I think Alex and Sheri did something different). Then came test #2.
The following chart, although hard to read, gives you an idea of the number of activities and which expectations they are hitting.
Alex also did a card tossing activity which we got participants to try out at TMC14. It is a lot of fun to do and hits a lot of curriculum expectations. I find that the more of this I do, the more I can see how to extend an activity to get more out of it.
(thanks to Nathan Kraft for the photo)
Throughout the course students saw the same concepts several times. For example, in cycle 1 they solved systems of equations only with manipulatives. They did not even write equations to represent the situation. In cycle 2, they did the same but also started to write something to represent the situation - some wrote equations, some used symbols or pictures. In cycle 3, they learned how to use elimination through a very logical progression of questions that made sense in context. And we reasoned through the answer. They may not have been able to present a beautiful algebraic solution, but they could solve the system and could explain to you how they did it. They were not following an algorithm - they understood what they were doing. In cycle 4 they solved systems to work through the cup stacking activities. We created a solid foundation and built upon it each cycle.
The benefits from the PowerPoint are shown below, but one of the big ones for me is time - you have time to get through the course - in fact they see most of the the curriculum in the first 6 weeks; you don't need to feel rushed to get an activity done - if students need an extra day, take it; if someone is away for an extended period of time, they miss an activity or maybe 2, but we will cycle back and see it again.
As a side note, I got comp books for my students because I enjoy structure a little more than Alex. (By "enjoy" I really mean "need".) For each topic I would print out an example or fill-in-the-blank type of sheet for students to glue in their comp book and fill in. This way they all had a resource to refer to. Some students took their comp books home to help them study for tests and they were allowed to use them for the end-of-year summative task.
I hope this helps shed a little light on what is involved in spiraling through the curriculum with activities. Please throw any questions my way in the comments. Perhaps the strongest endorsement I can give is that I will never teach this course in a "traditional" way again, and that I have volunteered to teach it (the course that no one wants to teach) both semesters next year.