I had a good time this past year playing around with new resources and teaching methods as I worked with my Intensive Algebra students. The Formative Assessment Lessons (FALs) were a great help to me, and I used a number of them both as-is, and as inspiration for developing my own materials.
This year, I will again be teaching two sections of Intensive Algebra 1, along with three sections of IB precalculus. Because the IB curriculum and assessments are pretty clear and established, this will really give me the time and flexibility to focus on the needs of my lower-skilled freshmen, which I am happy about.
My district has been partnering with the Silicon Valley Math Initiative (SVMI), and they provide numerous resources, such as the MARS tasks and Problems of the Month. They have also created a format, based on the work of Phil Daro, for generating units of study to be used as we transition from California State Standards to CCSS, before high-quality curricula are commercially available (if ever!) and districts adopt new materials.
The basic unit structure is as follows:
- Introductory lesson for engagement, to spark curiosity and interest.
- Several conceptual development lessons, after which you can expect student understanding to still be fragile. These lessons are what we typically think of as inquiry-based or constructivist lessons. (I think this is a good eye-opener for me, because it has always felt frustrating how my students would still not "get it" after we engaged in, what I considered to be, really powerful learning opportunities. Setting my expectation that students' understanding is going to still be fragile at this point will be key.)
- One or two getting precise lessons, in which the teacher attends to precision, definitions, conventions, symbols, etc. This is often going to be a more traditional "I-We-You" direct instruction approach.
- One or two getting general lessons. The goal of these lessons is not 100% clear to me, but some ideas for generalization are to use concepts across different contexts, generalize with variables and parameters, use different types of numbers, operations, functions, or structures in the same context, and so on.
- A formative assessment lesson (which often takes multiple days). These are intended to be done about 2/3 of the way through the unit. They all start with a pre-assessment, and a well-defined set of tasks to help students further develop their understanding of the concepts.
- Additional concept development lessons, as needed.
- One or two robustness and differentiation lessons. This is an opportunity to do re-engagement lessons with students who are struggling, as well as enrichment for students who are showing solid understanding. The goal is to move all students from a fragile to a more robust understanding via a variety of rich problem solving opportunities.
- An expert task assessment, in which students engage with tasks that have them operate at levels 3 and 4 on Webb's DOK.
- A closure lesson to revisit and organize the unit goals and outcomes.
- A summative assessment to see if students really have mastered the unit goals.