I posted last week in defense of my approach to curriculum — scouring the Math Twitter BlogoSphere, leaning heavily on a few resources, and filling in the gaps with stuff I create.
Brett Gilland pointed out in the comments that my choice not to use a traditional curriculum is contingent on my lack of high-quality, coherent curriculum at my school, and wonders whether my approach is useful for new teachers. Then he writes at his great blog, which seems to have been revived, a critique of my approach to curriculum. It’s spot on.
One of the things that concerns me about the MTBoS as a force for educational excellence is that the mindset he sets forth in his closing paragraph- crafting his own curriculum, for all its warts, has made him a better teacher than any ‘canned’ curriculum ever could– seems very very common. And maybe he is correct. Maybe teaching math really isn’t enough to develop as an instructor. Maybe taking on the full time job of curriculum designer (for multiple different courses at the same time!!!) is also necessary. If so, we are doomed to bad mathematics education in perpetuity.
Luckily, I think there is another way, one that the MTBoS is edging toward. One that I am hoping will come to fruition in the near future. The MTBoS needs to become a teacher’s lounge that shares ideas. It needs to become a teacher’s lounge that starts doing some damned vertical alignment and generating, as a group, a thought out curriculum, preferably one that includes not just the fun stuff, but also some assignment sets, test banks (or just high quality tests) and the like.
Brett is right, and he’s hitting on my pipe dream — of building exactly that curriculum, free and open source, for any and all math teachers. There are obviously plenty of curricula already out there. My question today is — what are the essential features of quality curriculum, not just for the MTBoS faithful, but for a brand new teacher or closed-door thirty-year veteran?
Things you could include in a curriculum
- Clear explanations of new topics (well-chosen examples, notation, connections to other topics)
- “Cool” ways of explaining new topics (here are some clever ways to make this fun and exciting for students)
- Motivating questions (this is why a student should care about this topic)
- Inquiry lessons (a task, series of questions, or other lesson plan that has students discovering key ideas)
- Problem sets (students need practice)
- Formative assessment tasks (rich tasks that see if a student really understands a topic)
- Extension and enrichment (higher DOK problems, connections to more advanced topic, extended thinking tasks)
- Modeling tasks (structured as three-act tasks, in the vein of Mathalicious, or another way)
- Projects (opportunities for extended thinking and the creation of a significant final product)
- Summative assessment (tests and quizzes, although publishing these online creates potential problems)
- Pedagogical tips (lesson plans for whiteboarding, speed dating, solve-crumple-toss, or other techniques to increase student engagement)
- Resources for remediation (assessments and resources to address skill gaps)
What it’s for
- A well-organized supplement to a traditional curriculum
- A stand-alone, coherent curriculum
How it’s used
- A sequence of activities (do this, then that, then the other)
- A “decision tree” (introduce with this, if that goes well do this, otherwise, try that, then use the other to see how much more of that they need)
- A collection of resources that leave all of the decisions to the teacher
- Modular (it’s easy to pull questions 4, 8, 9, 11, and 17 into a homework assignment, use formative assessment tasks 2 and 6, teach unit 5 before unit 3, and trim the test to fit my 43 minute class or break it into SBG-style assessments)
- Social (think Desmos activities that harness the collective power of student responses)
- Crowdsourced (do teachers get to vote up or down on lessons, questions, or tasks they like?)
I don’t have answers to any of these questions. I’m going to think a bit and try to offer something useful in the comments. I’m sure any one of these features is a must-have for some teacher. What is most important to focus on? What are the best ways of organizing? What possible features have I missed? Let’s figure this out.