I (might have) had a momentous week in my Building A Thinking Classroom journey this week.
In the Using Hints and Extensions, chapter, Liljedahl talks about how to sequence curricular tasks using variation theory, giving this example regarding factoring polynomials:
For the nonmath teachers out there reading, any where you see red in the sequence above would typically be a new lesson when teaching factoring polynomials, as each new red spot represents a new level of complexity. So according to the sequence above, teaching factoring might take about 56 days, which feels about right based on my longago experience teaching 8th grade and doing so.
Liljedahl tells that, in his experience, when things get humming in a Thinking Classroom and a curricular task like the one above is sequenced and varied (I also read and hear this called "thin slicing" among other Building Thinking Classrooms gurus) just right according to variation theory, that "we get through the entire [56 day] sequence in 4060 minutes. Balancing ability and challenge," he goes on to say, "allows you to cover a huge amount of content in a single lesson" (p.151). I may have just had my first experience with this. And I didn't even do that good of a job with my "thin slicing." This week I started teaching ratio problems. A basic example would be a problem like "if 2 cups of flour are needed to make 5 batches of cookies, how many cups of flour are needed to make 30 batches of cookies." According to my notes from last year, I spent twelve days teaching about ratio situations:
I don't have to teach quite so many strategies this year because of a state curriculum change in Georgia this year, but suffice it to say it still would have been an 810 day sequence (and I planned it as such for this year, too).
I used a 3act task as the impetus for a "thin sliced" curricular task every day last week (except for Wednesday, when I made up my own) and asked similar questions every day. This is Tuesday's, which I'll refer to as an example below.
Nonetheless, here are some positive outcomes:
I really wish I had had the assessment planned for this topic ready earlier. I might have given it to some kids on Wednesday to see if they really did learn two weeks of content in two days. I suspect at least a quarter of them did. I wish I had some evidence, but I wasn't on my formative assessment game. I would love to see just how extensive this accelerated learning was. Pretty exciting.
If you enjoyed this post, please share it!
Want to make sure you never miss a new post? Subscribe below for email notifications of new content.
Want to read more right now? You're in luck  this is my 69th post! You can browse past posts by category:
1 Comment
Seth
9/23/2023 09:12:10 pm
i will be doing ratios next month with my 6th graders. Care to share your lessons?
Reply
Your comment will be posted after it is approved.
Leave a Reply. 
About MeI'm an awardwinning teacher in the Atlanta area with experience teaching at every level from elementary school to college. Categories
All
