I’m the worst at thinking about alignment. My answer: “whatever age students who would find the question interesting and developmentally appropriate!”

Thanks for the feedback, Kristina! If you’re writing at all about your work in digital learning, please pass along a link.

Thx for the feedback, Martin. Never a bad idea to skip one of my talks since they generally find their way online sooner or later.

I’ve also noticed (pun unintended) that the Notice and wonder routine really seems to increase the cognitive work kids do. Thanks.

Thanks for the update, Bethany. Really fun to recall my time at Madison.

I also find these terms can occasionally squish together in ways that leave teachers just leaning on their existing ideas — “contextualized,” “productive struggle,” “non-routine,” etc.

That’s why I like Autor & Price’s description of “routine cognitive work”:

“The core job tasks of [routine cognitive] occupations in many cases is to follow precise, well-understood procedures.”

Precise well-understood procedures shouldn’t be avoided in math instruction, but we need to balance them in accordance with their value to a student’s math education and their preparation for future work.

Just to comment on ‘how best to enact non-routine teaching.’ I have first hand experience with getting excellent instructions for teachers for non-routine tasks. I teach the Carnegie Math Pathways (CMP) materials at a 2-year college, and the entire structure of the curriculum is contextualized lessons. The implementation of the lessons is meant to provide ‘productive struggle’ for students. I think their term ‘contextualized lessons’ and your term ‘non-routine tasks’ get at a very similar point… both are attempting to create a space where students engage fully in the learning. The folks at CMP call that full engagement ‘productive struggle.’ I have been teaching their curriculum for 4 years, and I love it.
In the curriculum, there is very minimal instructions for students and almost every lesson starts with asking students to estimate and/or predict. A typical lesson for a student is about 4 pages. The Instructor Notes that go with it are more like 14 pages. In the instructor notes there are suggested ways to have students work on a problem (small group, class discussion), there are also suggested ways to question students to encourage them to think through the problems. There are also lots of possible solutions given that students might come up with and how to address misconceptions while still keeping the students in charge of their own learning. Another support provided to help me and other faculty teach non-routine content to students is professional development training. In the training we get to watch videos of experienced faculty engaging with students. We also get to collaborate and discuss how we would teach a lesson and support non-routine learning for our students. I have learned a lot about how to ‘be less helpful’ and support students through productive struggle from those instructor notes and the training. Finally, another support provided is a faculty mentor during the first year you teach it. I had a mentor my first year and now, full disclosure, I was so impressed and transformed by what I learned, that now, besides still teaching math, I am paid to mentor other new faculty.
All of these supports make supporting non-routine thinking for students much more accessible and less scary for faculty that have little experience with it.
Also, as a side note… Dan, you came to my college back in 2012 and did an absolutely amazing workshop around the 3-act tasks. I learned so so much from you in that workshop. One of the biggest things I learned was that I was delivering the first act all wrong. I was asking… “what questions come to mind” but really, what the student knew I was asking was “which student can tell me the question I am looking for.” Even with that knowledge, I still struggle with my delivery and with student engagement in the tasks. I think some of my struggle could be helped if I utilized the math community on twitter more. But, one way that I think it could also be alleviated (somewhat) is by creating instructor notes. Because it’s not just the *what* it’s the *how*