My colleague Liz created this graphic which nicely summarizes our project’s position on the relationship between conceptual understanding, procedural fluency, and application.
A typical week of teaching
The balance between conceptual understanding, procedural fluency, and application depends on your goals with your students and those goals should depend on what you know about your students. This is why I’m opposed to “Problem Solving Fridays” and “Practice Tuesdays” as these ways of deciding on goals over-simplify teaching to the detriment of student understanding.
Rachel says:
This would be a nice graphic for students to engage with, as well, for self-assessment. Curious if you’ve done this? Seems it would build great metacognition in students and help them self-monitor and reflect on where they are in the learning process! Some are likely to need more time in one area over another, which would stretch the Mon-Fri timeframe across a greater length of time.
September 14, 2016 — 2:30 pm
David Wees says:
I’ve only ever seen this used once in a PD workshop. I don’t how students would use this. Given how much we differ as educators on the meanings of “conceptual understanding”, “procedural fluency”, and “application” my suspicion is that students would likely have little to no agreement on what those terms mean.
However I haven’t actually thought about using this image with kids or even unpacking those ideas with kids. It sounds like an interesting way to be transparent with students. “You will know you understand this idea if you are able to link it to other mathematical ideas you know” or “You will know you understand this idea if you are able to follow all the steps with minimal errors.”
September 14, 2016 — 5:58 pm