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MAA Instructional Practices Guide - Part 3 of 7

We continue our series of reading and working through the MAA Instructional Practices Guide. This is part 3, in which we review pages 26-44 on selecting mathematically appropriate tasks.

Framing Questions #

The guide provides some good questions we can ask and reflect on together (page 29):

  • Do I have clearly-stated and concrete learning objectives defined for the lesson in which the task is going to appear, and do students have access to those objectives?
  • Does the task align with my learning objectives?
  • Do I have actionable information, based on formative assessment or surveys, about my students’ motivations, attitudes, and mathematical readiness for the task?
  • Based on that information, does the task meet students at their level of expertise (not too easy, not too hard) and at their level of readiness (they are prepared to do the task apart from having the right level of expertise) and motivation (students have a reason to perform the task apart from extrinsic rewards and punishments)?
  • Is the task well-constructed in terms of building students’ intellectual development, competence, and autonomy? Does it leverage the social context of the class to promote relatedness?
  • Is the task suitable for the physical environment of the class meeting?
  • Is the task suitable for the mode of instruction (face-to-face vs. online)?

Cognitive Demands #

Contrast Low-level vs. high-level

  • Imagine we’re teaching an algebra course
  • Sticky notes!
  • Small groups, come up with ideas of activities that are:
    • low-level
    • high-level

Neat results #

Initially, I’d expected us to conclude most of our activities in college algebra being low-level (and it’s true, many are “what is 5*9?” etc), but we came up with a very large list of high-level activities that, when we put them on post-its on the board and really discussed them, are giving some deeper thinking on the part of students.

My biggest regret is that I didn’t take a picture of the post-its on the board 😩 It was a neat natural histogram of pedagogy!