Barry Garelick has published a second collection of blog posts, Teaching Math in the 21st Century, based on his experiences as a long term substitute math teacher in California. It’s been out for a few weeks, but I’m just now getting around to reading it in book form, having read the posts previously as they originally appeared on the blog Out In Left Field.
Given my service on the Assessment Task Force and that Iowa is still on the long and winding road to adopting the Smarter Balanced assessments, I was interested to be reminded that Garelick had written about administering the practice Smarter Balanced assessments to his students. (Chapter 12: Teaching to the Authentic Assessment).
At the end of sixth period, I dismissed the students, and went back to my classroom. I realized that when Common Core kicked in students would be “taught to the test” for all of these particular types of questions. I have no problem with teaching to a test if the test covers material that should be mastered. I do have a problem when part of this is learning how to write explanations that will pass muster according to scoring rubrics that more than likely will be questionable.
Garelick, and Out In Left Field blogger Katharine Beals, have more to say about SBAC/PARCC in a new article at Education News, Math Problems: Knowing, Doing, and Explaining Your Answer. Opening with a middle schools student’s complaints about being required to explain her answers on the Smarter Balanced assessments (“Why can’t I just do the problem, enter the answer and be done with it?”) and ending with their answer to the question: what is really being measured?
Measuring understanding, or learning in general, isn’t easy. What testing does is measure “markers” or byproducts of learning and understanding. Explaining answers is but one possible marker.
Another, quite simply, are the answers themselves. If a student can consistently solve a variety of problems, that student likely has some level of mathematical understanding. Teachers can assess this more deeply by looking at the solutions and any work shown and asking some spontaneous follow-up questions tailored to the child’s verbal abilities. But it’s far from clear whether a general requirement to accompany all solutions with verbal explanations provides a more accurate measurement of mathematical understanding than the answers themselves and any work the student has produced along the way. At best, verbal explanations beyond “showing the work” may be superfluous; at worst, they shortchange certain students and encumber the mathematics for everyone.
I enjoyed this collection, Teaching Math in the 21st Century, as much, perhaps even more, than the first, Letters From John Dewey/Letters From Huck Finn: A Look at Math Education From the Inside. [Note: both books are currently available for the Kindle at low prices at Amazon.] Garelick writes knowledgeably about teaching 21st century math with an appealing mix of seriousness and humor, as well as obvious affection for his students. My only complaint is being left feeling vaguely disheartened about the likely near future of math education in Iowa, if Garelick’s experiences are any guide.