The Common Core State Standards for Mathematical Practice (SMP) were written for educators to develop in their students. However these same standards also shed light on great practices for reflective teachers.
“Mathematically proficient students…bring two complementary abilities to bear on problems… the ability to decontextualize…and the ability to contextualize…”
Two key words in this standard are contextualize and decontextualize. Often US students have picked two numbers out of a word problem and done whatever they did last (multiply, divide, add, or subtract). Because the word problems are associated with the chapter, the answers have typically worked out quite well. Now, students are expected to understand how the numbers are related. They might need to both add and multiply. They might need to convert units of measure.
Maybe it’s a stretch, but I see such simplistic responses (just pick two numbers and put them together) in the way teachers might relate to their students if they do not take time to reflect on underlying contexts. We are especially at risk when we are tired and time is waning thin.
It isn’t the 150 tests we need to grade that seems to drain our time so much as the dozen make-ups and late work requests. It isn’t the general class atmosphere that is challenging to establish but the exceptions to the rules, the special situations that require regular workarounds and communication that can get under our skin. It isn’t the top ten in the class that sap our strength, rather the bottom who, at times, would seemingly hide under their desks to avoid learning. It’s all the cases where can’t just give a standard response that make our jobs so much more difficult. In those cases our jobs need to look more like SMP 2:
“…creating a coherent representation of the problem… considering the units involved; attending to the meaning…flexibly using different properties of operations…”
If we begin to feel dragged down with all the exceptions and special cases, reacting to these situations as if they were distractions, then SMP 2 might help paint a prescription: decontextualize – contextualize. Is there a superstructure that could be put into place to handle exceptions? When we understand how underlying components interact, we can anticipate them and plan for better responses to them (operations).
I take homework grades from Khan Academy assignments. When I first began doing that, I noticed I was spending a lot of time trying to accommodate students who were late completing those. I understood that the technology and expectations were new to them and wanted to be merciful in grading. But it took so long to retrieve their individual late grades and find the appropriate blank in the grade book to fill, that it was frustrating. At the same time, students were asking me about making up tests. These two contexts ended up requiring completely different operations to effect efficient solutions. I discovered that if I waited a few days to record homework grades, then there were few excuses that would merit additional, additional more time. But I didn’t want to delay grading and entering tests scores because I want to give my students prompt feedback. So I haven’t really figured out a great solution to the late-test time gouge. But at least the Khan issue has been solved with my new sequence of operations.
“Considering the units involved: attending to the meaning of quantities”
If we associate students’ non-compliance with laziness, we can find ourselves frustrated with them. However, when we understand that our students are changing (unit conversion?), and they have difficulty understanding why what we teach is so important, it is much easier to face that student with uplifting responses if we have planned for that.
Even though the SMP were written for students, I continue to find ways to apply them to my practice as a teacher. Much in those standards comes naturally as a part of being a reflective practitioner, but the SMP also provide encouragement to be increasingly more intentional in growth and application. I know the standards aren’t perfect, but I remain deeply indebted to the writers for their genius insights to accomplish the goals set before us.