In the video below, Phil Daro discusses a central change he and his fellow Common Core Math co-authors sought to bring about as they developed the standards: a de-emphasis on answer-getting. Daro introduces this by contrasting the goal of American teachers with that of Japanese teachers:
"The American teacher looks at a problem they're going to use in a lesson and asks themselves, 'How can I teach my kids to get the answer to this problem?' The Japanese teacher asks, 'What's the mathematics they're supposed to learn from working on this problem, and how can I get them to learn that mathematics?'"
Of course, as with any longstanding practice, the emphasis on answer-getting isn't going away overnight. Teachers will need practical PD and coaching in order to make the change Phil Daro and his co-authors envisioned. Still, there are some easy ways for teachers to de-emphasize answer-getting, and I'll share one of them now.
Because we've trained students to focus on getting answers, many of them race through problems and ask the teacher, "Is this right?" And most teachers oblige students by looking over their papers and telling them which answers are or aren't correct. My message to teachers I coach is that you're too valuable to relegate yourself to answer-checking for students engaged in answer-getting. And a great way to prevent this is answer-giving: posting answers for students to check themselves (see photo above). Not worked-out solutions, just answers.
Answer-giving frees teachers up to do what students need us to do when they're working on problems: assess and, as necessary, scaffold their understanding. Even better, it has a positive effect on students as problem solvers. You might expect students to run to the answer station as soon as they begin to struggle with a problem, or look at the answers without even trying to solve problems. But that's not what I've seen happen. Instead, I've noticed answer-giving having the same effect on students as the red cup, green cup method for signaling when they need the teacher's help: they solve problems with more determination, deliberation, and collaboration. Even answer-getters who were once quick to ask "Is this right?" put off looking at the answers until they're confident in their solutions.
But why would students be more diligent when the answers are available to them? I think in part it's because of their competitive instinct and pride. But I also think that by giving students access to the answers up front, teachers convey to them that what matters most is the problem-solving process. And that message is reinforced when students do eventually check their answers. As one student said to me, "If you did it right, congratulations. If you didn't, then go back and find what you did wrong inside your work."
So, whether students solve problems with persistence before checking their answers or revisit problems upon discovering their answers are incorrect, answer-giving helps shift the focus away from answer-getting. And that's what the Common Core authors had in mind. As Phil Daro says, "Correct answers are essential... but they're part of the process, they're not the product. The product is the math the kids walk away with in their heads..."
Top photo provided by GECC, LLC with permission
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