Don't Wait for Problem Solving
Tracy Zager has a nice summary of a talk given by Megan Franke and the way that Tracy changed her classroom in response to Megan’s ideas. Megan is one of the authors of Young Children’s Mathematics, the newest book by the authors behind Cognitively Guided Instruction.
In the book, the CGI authors make the case that young children can develop their skills as counters and problem solvers simultaneously. Many teachers only give students opportunities to solve problems once they have become fluent with the underlying skills, but Megan and her co-authors argue that children become more fluent and agile with counting facts (and later math facts) when they are practiced in the context of problems, not solely in isolation.
Tracy realized that she had been doing lots of work with counting collections, but she hadn’t used these counting activities as a springboard for problem-solving. So she recounts how she and her colleague Debbie Nichols turned a traditional counting activity into a multi-part lesson where students were counting, solving problems, and even posing and sharing problems that they invented. Tracy’s report includes a couple of examples of students stumbling upon new mathematical ideas through their problem-solving experiences. I won’t give them away - you’ll have to click through!
Although this post has a focus in early elementary, I think the lesson is one that can be extended into all levels of math teaching. It’s important to remember to give kids problem-solving opportunities as they build fluency with counting, addition, multiplication, factoring, and so on. We shouldn’t wait or expect total mastery before giving kids a chance to think through an interesting problem with their new tools.
Written by Kent Haines (@KentHaines)