Today's quote comes from Share & Compare: A Teacher's Story About Helping Children Become Problem Solvers in Mathematics. Maybe it will make a bit more sense after reading this thought.
"Children's problem-solving accomplishments can sometimes be characterized as 'unconscious competence.' They can solve problems and communicate their solutions using drawings and manipulatives, but they seem unaware of the thought processes taking place."
Larry Buschman, Share & Compare 17
These quotes challenge my way of thinking and operating as a math teacher. To me, they're saying that it's not all about the solution, and drawings and manipulatives aren't even the most sought after goal in a child's mathematics instruction. A mathematician's ability to communicate about their problem solving strategies is proof that something worthwhile is going on. I've been taking steps in the right direction. I've added "How do you know?" to my math conversations. I've been more aware of expecting my kids to teach their strategies to the class as well as informally with partners. Yet in spite of the positive changes I'm making, there are levels of communicating about math that my kids have yet to experience. Just finding the answer and showing the work isn't enough. The math talk that kids engage in is where it's at.
I like this that it isn't just about the answer, but how you got there and can you tell others how you got there. That is difficult for a lot of students (and adults) to do sometimes. Me included. Thanks for making me think!
ReplyDeleteLori
Conversations in Literacy
Lori, I'm sure hoping that these young mathematicians will become adults who can communicate their thinking better than I can. :)
DeleteI agree with this as well. And I think it's a challenging concept for the kiddos. I know when I try to model problems with them step by step; I'll read the problem and then try to discuss whether we'll add or subtract and how do we know what to do, I will have kiddos just yelling out the answer. It's frustrating to try to explain to the students that it's as important to know how we got to that answer as the answer is itself.
ReplyDeleteNotJustChild'sPlay
Miss Trayers, hopefully we can train kids to think more about their thinking, huh?
DeleteTeaching children to think, ponder, wonder...That should be our goal. Bringing them to a point where they can articulate their thinking is not easy, but so important! Thanks for the thoughtful saying...I was expecting Vygotsky!
ReplyDeleteJenny
Jenny, you're very right, and they'll be better off if they can learn how to communicate their thinking. I think Vygotsky would approve. :)
DeleteThanks for the post. My team mate teaches ONLY math to our firsties and I support her with our struggling students. This will be something that we read and talk about together. Thanks.
ReplyDeleteEm
Curious Firsties
Em, I hope this proves helpful. It's really been a good challenge for me.
DeleteI need to do better with this! One of my goals for this year.
ReplyDeleteCrystal
Teaching Little Miracles
Crystal, it's one of mine too!
DeleteUnconscious competence ... I like that. Roger Lewin said, "Too often we give children answers to remember instead of problems to solve" and that's stuck with me. If we'd ask them more often how? and why?, I think we'd be amazed at the places they'll take us! Thanks again for a thought-provoking post!!
ReplyDeleteBarbara
Barbara, I like that quote. Thank you for adding your wise thoughts to the day!
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