When we are teaching new concepts, the way that we ask a question can create clear or murky understanding. Posing a quiding question that is open is essential, so that there is room for inquiry and student exploration into the answer. Students
need to search out the answer by creating connections, adding vocabulary, and collecting their own data. Using the data and discussing their understanding will lead them forward. But it is up to us, as educators to create the "right" questions, questions that leave room for student thinking and lead into the concept that is to be discovered.
There is a text titled, "Good Questions for Math Teaching" by Peter Sullivan and Pat Lilburn.
I think that if we want students to investigate and learn the what and why of math before we introduce the symbols, than we need to be very careful of our language and the questions we ask in math. Students need to gain confidence in inquiry and dare to make mistakes along the way to be stronger thinkers and problem solvers, "math thinkers", who can take the challenge as we teach new concepts throughout the year.
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6 comments:
I just started reading that book myself!!!! I really like the way the authors show ways to expand student thinking, drawing the focus away from a right or wrong answer, but instead helping the teacher pose more open-ended questions. They say it is far easier for teachers to ask open-ended questions in the areas of reading and social studies, while math questions tend to be more of the right or wrong variety.
There are many examples in this teacher-friendly book that not only model "good" questions, but also help reframe my own thinking about formulating other questions. I got the book on Amazon.
Great minds think alike! I also bought this book recently at Amazon and found that it was a storehouse of useful open-ended math questions in the various math strands. I like the fact that the questions are leveled for K-2, 3-4, and 5-6. I'm excited to try some of these types of questions with my kids this year. They really challenge kids to go deeper with their math thinking. But it will also challenge me to learn how to use these questions effectively.
Thank you for reminding me of this book. I had borrowed it from a friend awhile back with the intention of buying (put it on the list). Your comments regarding posing the right question reminded me of a vignette on the first day of school.
The kindergarten teachers were all greeting the buses as the students disembarked. We sat together (students and teachers) waiting for all the buses and children to arrive. I was sitting next to a group of 5 of my new students. They were discussing the numbers of their buses.
Boy 1, "I ride bus 15."
Girl 1, 'What's that?"
Boy 1, "A 1 and a 5 next to each other."
Boy 2, "Yeah, my bus has a 3 and 5, threedy five!" Boy 1, "No, not threedy five. It's called thirty five!" Girl 2, "Is that right Mrs. Smith?"
Here was a teacher moment. As I paused thinking about what I wanted to say the 5th child piped up. "No! 3 and 5 is 8."
Wow! What different understandings each child had of what these numerical constructed meant. I asked the 5th child, a little girl, what she thought would happen if I put 3 and 5 together? Before she could speak, Boy 1 bellowed, "It will always be 35!" Thank you boy1.
I held up three fingers on one hand and 5 fingers on the other. As I showed them the two quantities of fingers I asked them what would happen if I put them together? Needless to say, we sat there grappling with fingers and putting numbers together, as well as connecting ideas. It was exciting to watch how each child constructed a meaningful exploration based on his or her knowledge base. I found myself in an authentic assessment moment given the various understanding my new students were bringing to school. I clearly felt the importance of posing a question that would enhance their interaction with one another and support a meaningful investigation on the curb outside the school.
Thank you for that referral. I find that is one of the most challenging aspects of teaching; posing open ended questions that are not only designed to further the student's thinking; but are also developmentally appropriate for that particular student. Sometimes in a classroom of over 20kids I find it hard to slow down enough to take the time to be where the individual student is without feeling a sense of urgency or need to move ahead for the others. This resource may be helpful in providing ideas for differentiating.
Maddy, your post made me think about how my students and I are in similar positions. I know that I need to gain confidence in inquiry and dare to make mistakes along the way. I need to constantly remind myself to slow down, ask the right questions, and give time for kids to think and problem solve. As I am starting this new school year with 27 kids, I am questionning how to be sure that all my students can gain confidence in themselves as math problem solvers. I am feeling a bit overwhelmed myself and know that my kids will feel the same way as we go through the year. I will probably be tempted to hurry things along, and hope to be able to realize that I am doing that. So many ideas are going through my head at one time, and panic sets in. Do my kids feel the same way?
I am going to get my hands on a copy of that book right away! As I read through the comments it occurred to me that instead of the teacher trying to come up with the "right" question it would be even better if students could come up with the questions. I think we all know a good question when we hear it, but some of the best questions I ever heard during book discussions with elementary children often came from the children themselves. I find that I often complicate the matter and it makes the whole process so much clearer when the question is coming
from the child's experience and interest. ( I think I blog too late at night and tend to ramble...)
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