Recently, I mentioned that for my Annual Learning Plan, I’ll be focusing on increasing student communication in math. One tool that I’m using to help me with my professional goal is the flipcam: I’m videotaping math discussions with students, and then watching them afterwards, to guide my own growth as well as to help me guide the students.
Today in class, we started a new unit on addition and subtraction of whole numbers. As an introductory activity, the students had a math problem from the Math Makes Sense textbook on cell phone purchasing over various months. To help push their thinking further, I created a bonus question where students were given an increased yearly total of cell phone purchases, and they had to figure out different combinations of cell phones they would need to sell per month to reach this new total.
The interesting thing about math problem solving is that sometimes students approach a question completely differently than you expect. Your math discussion then evolves from these different approaches. Today, I saw this happening numerous times: from how the students added up the initial totals to their explanations of why they did what they did to how they checked their work to how they approached the bonus question. By not expecting the responses that I got, I really had to change my anticipated questions throughout the discussions.
While at the time, I found that my questions helped guide the discussion and helped the students make some good decisions about what to do next, now watching the videos have me wondering.
- Did I guide too much?
- How do I get the students to see what to do next without directing them on what to do next?
- When I know that an error is going to occur, how do I get students to switch their approach?
- When should I let students make mistakes, and when should I help direct them before the mistakes happen?
- How do I get all students equally involved in math discussions?
- When should I give more “wait time,” and when I should let other group members help guide the discussion instead?
I think you asked a lot of great questions and it is nice to see how well your students are communicating. I think the question that you may want to consider is how do you know your answer is right? Does it make sense? Students need to learn to consider the reasonableness of their answers as a regular part of problem solving. As always, you really brought in real world math that got their attention.
Thank you so much Kelly for your comment and your suggestions! I really like your suggested questions, and it was something I hadn’t really thought of before. I will definitely ask these questions now. Thank you for always giving me so much to think about.