Marilyn Burns
Paul, a fourth grader, is an example of the struggling students we have in mind as we write Do The Math. His class was studying multiplication and Paul's teacher was concerned about him. She told me that he typically worked very slowly in math and "didn't get much done." I agree to talk with Paul and see if I could figure out the nature of his difficulty. Here's how the conversation began:
Marilyn: Can you tell me something you know about multiplication?
Paul: (Thinks for a bit and then responds) Six times eight is forty-eight.
Marilyn: (Nods to accept the answer) Do you know how much six times nine is?
Paul: (Shrugs) I don't know that one. I didn't learn it yet.
Marilyn: Can you figure it out some way?
Paul: (Sits silently for a moment and then shakes his head "no")
Marilyn: How did you learn six times eight?
Paul: (Brightens and grins) It's easy- goin' fishing, got no bait, six times eight is forty-eight.
My exchange with Paul reminded me of three issues about teaching mathematics that are essential to keep in mind.
It's important to help students see relationships and make connections so that they don't treat mathematical ideas as isolated and disconnected from one another. (Paul, I learned as I probed, saw each multiplication fact as a separate piece of information to memorize.)
It's important to build on students' prior learning so that they build new understanding on a foundation of their existing knowledge. (Paul was not able to rely on what he knew about addition to figure products.)
It's important when asking questions to remember that answers by themselves, without students' explanations
Marilyn: Can you tell me something you know about multiplication?
Paul: (Thinks for a bit and then responds) Six times eight is forty-eight.
Marilyn: (Nods to accept the answer) Do you know how much six times nine is?
Paul: (Shrugs) I don't know that one. I didn't learn it yet.
Marilyn: Can you figure it out some way?
Paul: (Sits silently for a moment and then shakes his head "no")
Marilyn: How did you learn six times eight?
Paul: (Brightens and grins) It's easy- goin' fishing, got no bait, six times eight is forty-eight.
My exchange with Paul reminded me of three issues about teaching mathematics that are essential to keep in mind.
It's important to help students see relationships and make connections so that they don't treat mathematical ideas as isolated and disconnected from one another. (Paul, I learned as I probed, saw each multiplication fact as a separate piece of information to memorize.)
It's important to build on students' prior learning so that they build new understanding on a foundation of their existing knowledge. (Paul was not able to rely on what he knew about addition to figure products.)
It's important when asking questions to remember that answers by themselves, without students' explanations