WEBVTT

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[Music]

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I am Mark Driscoll at Education
Development Center.

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Education Development Center is
also known as EDC, Incorporated.

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Teachers can build to debriefing
multiple problem-solving strategies

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with students systematically.

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Teachers have several ways--proven
ways--to help students become more skilled

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in discussing multiple solutions to problems,
and one is to structure the discussion at table

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with written tools that the students can use.

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Like one that's commonly used
today is sentence frames.

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So a sentence frame might do something like
"I tried [blank] because I thought [blank]."

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I mean, this is along those lines

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of structuring the student's statement along
the lines of being reflective, about thinking,

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and then having the student
personalize it by putting in the answers

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to that and then having them compare.

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Students can talk about that together and
begin to develop this kind of normal discourse

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that we share our mathematical thinking.

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The research does back up a lot of this
by way of the importance of metacognition,

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which is a fancy word for saying we

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as problem solvers become more
reflective about our thinking.

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And so helping students to do
that with the simple problems

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like sentence frames can carry--in my experience,
kids will start to ask each other the kinds

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of questions that the teacher asks
them, and kind of spontaneously.

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And so I think making sure those questions
really help the students express their thinking,

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their mathematical thinking, that I
think has a lot of long-term value

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for the kids as mathematical problem solvers.

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Teachers can prompt student sensitivity and
student awareness of strategies being employed

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in a number of ways, and one is through
a set of questions that really try to get

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at what the students are
noticing in a particular solution.

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If a teacher has student solutions up on chart
paper or up on the board, can ask the questions,

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"What do you see in diagram A from student
A that's giving information that isn't

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in the diagram of student B. Now what do you
see in B that's not in A" to develop that eye;

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it is an eye and it's a habit of
learning to be more analytical.

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And then broadening the questions out, I
think it's a matter of prompting students

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to become aware of their own thinking.

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It's a set of metacognitive skills that
has the student really thinking about his

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or her own thinking and then
being able to put it to words.

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And those questions can be
"What did you try first

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and why?" not just "What did you try
first?" It's,"Why did you try that?"

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and "Why did you decide to try something
different?" It's those why questions

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and when questions and how questions that I
think become habitual, and kids will start

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to use those questions themselves.

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Another prompt is for students to learn from
their mistakes, and one way to do that is

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for the teacher to have the students
value in their written student work

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that they are showing false starts
and to inculcate in the students

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that that's what mathematicians do;
they have false starts all the time.

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If you look at the current mathematical
practice standards of the Common Core Standards,

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the first of the eight mathematical
practice standards is make sense

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of problems and persevere in solving them.

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Well, there aren't any formulas for making
sense of problems and certainly not any

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for persevering unless it becomes
part of the culture in the classroom.

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And that students learn that even great
mathematicians learn from their mistakes

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and that the teacher should be an
agent in helping the student do that,

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by looking at the student work and helping
the student become more reflective of his

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or her thinking about the problem.

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