WEBVTT

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[Music]

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I am Mark Driscoll at Education Development Center,

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where I am a managing project director,

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and Education Development Center is also known

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as EDC Incorporated.

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The value of teaching multiple problem-solving strategies

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to students is an opportunity

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to learn flexibility in problem solving.

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Teaching multiple strategies, there is evidence

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that that does produce flexible thinking in terms

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of the students seeing options for different strategies

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and then choosing according to the situation.

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Teaching students to approach problems not just

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with the verbal analysis, but with the spatial analysis.

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Using visual tools--

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those strategies of using visual tools provide greater

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access to special need students in areas like ratio

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and proportion,

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which traditionally have not been accessible to a lot

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of middle grade students.

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The use of multiple problem-solving strategies

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contributes to student learning in a couple of ways.

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And one way, I think, is that by a regular exposure

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to other students or the teacher's alternate ways

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to approach problems, the student can learn

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to see the problem and the problem types in new ways.

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The other way is that multiple strategies allow the student

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to become more analytical about problem context.

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So if, for example, the student's inclined

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to use numbers to approach geometry problems--say,

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similarity problems in the middle grades--that the numbers

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in a particular problem may be particularly difficult

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for the student.

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And so in that case, to have an alternate approach,

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a strategy, that's more spatially oriented based, say,

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on the dilation to get a similar replica of a triangle,

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then that student can, for the time being,

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ignore the difficult numbers and reason his or her way

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through to a solution.

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So I think I can point to an example

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from the National Assessment

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of Educational Progress showing the advantages

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of multiple problem-solving strategies.

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Typical eighth-grade students

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in this country have pretty much one way

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to approach these proportional reasoning problems,

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and that is to set up a proportion

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and do a cross-multiplication.

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Setting up a cross-multiplication can be challenging

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and apparently is for many students.

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What's the alternative?

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If a student has another strategy

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in mind that's more geometric, and the student has learned

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that two triangles are similar if one is a dilation

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of the other, then you could start to look at it spatially

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and not worry about the cross-multiplication.

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The student knows dilations and says, well,

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it's a three dilation--it's a scale up by three.

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So now the question is, so what's X?

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So we know that now we know it's a dilation of three,

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that whatever X is is going to be repeated three times

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in that segment there.

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Which means that X is going to be repeated twice

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in that piece of the segment, which is 40.

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And two even pieces into 40 means

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that each one has a length of 20, which tells you

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that X should be 20.

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So that's an alternative, that's a case

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where I think not having multiple strategies can get

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the students in trouble.

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Several techniques come to mind

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for how teachers can promote the use

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of multiple problem-solving strategies.

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And one is to create a culture

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of multiple problem-solving strategies in the classroom.

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The second technique that comes

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to mind is the frequent use of questions

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that ask students not just what they did,

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but what they were thinking, so that making the thinking

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and the expression of thinking, again,

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part of the classroom culture--students talking

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to each other, students talking to the teacher.

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Teachers giving the worked examples early on

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and emphasizing multiple strategies I think would

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be valuable.

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And to do it in a way where the students see

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at least two worked examples by the teacher in terms

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of two different strategies.

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Having the teacher gradually open the door

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and ask students, using his or her own judgment

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about the students, what other kinds

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of diagrams might help here, for example,

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what other strategies are there that you can think of?

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And to have them get those out and have the teacher then act

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as an agent to help them compare and contrast,

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which cognitive science shows is really important

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contributor to learning--comparing

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and contrasting examples.

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For students to be able to compare their strategy

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with another student's strategy

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and maybe a third student's strategy, the value is

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that they then can develop that kind of set of skills,

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set of strategies themselves

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that makes their thinking much more flexible.

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[Music]