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Philip Ogbuehi: My
name is Philip Ogbuehi.

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I am a Pre-K 12
mathematic specialist

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with Los Angeles
Unified School District.

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Patricia Herzig: Hello, my
name is Patricia Herzig,

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and I am a math
consultant and I work

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with various school districts
helping their teachers

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and students with math.

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Philip and I were
the two practitioners

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on the Problem Solving
Guide panel.

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We both have advice
for teachers

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who will be using
the Practice Guide

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and some concepts we
would like to emphasize.

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Philip and I agree that
it's very important

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to incorporate problem
solving activities

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into whole-class instruction.

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One of the things
that I have observed,

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and I am sure Philip
has also, is that much

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of the math instruction
is limited to learning

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and practicing new concepts,

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and this leaves
very little time

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for the incorporation
of problem solving.

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Ogbuehi: Mathematics cannot
be learned and understood

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in isolation without
being taught in context.

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The context will help the
students to make meaning

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out of mathematics, and hence
help them to become adept

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in solving problems.

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Applying skills in complex
problem-solving situations is

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one of the ways in which
students not only refine their

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skills, but reinforce
and strengthen them.

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Herzig: It is not
difficult--with some

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structure--to model problem
solving at the same time

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that you are teaching
concepts.

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One of the things that
I observed recently

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in a classroom--and this was
a seventh-grade classroom--the

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teacher was teaching how
to solve proportions.

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She was teaching it very
traditionally using the

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means-extreme property.

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When the students got
into the application part,

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where they had to
read a problem and set

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up a proportion, they
had a very difficult time

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doing this.

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This would have been an
easy thing for the teacher

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to model using whiteboards
in the classroom,

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having reading problem
situations,

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and having students set
up for the proportions,

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and then being able
to immediately check

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for understanding to see

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if the students actually
could apply the proportional

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reasoning rather than
just solving a proportion.

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Both Philip and I believe

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that in today's diverse
classrooms teachers really

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need to carefully
select problems,

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and these problems need to
include context and vocabulary

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that are familiar
to their students.

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There have been studies
that show that students

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that have practiced with word
problems involving people,

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places, and things
they know do better

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on word problem tests.

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Ogbuehi: The question to ask
is this: Is the problem given

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in the context a way the
student will understand?

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The teacher will endeavor
to select a problem

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or write problems that
are culturally relevant

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and responsive.

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Certain words in mathematics
have multiple meanings,

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which can confuse
some English learners.

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A word such as table,
we use it a lot in math,

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but it has a different meaning
than the table where we eat.

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Analyzing the problem earlier
and identifying the vocabulary

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which will be problematic
to the understanding

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of the math problem itself.

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We adjust how we teach to
the needs and experiences

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of students by using
their cultural knowledge

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to make learning in
context more relevant

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and effective for them.

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It's not to make the
problem less challenging,

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instead to allow
students to focus

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on the mathematics
and the problem.

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The teacher has to consider
whether the problem is

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rigorous enough; whether it
is routine or nonroutine;

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is the problem open-ended,

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which can have multiple
entry points.

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By multiple entry points,

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we mean different solution
strategies, not just one

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or two; which familiar

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or unfamiliar words are
contained in the problem.

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By looking at all this, the
teacher will know the best way

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to package a problem
before implementing it

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in the classroom.

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Herzig: It's very
good for teachers

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to use nonroutine
problems periodically,

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and the reason is because
it helps children develop

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strategic thinking.

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Routine problems can be
solved using methods familiar

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to students by replicating
previously learned methods

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in a step-by-step fashion.

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A nonroutine problem,
they are problems

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for which there is
actually not a predictable,

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well-rehearsed approach or
pathway suggested by the task.

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A good example of this is that
there are 20 people in a room,

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everybody high-fives
with everybody else,

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how many high-fives occurred?

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The interesting thing is,
what is a nonroutine problem

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for some people can be a
routine problem for others.

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And let me give you
an example of that.

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For a third, fourth,
or fifth grader,

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the high-five problem
would be nonroutine

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because they do not have
the algebraic knowledge

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to be able to solve it.

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For an algebra student,
however,

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the high-five problem
would be very routine

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because they have the
concept of algebra enough

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that they would be able
to solve that problem.

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Ogbuehi: I will use this
guide with my teachers

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in planning professional
development.

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We have diverse student
population in our classrooms,

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and we have to consider them
as we plan lessons and also

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as we deliver problem
solving in the classroom.

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