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[Music] Welcome to the overview

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on Preparing Problems for
Classroom Instruction.

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When students are given mathematical
challenges in meaningful real-

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world problems, they are more
likely to strengthen their skills

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and gain a deeper understanding
of math concepts.

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Problem solving should not be
reserved solely for homework

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and individual practice assignments.

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It should be an active part

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of mathematics teachers'
classroom instruction.

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In order to effectively incorporate
problem solving into daily instruction,

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teachers need to allocate time to allow
for thoughtful selection of problems

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as they do their advance preparation.

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They will likely need to explore a
variety of supplementary materials

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to find relevant and appropriate
problems to extend the examples provided

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in their mathematics textbooks.

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For students to be able to focus on
the mathematics and reasoning required

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to solve a problem, they need
to be familiar with the context

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and language of that problem.

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Trying to learn background knowledge
and vocabulary at the same time

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as problem solving can
be counterproductive.

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When a math problem is couched in
terms and concepts that are foreign

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to students, they become distracted
from the goal of the exercise.

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Instead of focusing on the
mathematics and reasoning required

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to solve the problem, they focus on the
unfamiliar situation and vocabulary.

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Teachers can help students
by rewording problems,

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placing them in familiar contexts that
better align with students' backgrounds,

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and clarifying unfamiliar
words in advance.

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Students tend to engage more
actively and perform better

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when problems are presented
in personalized contexts

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that appeal to their interests.

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For example, consider the following
problem about grocery shopping:

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Mrs. Sears spent 2/5 of the money she
had for groceries at the meat store

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and then spent 1/3 of what
was left at the fish market.

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She had $30 left.

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How much did she start with?

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Changing the context of this question
so that it is about using gift cards

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at an electronics store may more
effectively engage students:

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On his first visit to Gadgets
Galore, Lee used 2/5 of the value

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of the gift card he got for Christmas.

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The next day he used
1/3 of what was left.

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$30 remained on the card.

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How much was the gift card
worth when he received it?

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To check on whether the context of
a problem is familiar to students,

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teachers might ask the class
to share what they know

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about that context before
working on the problem with them.

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These strategies are especially
important for English language learners

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and for students who are currently
struggling with mathematics.

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When considering whether
or not to use a problem,

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the teacher should take
some time to review

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with the class the mathematics
concepts required to solve it.

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The longer it has been since the
underlying concepts have been addressed,

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the more beneficial such a review will
be, especially for struggling students.

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It is important to explicitly teach
academic language and review the meaning

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of specialized mathematics vocabulary,
such as divisor or hypotenuse.

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For words that have multiple meanings,
such as area, table, root, and volume,

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teachers should be careful to note

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and distinguish how these words
are used in a mathematical context.

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This is particularly essential
for English language learners.

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To facilitate lively class
discussion about different approaches,

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teachers should try to present
problems with multiple entry points.

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To get started on a problem,
students might begin a problem

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by drawing a picture of key problem
elements, or preparing a representation

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such as a strip diagram, listing
what they know and need to know,

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or even acting out a
transaction in the problem.

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As students discover more than
one way to solve the problem,

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it may spur their curiosity,
deepen their engagement,

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and solidify their understanding
of mathematical concepts.

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Finally, teachers should
try to strike a balance

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between routine and non-routine
problems.

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Routine problems are those that can
be solved using familiar methods

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in step-by-step fashion -- even

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if the problem is cognitively
demanding and requires many steps.

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Routine problems can help students
strengthen their understanding

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of an operation or mathematical idea.

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Non-routine problems, on the other
hand, require that students grapple

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with new skills and mathematical
concepts

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that they may not yet have mastered.

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Unlike routine problems, these don't
have predictable solution paths.

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Non-routine problems help
students think strategically

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and apply mathematics in new situations.

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Of course, what is non-routine

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for a less experienced
problem solver may be routine

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for more advanced students.

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A teacher can increase students'
exposure to problem solving

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by providing worked examples
during seat-work and homework.

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Worked examples have benefits for
student learning, allowing students

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to see exactly how a new concept is applied,

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and can decrease the time needed to learn new skills.

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To learn more about Preparing
Problems for Classroom Instruction,

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please explore the additional resources
on the Doing What Works website.