WEBVTT

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[Music] Welcome to the overview

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on Developing Effective
Fractions Instruction

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for Grades K-8.

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U.S. students' mathematics
skills have fallen short

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for many years, lagging behind
the achievement of students

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in European and Asian countries.

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Alarmingly, only
a small percentage

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of U.S. high school graduates
have the mathematics skills

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needed for success
in the workforce

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and for postsecondary education
in science, technology,

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engineering, and
mathematics -- the STEM fields.

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Successive national
policy reports

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about reforming mathematics
instruction have consistently

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highlighted one particular
problem:

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U.S. students have a weak
understanding of fractions,

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which is impeding their
learning of algebra

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and advanced mathematics.

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The National Council of Teachers
of Mathematics' Focal Points,

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the National Mathematics
Advisory Panel,

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and more recently the
Common Core Standards,

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all have emphasized
the importance

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of building conceptual
understanding

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of rational numbers;
that is, fractions,

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decimals, and percents.

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Results from national
assessments underscore the

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weakness in student
understanding of fractions.

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On the National Assessment
of Educational Progress,

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only half of eighth graders
could order fractions

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from least to greatest.

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Less than one third of seventeen
year olds could accurately

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identify equivalent
fractions and decimals.

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Those and other results have
led researchers to conclude

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that a high percentage

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of students lack conceptual
understanding of fractions,

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limiting their ability to
solve problems with fractions

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and apply computational
procedures with fractions.

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Students don't often grasp that
fractions are numbers at all

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or they confuse the
properties of fractions

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with those of whole numbers.

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Lacking conceptual
understanding,

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students may simply try
to memorize manipulations

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of fractions as symbols, a
tactic that quickly breaks down.

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To improve the teaching
of fractions,

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experts recommend four practices

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that help children develop
skills as they progress

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from early elementary
school into middle school.

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The first is aimed at building
the foundational knowledge

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of young students.

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The other three recommendations
target students

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in the intermediate and
middle school years.

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Because children enter school
with a rudimentary understanding

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of sharing and proportionality,

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the first recommended
practice is

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to build basic fraction concepts

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from students' informal
understandings.

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Teachers can build on
what children as young

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as preschool understand
intuitively,

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such as how to share equally a
set of objects, such as cookies,

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among a group of people or how
to divide a single whole object,

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a sandwich, into equal shares.

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In this way, teachers
make connections

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between students'
informal knowledge

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and formal fraction concepts.

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The second recommendation
is to use number lines

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to develop students'
understanding

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of fractions as numbers.

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Number lines are a flexible
representational tool

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that can be used with simple as
well as more complex problems.

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They can be used to illustrate
the magnitude of fractions,

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the relation between whole
numbers and fractions,

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and the relations
among fractions,

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decimals, and percents.

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Understanding that fractions
are numbers with magnitudes

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that can be ordered

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or considered equivalent
is fundamental

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to grasping operations
with fractions.

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The third recommendation is

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to help students understand
why computational procedures

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with fractions make sense.

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Students need to understand
why procedures make sense

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to become truly proficient
with operations -- adding,

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subtracting, multiplying,
and dividing fractions.

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Students often cannot explain
why common denominators are

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necessary to add and subtract
fractions but not multiply

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or divide them, and
they may be puzzled

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when dividing a fraction
results in a quotient larger

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than the number being divided.

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The fourth recommendation
is to develop concepts

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about proportional
relationships before teaching

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computational procedures.

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Proportional thinking involves
understanding multiplicative

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relationships between quantities
and is a central preparation

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for more advanced
work in mathematics.

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Teachers should develop
students' understanding

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of proportional reasoning
before teaching the

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cross-multiplication
algorithm as a procedure

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for solving problems involving
ratios, rates, and proportions.

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All four recommended practices
depend on teachers' knowledge

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of mathematics and
their knowledge

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of strategies to
teach mathematics.

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Far too many teachers can
apply computational algorithms

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to solve problems with fractions

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but they don't know why
the algorithms work or how

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to explain alternative
procedures to their students.

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Effective instruction

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about fractions combines
conceptual understanding

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and procedural knowledge.

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It requires that teachers
have multiple ways to explain

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and represent fractions going
beyond part whole explanations.

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Teachers should be fluent with a
range of visual representations

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and know about the common
misconceptions that interfere

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with students' understanding
operations with fractions.

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Professional development
programs

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in mathematics should
place a high priority

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on improving teachers'
understanding of fractions

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and of how to teach them.

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You will find materials on this
site to provide information

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about the teaching of fractions

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across the elementary
and middle grades.

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Each recommended practice
includes background information,

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expert explanations of content
and pedagogy, and examples

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of how teachers have
implemented the practices.

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Begin with the multimedia
overviews and expert interviews

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for each practice in the
Learn What Works section.

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Watch teachers using the
recommended teaching practices

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in the See How It Works section
and download sample materials.

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Use the tools in the
Do What Works section

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to conduct your own professional
development, develop lessons,

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and review existing practices.

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[Music]