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Using the PLC Structure to Better Understand how
to Investigate the Iowa Core in Math
Brian Townsend
University of Northern Iowa
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Brian Townsend
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Associate Professor of
Mathematics at University of
Northern Iowa
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Specific area of research is
algebraic reasoning.
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brian.townsend@uni.edu
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Focus
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Iowa Core Math
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Specifically the Standards for Mathematical Practice
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Role of PLCs in improving mathematics instruction in
grades K-12
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 “We
are currently on a journey that has the potential
to make an unprecedented difference for students if
we think purposefully about how to change practice
and about the content that we teach.”
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NCTM President Linda M. Gojak referring to CCSSM in NCTM
Summing Up, July 9, 2013
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Poll: What is your role with PLCs?
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Poll: What is the role of the
mathematics teacher?
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What Do You Know About the Standards
for Mathematical Practice?
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Take a minute (especially if you’re meeting with a group) and
then document something that you know about the Standards
for Mathematical Practice.
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If you don’t feel that you know very much, please state that.
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Why Focus on Standards for
Mathematical Practice?
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The practices are important for teachers of mathematics at all
grade levels, K-12.
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“The Standards for Mathematical Practice describe varieties of
expertise that mathematics educators at all levels should seek to
develop in their students.” –IC Mathematics, page 8
Investigating the practices will help math teams develop a
shared vision of what teaching and learning mathematics
looks like.
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Why Focus on Standards for
Mathematical Practice?

Teachers can apply their learning directly to any
mathematical content.


Understanding the Mathematical Practices is important as PLCs
work on lesson development and assessment for all mathematical
topics at every grade level.
The Practices connect to other content areas.
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College instructors rate the Mathematical Practices as being of
higher value for students to master in order to succeed in their
courses than any of the CCSS content standards. This was true for
mathematics, language, science, and social sciences college
instructors. -Common Core Mathematics in a PLC at Work,
Leader’s Guide, pp. 27-28
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Standards for Mathematical Practice
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8 practices, IC pages 8-10.
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Not new, but based in best practice in mathematics education
over past 20-25 years - Based on NCTM process standards
(1989 and 2000) and National Research Council’s Report
Adding It Up (2001).
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Practices describe how students engage in learning
mathematics.

SMP are the key to improving mathematics teaching and
learning.
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SMP 1: Make Sense of Problems
and Persevere in Solving Them
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Refers to the ability of students to explain to themselves (and
others) the meaning of a mathematical task or problem and
look for entry points to its solution (NGA & CCSS, 2010, p. 5).
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Problem solving is one of the hallmarks of mathematics and
is the essence of doing mathematics (NCTM, 1989).
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When students are engaged in problem solving, it means
they are drawing on their understanding of mathematical
concepts and procedures with the goal of reaching a
successful response to the problem. (Kanold & Larson, 2012)
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Perseverance
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Teachers often avoid using problem-solving tasks and
activities that challenge students to persevere.

Often, teachers will take a challenging problem and make it
procedural.


TIMSS Videotape Classroom Study (Stigler et al.)
Reduces the level of cognitive demand (Smith & Stein, 2008)
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What Does SMP 1 Look Like?
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Students make conjectures about the meaning of a solution
and plan a solution pathway.
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Students try special cases or simpler forms to gain insight.
(They hypothesize and test conjectures.)
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Students monitor and evaluate their progress and discuss
with others.
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Students understand multiple approaches and ask the
question, “Does this solution make sense?”
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Students explain correspondence between equations, tables,
graphs, verbal descriptions, and data, an they search for
regularity, patterns, or trends. (Kanold & Larson, 2012)
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Beam Problem
The length of a beam is determined by the number of rods along the underside.
1. How many rods are needed for a beam of length 5? Length 10? Length 20? 47?
2. Write a rule that will allow you to determine the number of rods needed for a beam of
any length.
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Note:
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Successful problem solving does not mean that students will
always conclude with the correct response to a problem.
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Rather, students will undertake a genuine effort to engage in
the problem-solving process, drawing on learning resources
described in the other practices such as:
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appropriate tools
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using their prior knowledge
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engaging in mathematical discourse with other students
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and asking questions to make progress in the problem-solving
process. (Kanold & Larson, 2012)
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Chat:
1.
What might a teacher do to reduce the cognitive demand
of the task?
2.
What would the difference be in what the students would
learn?
3.
Why do we want our students to be able to solve nonroutine challenging problems?
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Chat: Role of Teacher
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How can Teachers Address
Mathematical Practice 1?

Teachers play the important role in supporting students’
ability to make sense of problems and persevere in solving
them. The first of these roles is the presentation of
appropriate problems or tasks for students to solve.
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Six questions to consider in your PLC when planning lessons
to assess the quality of problem solving within a common or
shared mathematical task. (Kanold & Larson, 2012)
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Six Questions:
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Is the problem interesting to students?
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Does the problem involve meaningful mathematics?
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Does the problem provide an opportunity for students to
apply and extend mathematics?
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Is the problem challenging for students?
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Does the problem support the use of multiple strategies or
solution pathways?
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Will students’ interactions with the problem and peers reveal
information about their mathematical understanding?
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Post Lesson Questions:
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Is there evidence that students are learning other ways of
solving the problem?
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Is there evidence that students are making and learning
mathematical connections to other problems?
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Is there evidence students are making the effort to
persevere when solving the problem? (Kanold & Larson,
2012)
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Next Webinar with Brian
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March 8th 3:30-4:30
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Connecting today’s learning to other standards of
mathematical practice.
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Survey