Baltimore day6 12breakouthandout

Leading the Teaching and Learning
of Mathematics in the CCSS Era!
As you enter the room
At your tables….
Choose a corner and list 2-3 vital teacher
team behaviors essential to highly effective
Instructional practices used in your school or
by your team…
Do not write in the middle circle of the sheet!
Thank you!
Dr. Timothy Kanold
tkanold.blogspot.com
Dr. Timothy Kanold 2012 tkanold.blogspot.com

Our outcomes for this session
1) Examine your history as a PLC
collaborative team

2)Examine Mathematics Teaching and
Learning through the lens of the CCSS
Mathematical Practices

2) Discuss Lesson Planning Tools to
implement the Standards for
Mathematical Practice

Common Core Mathematics in a
PLC at Work™ Series Ch. 2

Ch. 1: The Paradigm of
Collaboration

Using High Performing
Collaborative Teams
for Mathematics…

Better at …


Leading the Teaching and Learning
of Mathematics in the CCSS Era!
Complete
the Team
History tool
p.1 -2


Our 2nd outcome for this
session

Examine Mathematics Teaching and
Learning through the CCSS
Mathematical Practices


http://www.flickr.com
/photos/shawnparker
photo/6637823915/in
/photostream/

How students
learn... and
demonstrate
proficiency in
Mathematics…

Noel Tichy – Your Teachable
Point of View or TPOV

“A cohesive set of ideas and
concepts that a person is
able to clearly articulate to
others.”
Director, Global Leadership Program
& Professor of Management and
Organizations tkanold.blogspot.com
Dr. Timothy Kanold 2012

Your TPOV for Effective Instruction

Find your poster paper on
the Wall… work with your
colleagues to create a
“Matchbook” description of
your vision for effective
instruction…
18 words or less – pictures
allowed Dr. Timothy Kanold 2012 tkanold.blogspot.com

THE CCSS TPOV for Mathematics
Instruction

Unit and Lesson design will require a
depth of conceptual understanding
andprocedural fluency regardless of
the content…
demonstrated by the students.


Learning how and why is now part
of the guaranteed and viable
curriculum!
Common Core State Standards

U
N
D
E
R
Mathematical S
Mathematical
T

Content
A Practices
N
D
I
N
G


THE CCSS TPOV for Mathematics
Instruction HO p.3

Built on a foundation of the 8 standards
for Mathematical Practice


The Standards for Mathematical
Practice (See Handout p.3-7)

Choose Practice 1,2, 3, 4, 5 or 6
Highlight the verbs that illustrate
student actions!
Circle, highlight or underline
phrases for your chosen
practice…

• PaBook page 29

HS Book page 29…

The Common Core Standards for
[Student] Mathematical Practice p.29
1. What is the intent and why it is
important?
2. What teacher actions help to
develop this CCSS MP?
3. What evidence exists that students
are demonstrating this MP?
MP1: Explain and Make Conjectures…

Book p. 31-32


Developing Reasoning Habits of Mind

1)Provide tasks that require students to figure things
out for themselves (The AHA moment)
2)Move from Empirical (experiment that supports
some cases), to pre-formal (intuitive) to formal
(arguments for mathematical certainty)
3)Plan for and expect student communication of
their reasoning to classmates and the teacher –
using proper vocabulary
4)Use questions and prompts such as “How do you
know?” And “Why does this work?”


The Standard for Mathematical
Practice #3 Book p. 37
MP # 3 Construct viable arguments and
critique the reasoning of others
1) Students make conjectures
2) Students justify their conclusions
and communicate them to others
3) Students compare the effectiveness
of two plausible arguments
4) Students listen and respond to the
arguments of others for sense making
and clarity Dr. Timothy Kanold 2012 tkanold.blogspot.com

3. Construct viable arguments and
critique the reasoning of others


The Standards for Mathematical
Practice HO p.8
Rich Mathematical Tasks…
Qualitative Reasoning and McDonald’s

With a shoulder partner!

Wikipedia reports that 8% of all
Americans eat at McDonalds every
day
310 Million Americans and 12,800
McDonalds…
Make a conjecture and create a
mathematical argument…

The Standards for [Student]

SMP # 4 Model with Mathematics
Mathematically proficient students
can apply the mathematics they
know to solve problems arising in
everyday life, society, and the
workplace…



SMP # 2 Reason abstractly and
quantitatively
Mathematically proficient students
make sense of quantities and their
relationships in problem
situations…
Contextualize and
De-contextualize

Unit by Unit planning for high
cognitive demand tasks…

N.Q.1: Use units as a way to
understand problems and to guide the
solution of multi-step problems;
choose and interpret units consistently
in formulas;
N.Q.3: Choose a level of accuracy
appropriate to limitations on
measurement when reporting
quantities.

The Power of a Stage 6 and 7
Collaborative Team…) HO p. 8
In your teacher Teams:
Discuss your expectations for student
demonstration of quality work in defense of
their mathematical argument for the
problem.

Discuss how your lesson plan for this
problem would promote student
communication of their argument with
others and respond to one another based
on their solution defense.


HO Page 9

Shoulder Partner Discussion…

•To what degree do you believe your
students are currently demonstrating
proficiency in the standards for
mathematical practice?

• How might you use this information so far
to identify starting points for your work
with the Standards for Mathematical
Practice?

Our 3rd outcome for this
session

3) Discuss Lesson Planning Tools to
help you implement the Standards
for Mathematical Practice


Planning Lessons Together!

• Professional Learning Communities
are essential to good planning.

• Read the Elements of Effective
Lesson Design (HO p.10-11)
Or book p.46-49 Explanations – page 49-57

• How are each of these elements
connected to your current
teaching? Dr. Timothy Kanold 2012 tkanold.blogspot.com

CCSS Mathematical Practices
Lesson Design Tool… HO p.12-13


CCSS Mathematical Practices
Lesson Design Tool

Take a moment to scan the elements
of this lesson design and/or reflection
tool…

How could you use this tool with your
team in 2012-2013?


Our outcomes forthe content
session
1) Examine the difference between
relevant and meaningful mathematics

2)Examine parts of the CCSS High
School content and 6-12 progressions

3) Discuss Course Scope and
Sequencing for grades 6-12

Common Core Mathematics in a
PLC at Work™ Series Ch.3

The Mathematics Curriculum
of the CCSS…

With a shoulder partner…
– Share your understanding of
the difference between
relevant mathematics and
meaningful mathematics


Relevance Vs. Meaning

Relevant mathematics:
References the context for the lesson
as part of essential mathematics
and mathematical tasks the
student needs to know. Ask
yourself….Does the lesson present
important and essential
mathematics?


Relevance Vs. Meaning

Meaningful mathematics:
References the context for the lesson
as containing elements that create
meaning, reasoning and sense
making for the student - while also
connecting to the students’ prior
knowledge and understanding…


Our 2nd Outcome for this
session

Examine parts of the CCSS High School
content and 6-12 progressions


Standards for Mathematical
Content (book p. 66)


High School Conceptual Categories
Conceptual categories in high school (App. C p. 175)
• Number and Quantity
• Algebra
• Functions
• Geometry
• Statistics and Probability
College and career readiness threshold
• (+) standards indicate material beyond the threshold
or needed for advanced courses; can be in courses
intended for all students.
• (*) specific modeling standards

Standards for Mathematical Content

Conceptual Categories
• Domains are larger groups of
related standards.
• Clusters are groups of related
standards.
• Standards define what students
should understand and be able to
do during a unit…


HS: Conceptual Category - Geometry

The 6 Domains
– Congruence
– Similarity, Right Triangles, and
Trigonometry
– Circles
– Expressing Geometric Properties with
Equations
– Geometric Measurement and
Dimension
– Modeling with Geometry

Conceptual Category– Geometry
Sample
book p. 183-187
• List the domainsforGeometry on chart
paper - horizontally
• List the clusters of standards for each
domain vertically…and count the number
of standards in each cluster (how many
are college prep and how many are
advanced?)
Which clusters/standards appear to be new
or more challenging for each of the
domains?


Geometry Progressions…

Middle school foundations
• Hands-on experience with transformations.
• Low tech (transparencies) or high tech (dynamic
geometry software).
High school rigor and applications
• Properties of rotations, reflections, translations,
and dilations are assumed, proofs start from
there.
• Connections with algebra and modeling

7-12 Increased emphasis…
• Statistics and Probability
– Interpreting Categorical and
Quantitative Data
– Making inferences and Justifying
Conclusions
– Conditional Probability and the Rules
of Probability
– Using Probability to Make Decisions


Discuss at your tables

What needs to be done in your district,
school or department to look at the
conceptual categories, clusters,
standards, and progressions in the 6-8
or the high school curriculum so that all
teachers understand…

The expectations of the grade level
content?


Our 3rd Outcome for this
session

Resources…


www.mathccc.org


Mathematics Assessment Project
(MAP)
http://map.mathshell.org.uk/materia
ls


Tools for the Common Core Standards
commoncoretools.wordpress.com


Mathematics Assessment Project
(MAP)
http://map.mathshell.org.uk/materia
ls
• 20 ready-to-use Lesson Units for Formative
Assessment for high school. cross referenced
to CCSS content and practices standards.
(Ultimately 20 per grade 7-12)
• Summative assessments, aimed at “College-
and Career-Readiness,” presented in two
forms:
(1) a Task Collection with each task cross-
referenced to the CCSS, and
(2) a set of Prototype Test Forms showing how
the tasks might be assembled into balanced
assessments.

The Illustrative Mathematics Project
illustrativemathematics.org

• Hyperlinked CCSS
• Developing a complete set of tasks for
each standard
– Range of difficulty
– Simple illustrations of single standards to
complex tasks spanning many standards.
• Provide a process for submitting,
discussing, reviewing, and publishing
tasks.


illuminations.nctm.org/Lessons.aspx


End of Day Reflections

1. Are there any aspects of
your own thinking and/or
practice that our work
today has caused you to
consider or reconsider?
Explain.

2. Are there any aspects of
your students’
mathematical learning that
our work today has caused
you to consider or
reconsider? Explain.

3. What would you like more
information about?

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