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Leading the Teaching and Learning of Mathematics in the CCSS Era!

As you enter the roomAt 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 PracticeDr. Timothy Kanold 2012 tkanold.blogspot.com

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

The Pursuit of Equity and Access

Building Teacher and Administrator knowledge Capacity…

Ch. 1: The Paradigm of Collaboration

Using High Performing Collaborative Teams for Mathematics…

Better at …

Dr. Timothy Kanold 2012 tkanold.blogspot.com

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

Ch. 2 Paradigm of Instruction

Teaching and Learning

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

http://www.flickr.com/photos/shawnparkerphoto/6637823915/in/photostream/

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

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 and procedural fluency regardless of the content…

demonstrated by the students.

Common Core State Standards

Learning how and why is now part of the guaranteed and viable

curriculum!

Mathematical

PracticesMathematical

Content

UNDERSTANDING

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. 31-32Dr. Timothy Kanold 2012 tkanold.blogspot.com

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 vocabulary4)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 conjectures2) Students justify their conclusions and communicate them to others3) Students compare the effectiveness of two plausible arguments 4) Students listen and respond to the arguments of others for sense making and clarity

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] Mathematical Practice

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…Dr. Timothy Kanold 2012 tkanold.blogspot.com

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. Dr. Timothy Kanold 2012 tkanold.blogspot.com

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?

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 for the 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 6-12Dr. Timothy Kanold 2012 tkanold.blogspot.com

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 ProbabilityCollege 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 standardsDr. Timothy Kanold 2012 tkanold.blogspot.com

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 Samplebook p. 183-187

• List the domains for Geometry 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/materials

Tools for the Common Core Standardscommoncoretools.wordpress.com

Mathematics Assessment Project (MAP) http://map.mathshell.org.uk/materials• 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 Projectillustrativemathematics.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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