baltimore day6 12breakouthandout
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September 24th presentationTRANSCRIPT
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
Dr. Timothy Kanold 2012 tkanold.blogspot.com
Our 2nd outcome for this session
Examine Mathematics Teaching and Learning through the CCSS Mathematical Practices
Dr. Timothy Kanold 2012 tkanold.blogspot.com
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/
Dr. Timothy Kanold 2012 tkanold.blogspot.com
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
Dr. Timothy Kanold 2012 tkanold.blogspot.com
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.
Dr. Timothy Kanold 2012 tkanold.blogspot.com
Common Core State Standards
Learning how and why is now part of the guaranteed and viable
curriculum!
Mathematical
PracticesMathematical
Content
UNDERSTANDING
Dr. Timothy Kanold 2012 tkanold.blogspot.com
THE CCSS TPOV for Mathematics Instruction HO p.3
Built on a foundation of the 8 standards for Mathematical Practice
Dr. Timothy Kanold 2012 tkanold.blogspot.com
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…
Dr. Timothy Kanold 2012 tkanold.blogspot.com
• 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?”
Dr. Timothy Kanold 2012 tkanold.blogspot.com
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
Dr. Timothy Kanold 2012 tkanold.blogspot.com
3. Construct viable arguments and critique the reasoning of others
Dr. Timothy Kanold 2012 tkanold.blogspot.com
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
The Standards for [Student] Mathematical Practice
SMP # 2 Reason abstractly and quantitatively
Mathematically proficient students make sense of
quantities and their relationships in problem
situations… Contextualize and De-contextualize
Dr. Timothy Kanold 2012 tkanold.blogspot.com
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.
Dr. Timothy Kanold 2012 tkanold.blogspot.com
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
The Standards for [Student] Mathematical Practice
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?
Dr. Timothy Kanold 2012 tkanold.blogspot.com
Our 3rd outcome for this session
3) Discuss Lesson Planning Tools to help you implement the Standards for Mathematical Practice
Dr. Timothy Kanold 2012 tkanold.blogspot.com
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
Dr. Timothy Kanold 2012 tkanold.blogspot.com
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?
Dr. Timothy Kanold 2012 tkanold.blogspot.com
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
Dr. Timothy Kanold 2012 tkanold.blogspot.com
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?
Dr. Timothy Kanold 2012 tkanold.blogspot.com
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…
Dr. Timothy Kanold 2012 tkanold.blogspot.com
Our 2nd Outcome for this session
Examine parts of the CCSS High School content and 6-12 progressions
Dr. Timothy Kanold 2012 tkanold.blogspot.com
Standards for Mathematical Content (book p. 66)
Dr. Timothy Kanold 2012 tkanold.blogspot.com
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…
Dr. Timothy Kanold 2012 tkanold.blogspot.com
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
Dr. Timothy Kanold 2012 tkanold.blogspot.com
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?
Dr. Timothy Kanold 2012 tkanold.blogspot.com
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
Dr. Timothy Kanold 2012 tkanold.blogspot.com
Dr. Timothy Kanold 2012 tkanold.blogspot.com
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
Dr. Timothy Kanold 2012 tkanold.blogspot.com
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?
Dr. Timothy Kanold 2012 tkanold.blogspot.com
Our 3rd Outcome for this session
Resources…
Dr. Timothy Kanold 2012 tkanold.blogspot.com
www.mathccc.org
Dr. Timothy Kanold 2012 tkanold.blogspot.com
Mathematics Assessment Project (MAP) http://map.mathshell.org.uk/materials
Dr. Timothy Kanold 2012 tkanold.blogspot.com
Tools for the Common Core Standardscommoncoretools.wordpress.com
Dr. Timothy Kanold 2012 tkanold.blogspot.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.
Dr. Timothy Kanold 2012 tkanold.blogspot.com
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.
Dr. Timothy Kanold 2012 tkanold.blogspot.com
illuminations.nctm.org/Lessons.aspx
Dr. Timothy Kanold 2012 tkanold.blogspot.com
Dr. Timothy Kanold 2012 tkanold.blogspot.com
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?