what instructional coaches need to know ... is in the room? instructional coaches? classroom...
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WHAT INSTRUCTIONAL COACHES NEED TO KNOW
ABOUT TEACHING MATHEMATICS
Jeanne Simpson
AMSTI Math Specialist
Who is in the room?
◦ Instructional Coaches?
◦Classroom teachers?
◦Administrators?
◦Support math only?
◦Elementary? Secondary? Both?
◦Have a math background?
◦How long have you been coaching?
Our Work with Coaches
Year 1 (2013-14)• Eleven districts, 87 coaches
• Three groups; two elementary and one secondary
Year 2 (2014-15)• Thirteen districts
• Forty additional coaches
Year 3 (2015-16)• Elementary - onsite support to coaches in 16 schools
• Secondary - monthly PLC for 17 coaches from 7 districts, plus onsite
support
What You Need to Know!
Standards for Mathematical Practice
Best Practices for Teaching Mathematics
Content Standards
Resources for Math Lessons
Coaching Skills
coachingformath.wikispaces.com/nctm+2016
Recommended Resources
1. Introduction
2. Leading high-performing collaborative
teams
3. Standards for Mathematical Practice
4. Content Standards
5. Teaching-Assessing-Learning Cycle
6. Response to Intervention
Principles to ActionGuiding Principles Teaching and Learning
Access and Equity
Curriculum
Tools and Technology
Assessment
Professionalism
Mathematics Teaching Practices
STANDARDS FOR MATHEMATICAL
PRACTICEWhat students should be doing as they learn mathematics
10
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments & critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
Jordan School District
PostersSMP Illustrations PD Modules
Tasks, student dialogue, mathematical
overview, PD course
Video, grade-specific, mentors
Standards of Mathematical Practice Proficiency Matrix
◦ Think-Pair-Share
◦ Showing thinking in classrooms
◦Questioning and wait time
◦Grouping and engaging problems
◦Using questions and prompts with groups
◦Allowing students to struggle
◦Encouraging reasoning
Students: (I) Initial (IN) Intermediate (A) Advanced
1a Make sense of
problems
Explain their thought processes in solving a
problem one way.
Explain their thought processes in solving a problem
and representing it in several ways.
Discuss, explain, and demonstrate solving a
problem with multiple representations and in
multiple ways.
1b Persevere in
solving them
Stay with a challenging problem for more
than one attempt.
Try several approaches in finding a solution, and
only seek hints if stuck.
Struggle with various attempts over time, and learn
from previous solution attempts.
2 Reason
abstractly and
quantitatively
Reason with models or pictorial
representations to solve problems.
Are able to translate situations into symbols for
solving problems.
Convert situations into symbols to appropriately
solve problems as well as convert symbols into
meaningful situations.
3a Construct viable
arguments
Explain their thinking for the solution they
found.
Explain their own thinking and thinking of others with
accurate vocabulary.
Justify and explain, with accurate language and
vocabulary, why their solution is correct.
3b Critique the
reasoning of
others.
Understand and discuss other ideas and
approaches.
Explain other students’ solutions and identify
strengths and weaknesses of the solution.
Compare and contrast various solution strategies
and explain the reasoning of others.
4 Model with
Mathematics
Use models to represent and solve a problem,
and translate the solution to mathematical
symbols.
Use models and symbols to represent and solve a
problem, and accurately explain the solution
representation.
Use a variety of models, symbolic representations,
and technology tools to demonstrate a solution to
a problem.
5 Use appropriate
tools
strategically
Use the appropriate tool to find a solution. Select from a variety of tools the ones that can be
used to solve a problem, and explain their
reasoning for the selection.
Combine various tools, including technology,
explore and solve a problem as well as justify their
tool selection and problem solution.
6 Attend to
precision
Communicate their reasoning and solution to
others.
Incorporate appropriate vocabulary and symbols
when communicating with others.
Use appropriate symbols, vocabulary, and labeling
to effectively communicate and exchange ideas.
7 Look for and
make use
of structure
Look for structure within mathematics to help
them solve problems efficiently (such as 2 x 7 x 5 has
the same value as 2 x 5 x 7, so instead of multiplying 14 x 5, which
is (2 x 7) x 5, the student can mentally calculate 10 x 7.
Compose and decompose number situations and
relationships through observed patterns in order to
simplify solutions.
See complex and complicated mathematical
expressions as component parts.
8 Look for and
express
regularity in
repeated
reasoning
Look for obvious patterns, and use if/ then
reasoning strategies for obvious patterns.
Find and explain subtle patterns. Discover deep, underlying relationships, i.e.
uncover a model or equation that unifies the
various aspects of a problem such as
discovering an underlying function.
SMP Proficiency Matrix
Grouping/Engaging
Problems
Grouping/Engaging
Problems
Grouping/Engaging
Problems
Pair-Share
Showing Thinking
Showing Thinking
Questioning/Wait Time
Questioning/Wait Time
Questioning/Wait Time
Questions/Prompts for
Groups
Questions/Prompts for
Groups
Pair-Share
Grouping/Engaging Problems
Questioning/Wait Time
Grouping/Engaging Problems
Grouping/Engaging Problems
Grouping/Engaging Problems
Allowing Struggle
Allowing Struggle
Allowing Struggle
Grouping/Engaging Problems
Showing Thinking
Encourage Reasoning
Grouping/Engaging Problems
Grouping/Engaging Problems
Showing Thinking
Showing Thinking
Encourage Reasoning
Encourage Reasoning
Encourage Reasoning
BEST PRACTICES IN MATHEMATICS
Mathematics Teaching Practices
1. Establish mathematics goals to focus learning.
2. Implement tasks that promote reasoning and problem solving.
3. Use and connect mathematical representations.
4. Facilitate meaningful mathematics discourse.
5. Pose purposeful questions.
6. Build procedural fluency from conceptual understanding.
7. Support productive struggle in learning mathematics.
8. Elicit and use evidence of student thinking
High-Leverage Team ActionsBefore the Unit
1. Making Sense of the Agreed-On Essential
Learning Standards and Pacing
2. Identifying High-Level-Cognitive-Demand
Mathematical Tasks
3. Developing Common Assessment Instruments
4. Developing Scoring Rubrics and Proficiency
Expectations for the Common Assessment
Instruments
5. Planning and Using Common Homework
Assignments
High-Leverage Team ActionsDuring the Unit
6. Using High-Level-Cognitive-Demand Mathematical Tasks Effectively
7. Using In-Class Formative Assessment Processed Effectively
8. Using a Lesson-Design Process for Lesson Planning and Collective Team Inquiry
After the Unit9. Ensuring Evidence-Based Student Goal Setting and
Action for the Next Unit of Study
10. Ensuring Evidence-Based Adult Goal Setting and Action for the Next Unit of Study
CONTENT STANDARDS
19
Structure of the Standards Content standards define what students should understand and be able to do
Clusters are groups of related standards
Domains are larger groups that progress across grades
Content Standard IdentifiersDomain
Standards
Cluster
Cluster
Statement
Standards Progressions
RESOURCES FOR MATH LESSONS
COACHING SKILLS
My favorite math coaching book…
◦SMP Look Fors
◦Shifts Self-Assessment
◦Seven Essential Planning
Questions
◦Lesson Plan Template
◦Vignette Sorting Activity
Other Great Books
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