Discuss homework at your table:

Building Students’ Understanding:
The Equal Sign
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Resource Inventory (what do you use?)
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Growth Mindset
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Focal Student Update
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Michigan Integrated Mathematics Initiative
MI 2 – Day 3
8:00 a.m. - 3:00 p.m
.
2

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Warm-up & Address Homework
Common Core State Standards
Smarter Balanced Assessments
Atlas Rubicon
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Unit Perspective
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8 mathematical practices
Lessons 6 – 8
Lunch
Atlas, Progression, & Turn on math
TTLP Article
Lesson Planning Tool (with focal student in mind)

(CCSSM)
“ These standards are not intended to be new names for old ways of doing business. They are a call to take the next step.
”
4

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Deepen understanding of CCSS
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Content
Practice
Instruction
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Assessment (day 5)
Explore CCSS Units
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Atlas
Turn on CC
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Highlight Lessons
Consider strategies for increasing accessibility
5

Why do the
Standards for
Mathematical
Practice matter?
6

Working Together:
Governors and Chief State School Officers http://www.corestandards.org/
8

Standards for Practices
Standards for Concepts and
Procedures
 Greater balance of concept and skill development
 Greater access for all students
 Major shifts include:
• Standards for Mathematical Practices
• Attention toward content as it develops within and across grades levels (trajectories)
• Teaching with and assessing high demand tasks
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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. These practices rest on important ‘processes and proficiencies’ with longstanding importance in mathematics education.
” (CCSS,
2010)
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William
McCallum
Standards for
Mathematical
Practice
Tucson, April
2011
Reasoning and explaining
Modeling and Using tools
Seeing Structure and
Generalizing
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Mathematics
 Standards for Practice
 Standards for Concepts and Procedures
What implications do you foresee as you consider attending to both types of standards?

Learning Trajectories and the
Common Core State Standards
“ A teacher or test designer seeing exclusively within the grade level will miss the point [of the number line]. Multi-grade progression views of standards can avoid many misuses of standards ” (p.43).
13

CCSS States and the
Balanced Assessment Consortium http://www.corestandards.org/ http://www.smarterbalanced.org
14

Claims for Mathematics
Summative Assessment
Claim 1:
Concepts and
Procedures, ≈ 40%
“Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.”
Claim 2:
Problem Solving
≈ 20%
Claim 3:
Communicating
Reasoning ≈ 20%
“Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.”
“Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.”
Claim 4:
Data Analysis and
Modeling ≈ 20%
“Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.”
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These new assessment are scheduled to begin in the spring of 2015!

 What do the tasks in each color category have in common?
 What do tasks like these potentially reveal about student understanding?
 What do the tasks like these potentially mislead about student understanding?
17

The goal of the Common Core State Standards
Initiative (CCSSI) is to provide support and direction for educators as they move toward full implementation:
CCSS are organized into an aligned curriculum of coherent units of study. The resources are particularly designed to highlight needed shifts in content related and pedagogical practices.
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Unit Template
Highlight Lesson
Formative Assessment
Resources (video, sample student work, rubrics, instructional websites, etc.)

 Emphasis on the use of student thinking within instruction and assessment
 Content and practice standards that call for a balance of conceptual understanding and procedural fluency
 Incorporation of mathematical explanations
 Use of multiple representations (Technology)
 Integration of accessibility strategies (Universal Design for
Learning, UDL)
 Learning opportunities and assessments that include inquiry and exploration
Tools to support implementation …
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Grade Level Unit Components
1.
2.
3.
4.
•
•
•
•
Unit Themes
Graphic
Focus Questions
Intellectual Processes
Key Concepts
•
•
Content Standards
Abstract
CCSS Standards
•
•
•
•
•
Instructional Resources
Illuminations
Children ’ s Literature
Texas Instruments
References
Applets
•
•
Professional Resources
NCTM Articles
Books
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Refer to one unit of study for examples that articulate the components of the unit template.
1.
2.
What opportunities for helping teachers understand the standards as a set of related ideas and teach the mathematics in a way that emphasizes connections between and among mathematical ideas?
How might a single unit support teachers in making both content related and pedagogical shifts in practice?
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 Read Units
 Record your findings
 1 person report
26

We will reconvene at 12:45 p.m. to begin work on the formative assessment.
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1.
3.
2.
•
•
•
•
Model Lesson Themes
Graphic
Focus Questions
Intellectual Processes
Key Concepts
•
•
•
Model Lesson Content
Standards
Abstract
CCSS Standards
Lesson Instructional
Resources
•
•
•
•
Sequence of Lesson Activities
Selecting and Setting up a
Mathematical Task
Launch
Supporting Students ’
Exploration of the Task
Sharing and Discussing the
Task
28

29

 Do the Math
 Discuss the Teacher Resource Materials Available
 Browse Atlas
 Lesson Planning Groups
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Units, Highlight Lessons, Formative Assessments and other resources available in Atlas by Rubicon http://tinyurl.com/MAISAunit
31

 Units of Study
 Lesson resources
 Assessment resources
 Professional resources
• Video
• Sample student work
• And more
32

and
The Mathematical Tasks Framework
Tasks as they appear in curricular materials
Tasks as set up by teachers
Tasks as enacted by teachers and students
Student learning
Stein, Grover & Henningsen (1996)
Smith & Stein (1998)
Stein, Smith, Henningsen & Silver (2000)
33

Smith, M.S., Bill, V., & Hughes, E.K.
(2008). Thinking through a lesson:
Successfully implementing highlevel tasks. Mathematics Teaching in
the Middle School, 14, 132-138.
34

 Insert 5 minute timer here
35

Orient yourself with the format of a Highlight
Lesson .
1.
2.
Compare a Unit and the corresponding Highlight
Lesson, how are they related and how are they unique?
What about this lesson format might support teachers in making both content related and pedagogical shifts in practice.
40

Formative Assessment: A Difference that Can
Make a Difference!
Black and Wiliam (1998) report, based on their extensive review of research, typical effect sizes of formative assessment experiments are between 0.4 and 0.7.
• These results are larger than most instructional innovation strategies.
“…the evidence is that ways of managing formative assessment that work with the assumptions of "untapped potential" do help all pupils to learn and can give particular help to those who have previously struggled (Black and
Wiliam, p. 11).
”

A Formative Assessment Strategy
Reengagement:
 is a formative assessment strategy by which teachers use information from student work to design a learning opportunity that is an evolution of the original task and is focused on enhancing students’ current understandings ;
 is grounded in the effective and intentional use of student thinking to forward learning; and
 requires interactions between and among teachers, students, and the content to be learned.
42

1. Pick an idea that came up today and that you found particularly interesting. What is your current thinking about this idea? What questions do you still have?
2.What is your reaction to the work we did today?
What seems promising and/or challenging at this point?
49

Geraldine Devine geraldine.devine@oakland.k12.mi.us
Dana Gosen dana.gosen@oakland.k12.mi.us
Valerie Mills valerie.mills@oakland.k12.mi.us
Jim Randall james.s.randall@gmail.com
Carrie Zielinski carrie.zielinski@oakland.k12.mi.us
50

Connections Across Grade Levels:
Exploring a Trajectory
Review the three units in your grade band and consider how the mathematics progresses over time.
1.
What do you notice about the development of the mathematics?
2.
How might understanding this mathematical trajectory impact instruction?
51