Warm-Up
Discuss homework at your table:
 TTLP Thinking Through a Lesson
Protocol
 Resource Inventory (what do you
use?)
 Focal Student Update
 Growth Mindset
1
Michigan Integrated Mathematics Initiative
MI 2 – Day 3
8:00 a.m. - 3:00 p.m.
2
Agenda
 Warm-up & Address Homework
 Common Core State Standards
 M-Step / SBAC
 Atlas Rubicon
 Unit Perspective
 8 mathematical practices
 Lessons 6 – 8
 Lunch
 Atlas Rubicon
 Lesson Planning Tool (with focal
student in mind)
Common Core State Standards for
Mathematics (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
Goals
 Deepen understanding of CCSS
 Content
 Practice
 Instruction
 Assessment (day 5)
 Explore CCSS Units
 Atlas
 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/
Mathematics Standards
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
9
Standards for
Mathematical Practice
“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)
10
Standards for
Mathematical Practice
William
McCallum
Standards for
Mathematical
Practice
Tucson, April
2011
Reasoning and explaining
Modeling and Using tools
Seeing Structure and
Generalizing
11
Common Core State Standards
Mathematics
 Standards for Practice
 Standards for Concepts
and Procedures
What implications do you foresee as you
consider attending to both types of standards?
CCSS States and the
Balanced Assessment Consortium
http://www.corestandards.org/
http://www.smarterbalanced.org
14
Assessment Transition
 M-STEP includes the following assessments:
• A Spring summative assessment for grades
3-8
• A Michigan Merit Exam (MME) for grade 11,
which includes a college entrance exam; a
work skills component; and a summative
component aligned to Michigan content
standards
Assessment Transition
 MDE will be working with the USED to update
Michigan’s school accountability model used in its
flexibility waiver to the federal No Child Left Behind Act.
 In these discussions with USED, it will be the Michigan
Department of Education’s intent to use the test data
from this transitional year for a trial run of a revised
accountability system. It is the intent of the Department
that the results of the trial run of accountability would
be shared with schools and districts for local decision
making, but that no consequences would be applied.
M-STEP Components

The test is comprised of a:
• Computer Adaptive Test (CAT),
• Classroom Activity, and a
• Performance Task (PT).
M-STEP Components
 The purpose of the Classroom Activity is to
introduce students to the vocabulary and the
context of the Performance Task to follow.
 The Classroom Activity:
• is a 30-minute scripted lesson presented to the students;
• should be administered as close as possible, but no more
than 3 days prior to the administration of the Performance
Task (PT);
• may occur on the same day as the PT; and
• is delivered in class by the teacher, not online.
M-STEP Components
 The Performance Task (PT) is a multi-item task
administered online.
 Within this PT students are presented with several stimuli.
They will respond to a combination of:
• Technology Enhanced (TE) items,
• short Constructed Response (CR), and
• extended CR items.
 Administering the PT without first administering the
Classroom Activity is considered a testing irregularity.
Claims for Mathematics
Summative Assessment
Claim 1:
Concepts and
Procedures, ≈ 40%
Claim 2:
Problem Solving
≈ 20%
Claim 3:
Communicating
Reasoning ≈ 20%
Claim 4:
Data Analysis and
Modeling ≈ 20%
“Students can explain and apply mathematical concepts and
interpret and carry out mathematical procedures with
precision and fluency.”
“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.”
“Students can analyze complex, real-world scenarios and can
construct and use mathematical models to interpret and
solve problems.”
20
A Balanced Assessment System
These new assessment
are scheduled to begin
in the spring of 2015!
Smarter Balance Practice Tests
http://sbac.portal.airast.org/practice-test/
22
Testing Share Out
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Common Core State Standards
Oakland Initiative
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.




Unit Template
Highlight Lesson
Formative Assessment
Resources (video, sample student work,
rubrics, instructional websites, etc.)
Key Features of CCSS
Curriculum
 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 …
28
Grade Level Unit Components (Atlas)
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
29
Orientation to the Unit (Atlas)
Refer to one unit of study for examples that
articulate the components of the unit template.
1.
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?
2.
How might a single unit support teachers in making both
content related and pedagogical shifts in practice?
30
Atlas Unit Similarity & Differences
 Read Units
 Record your findings
 1 person report
31
Lunch
We will reconvene at 12:45
p.m. to begin work on the
formative assessment.
32
Highlight Lesson Components
1.
Model Lesson Themes
•
•
•
•
2.
Model Lesson Content
Standards
•
•
•
3.
Graphic
Focus Questions
Intellectual Processes
Key Concepts
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
33
Highlight Lesson
34
Baseball Lesson
 Do the Math
 Discuss the Teacher Resource Materials Available
 Browse Atlas
 Lesson Planning Groups
35
Atlas Curriculum Mapping
Units, Highlight Lessons, Formative Assessments
and other resources available in Atlas by Rubicon
http://tinyurl.com/MAISAunit
36




Units of Study
Lesson resources
Assessment resources
Professional resources
• Video
• Sample student work
• And more
37
Teachers and Tasks Matter
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)
38
Thinking Through a Lesson Protocol
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.
39
Lesson Planning & Article
 Insert 5 minute timer here
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).”
Reengagement
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
The CCSS Resources are…
• not self-enacting
• raw materials to
support teachers as
they reorganize their
instruction and work
to implement the
CCSS
44
Lesson Plan and Assessment
 Focal Student
 Smarter M-STEP connection to assessment
 Lesson Planning
 Performance tasks
45
End of Day Reflections
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?
46