Transcript Green Belt: Lesson # Lesson Title

Orange Lesson:
Identifying Student Outcomes
from Learning Progressions
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A Process of Discovery, Support and Mastery
THE NATIONAL PATHWAY
CONDITIONS FOR SUCCESSFUL
IMPLEMENTATION
Curriculum
Mapping Implementation
Vision
+
Skills
+
Incentives
+
Resources
+
Plan
Action Plan
=
Sustainable
Change
Skills
+
Incentives
+
Resources
+
Plan
Action Plan
=
Confusion
Incentives
+
Resources
+
Plan
Action Plan
=
Anxiety
Resources
+
Plan
Action
Plan
= Resistance
Plan
Action
Plan
=
Frustration
=
Treadmill
Vision
+
Vision
+
Skills
+
Vision
+
Skills
+
Incentives
+
Vision
+
Skills
+
Incentives
+
Resources
Key
Questions:
Plan: Provides the direction to
Vision:
The “Why are we doing this?” to combat confusion.
Resources -- "Do we have tools, time, and training to map effectively?"
Vision
-"Why
are
we
doing
this?"
eliminate the treadmill effect.
Skills: The skill sets needed to combat anxiety.
Skills -- "How do we build effective maps?" Action Plan -- "Over the next three years, do we have attainable
Incentives: Reasons, perks, advantages to timelines
combat resistance
and goals? Who will be the responsible parties for
Incentives -- "How will mapping improve
Resources:
Tools
and
time
needed
to
combat
frustration.
implementations,
monitoring, and feedback?"
teaching and learning?"
Knoster, T., Villa, R., & Thousand, J. (2000)
Learner Objectives
 Define Math Learning Progressions
 Learn strategies for quality student
demonstration of math learning
progressions
 Examine rubrics for documenting
student outcomes in math learning
progressions
Part I: A Closer Look at
Identifying Student Outcomes
from Learning Progressions
Defining Learning Progressions
“descriptions of the successively more
sophisticated ways of thinking about an idea
that follow one another as students learn”
(Wilson & Bertenthal, 2005)
“a picture of the path students typically
follow as they learn ... a description of skills,
understandings, and knowledge in the
sequence in which they typically develop”
(Masters & Forster,1996)
Using Learning Progressions
•
Analyze or plan mapping of existing major curricular units
•
Develop replacement units and assessment tools using “backward
design”
•
Conduct research or become action researchers in classrooms
•
Identify specific trouble areas along the learning continuum for
struggling students
•
Identify “must-learn” building blocks to plan instructional sequences
•
Form the framework for an optimally effective formative assessment
process
•
Create interim assessment items/tasks
Identify “must-learn” building blocks to plan
instructional sequences
1.
When teachers start from what it is they want students to know
and design their instruction backward from that goal, then
instruction is far more likely to be effective (Wiggins and
McTighe 2000).
2.
Sharing learning objectives or intentions offers pupils an
opportunity to become involved in what they are learning
through discussing and deciding the criteria for success, which
they can then use to identify evidence of improvements (Eric
Young 2005).
3.
Classroom where students understand the learning outcomes
for daily lessons see performance rates 20% higher than those
where learning outcomes are unclear. (Marzano, 2003)
Learning Progressions in the
Common Core
“The Common Core State Standards in
mathematics were built on progressions:
narrative documents describing the progression
of a topic across a number of grade levels,
informed both by research on children's
cognitive development and by the logical
structure of mathematics. These documents
were spliced together and then sliced into
grade level standards.”
-Bill McCullen, Progressions Document Project
The Common Core…
•
Identifies endpoints
o grade level targets for learning
•
Does not suggest an instructional
sequencing plan
o “…just because topic A appears before
topic B in the standards does not
necessarily mean that topic A must be
taught before topic B. A teacher might
prefer to teach topic B before A, or
might choose to highlight connections…
of her own choosing that leads to A or
B” (CCSSM p. 5)
Learning progressions are the
path that children might follow
as instruction helps them move
from novice ideas to more
sophisticated understanding.”
Learning Progression Pathways
Across Grade Levels
Within a Grade
With in Standard
LEARNING PROGRESSION ACROSS GRADE LEVELS
Second
Grade
First Grade
Kindergarten
LEARNING PROGRESSION WITHIN GRADE LEVEL
Grade Level
Sequencing
Grade Level
Content
Standard
Grade Level
Content
Standard
Defined by essential
skills and core
concepts to support
success
LEARNING PROGRESSION WITHIN STANDARD
Grade Level
Sequence
Instructional
Target Sequence
Grade Level
Content
Standard
Instructional
Target
Instructional
Target
Instructional
Target
Grade Level
Content
Standard
Take Note….
• There is no single “correct
order”.
• Learning progressions are
not developmentally
inevitable but depend on
instruction.
GUIDING PRINCIPLES OF LEARNING
PROGRESSIONS
1. Developed (and refined) using available research
2. Have clear binding threads that articulate the
essential/core concepts and processes
3. Articulate movement toward increased
understanding
4. Go hand-in-hand with well-designed/aligned
assessments
(Hess, 2008)
Pause and Discuss
• What resources will you need or already have
that will assist you in identify your learning
progressions
o Across grade levels
o Within your grade level
o Within your standards
Using Learning Progressions
•
Analyze or plan mapping of existing major curricular units
•
Develop replacement units and assessment tools using “backward
design”
•
Conduct research or become action researchers in classrooms
•
Identify specific trouble areas along the learning continuum for
struggling students
•
Identify “must-learn” building blocks to plan instructional sequences
•
Form the framework for an effective formative assessment process
•
Create interim assessment items/tasks
Form the framework for an effective
formative assessment process
•
Learning Progressions and better designed assessments help
teachers to go deeper into the content with instruction.
o “I’ve taught these benchmarks for years, but never really understood them
this deeply before using the progress maps to break down the benchmarks.”
o “I never really thought about each individual benchmark, and generally
taught and assessed many of them at the same time. So I never knew what
the next steps might be when they didn’t get it.”
•
Formative assessment data help design flexibly group students for targeted
instruction and support along the learning continuum.
o “It was a real eye-opener. Some students who I thought were proficient were
actually below proficiency according to what they could and could not do
on the formative and mid-assessments.”
National Center on Education Outcomes, Synthesis Report 87, 2012
On-Going Assessment
Feedback & Goal Setting
PreAssessment
• Finding Out
•Pre-test
•Inventory
•KWL
•Checklist
•Observation
•Self-evaluation
•Questioning
Formative
Assessment
• Keeping
Track &
Checking Up
•Conference
•Peer
Evaluation
•Observation
•Questioning
•Exit Card
•Portfolio Check
•Quiz
•Journal Entry
•Self-evaluation
Summative
Assessment
• Making Sure
•Unit test
•Performance
Task
•Product/Exhibit
•Demonstration
•Portfolio
Review
Types of Formative Assessments
Performance
Tasks
Written Tasks
Discussions
Tests
Student selfassessment
Task Specific Rubrics
Content
• Sharing information,
ideas, concepts,
research, expertise
Process
• Planning, goalsetting, defense of
viewpoint, research,
editing, work quality
Product
• Size, construction,
delivery, accuracy,
authenticity
Task Specific Rubric Sample
Generic Rubrics
1
Quality of Thought
Quality of Research
3
2
Quality of Expression
Habits of Mind
4
Pause and Discuss
• What formative assessment strategies do you
plan to use to identify student outcomes?
• How do you foresee using the data collected
from your formative assessments to drive
your instructional sequences and
progressions?
Part II: Using Learning
Progressions to find
Student Outcomes in the
Classroom
Identifying Student Outcomes
from Learning Progressions
Across
Grade
Levels
Use resources to
examine
progressions across
multiple grade
levels.
Within
Grade
Level
Use resources to
examine
progressions within
grade level.
Within
Standard
Use instructional
targets to
determine a
progression within a
standard
Where are students
coming from and going
to?
How does my grade
connect with those
above and below me?
What standards are
connected to one
another?
How are standards
dependent on one
another?
What are the critical
content in the
standard?
What is the DOK
progression within the
standard?
2.NBT.7
Add and subtract within 1000, using concrete
models or drawings and strategies based on place
value, properties of operations, and/or the
relationship between addition and subtraction;
relate the strategy to a written method. Understand
that in adding or subtracting three-digit numbers,
one adds or subtracts hundreds and hundreds,
tens and tens, ones and ones; and sometimes it is
necessary to compose or decompose tens or
hundreds.
Across Grade
Levels
Use resources to
examine progressions
across multiple grade
levels.
Where are students coming
from and going to?
How does my grade
connect with those above
and below me?
Turnonccmath.com
Within Grade
Level
Use resources to
examine
progressions
within grade
level.
What standards are
connected to one
another?
How are standards
dependent on one
another?
NBT.7
Add and subtract within 1000, using concrete models or drawings and strategies based on place
value, properties of operations, and/or the relationship between addition and subtraction; relate
the strategy to a written method. Understand that in adding or subtracting three-digit numbers,
one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is
necessary to compose or decompose tens or hundreds
OA.1
Use addition and subtraction within 100 to solve one- and two-step word problems involving
situations of adding to, taking from, putting together, taking apart, and comparing, with
unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown
number to represent the problem.
OA.2
Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from
memory all sums of two one-digit numbers.
OA.4
Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows
and up to 5 columns; write an equation to express the total as a sum of equal addends.
NBT.5
Fluently add and subtract within 100 using strategies based on place value, properties of
operations, and/or the relationship between addition and subtraction.
NBT.9
Explain why addition and subtraction strategies work, using place value and the properties of
operations.
Within
Standard
Use instructional
targets to
determine a
progression within a
standard
What do students need to
be able to do first?
What is the highest level of
DOK within the instructional
targets?
Know:
Understand place value within 1000.
Decompose any number within 1000 into hundred(s), ten(s),
and one(s).
Think
Choose an appropriate strategy for solving an addition or
subtraction problem within 1000.
Relate the chosen strategy (using concrete models or drawings and
strategies based on place value, properties of operations, and/or the
relationship between addition and subtraction) to a written method
(equation) and explain the reasoning used.
Use composition and decomposition of hundreds and tens when
necessary to add and subtract within 1000.
Assessment
Design
Mary read 573 pages during her summer reading
challenge. She was only required to read 399
pages. Use a strategy you know to determine how
many extra pages did Mary read beyond the
challenge requirements?
399 + 1=400
400 + 100=500
500 + 73 =573
1 + 100 + 73 = 174 pages
573 – 73 =500
500 - 100 = 400
400 – 1 = 399
100 + 73 + 1 = 174 pages
7.EE.1
7.EE.1 Apply properties of operations as
strategies to add, subtract, factor, and
expand linear expressions with rational
coefficients.
6-8 Progression on Expressions
and Equations
Working with Expressions
5.OA.1 Use parentheses, brackets,
or braces in numerical expressions,
and evaluate expressions with these
symbols.
5.OA.2 Write simple expressions
that record calculations with
numbers, and interpret numerical
expressions without evaluating
them.
Working with Expressions
6.EE.2.a Write expressions that record
operations with numbers and with letters
standing for numbers.
Working with Expressions
7.EE.1 Apply properties of operations as
strategies to add, subtract, factor, and
expand linear expressions with rational
coefficients.
6.EE.2.b Identify parts of an expression using 7.EE.2 Understand that rewriting an
mathematical terms (sum, term, product,
expression in different forms in a problem
factor, quotient, coefficient); view one or
context can shed light on the problem and
more parts of an expression as a single entity. how the quantities in it are related.
6.EE.2.c Evaluate expressions at specific
values of their variables. Include expressions
embedded in formulas or equations from
real-world problems. Perform arithmetic
operations, including those involving wholenumber exponents, in the conventional order
when there are no parentheses to specify a
particular order (Order of Operations).
6.EE.6 Use variables to represent numbers
and write expressions when solving a realworld or mathematical problem; understand
that a variable can represent an unknown
number, or, depending on the purpose at
hand, any number in a specified set.
6.EE.3 Apply the properties of operations to
generate equivalent expressions.
6.EE.4 Identify when two expressions are
equivalent (i.e., when the two expressions
name the same number regardless of which
value is substituted into them).
Instructional Target
Instructional
Progression
within standard
7.EE.1 Apply properties
of operations as
strategies to add,
subtract, factor, and
expand linear
expressions with
rational coefficients.
Progression
Knowledge:
o Write equivalent expressions with
fractions, decimals, percents, and
integers.
Reasoning:
o Rewrite an expression in an
equivalent form in order to provide
insight about how quantities are
related in a problem context
7.EE.1
Working with Expressions
5.OA.1 Use parentheses, brackets,
or braces in numerical expressions,
and evaluate expressions with these
symbols.
5.OA.2 Write simple expressions
that record calculations with
numbers, and interpret numerical
expressions without evaluating
them.
Working with Expressions
6.EE.2.a Write expressions that record
operations with numbers and with letters
standing for numbers.
Working with Expressions
7.EE.1 Apply properties of operations as
strategies to add, subtract, factor, and
expand linear expressions with rational
coefficients.
6.EE.2.b Identify parts of an expression using 7.EE.2 Understand that rewriting an
mathematical terms (sum, term, product,
expression in different forms in a problem
factor, quotient, coefficient); view one or
context can shed light on the problem and
more parts of an expression as a single entity. how the quantities in it are related.
6.EE.2.c Evaluate expressions at specific
values of their variables. Include expressions
embedded in formulas or equations from
real-world problems. Perform arithmetic
operations, including those involving wholenumber exponents, in the conventional order
when there are no parentheses to specify a
particular order (Order of Operations).
6.EE.6 Use variables to represent numbers
and write expressions when solving a realworld or mathematical problem; understand
that a variable can represent an unknown
number, or, depending on the purpose at
hand, any number in a specified set.
6.EE.3 Apply the properties of operations to
generate equivalent expressions.
6.EE.4 Identify when two expressions are
equivalent (i.e., when the two expressions
name the same number regardless of which
value is substituted into them).
Instructional Target
Instructional
Progression
within standard
6.EE.4 Identify when two
expressions are equivalent
(i.e., when the two
expressions name the same
number regardless of which
value is substituted into
them). For example, the
expressions y + y + y and
3y are equivalent because
they name the same
number regardless of which
number y stands for.
Progression
Knowledge:
• Recognize when two expressions are
equivalent.
Reasoning:
o Prove (using various strategies) that
two equations are equivalent no
matter what number is substituted.
When Watching….
• How and why does Ms. Barchi identify which
type of exit card a student completes?
• Notice how Ms. Barchi quickly sorts the exit
cards so she knows which students need
re-teaching. How does this strategy offer
immediate feedback to students and
differentiated support?
Knowledge Check
Question: Which of the following
statements is not true about
learning progressions?
A.
Learning progressions are not
developmentally inevitable but depend
on instruction.
B.
Learning progressions have clear
binding threads that articulate the
essential/core concepts and processes.
C.
Grade level progressions are defined in
the Common Core Math Standards.
D.
There is no single correct order for
learning progressions.
Homework
Assignments
Homework Assignment
In your resources, complete the “Identifying Student Outcomes
from Learning Progressions” Rubric. Based on your results,
select an area you would like to focus on. Create a SMART GOAL,
by filling in the blanks below
In case you need: SMART stands for Specific, Measurable,
Attainable/Achievable, Relevant, Time bound
•Find three resources to could assist you reach your goal. These
may be websites, books, other staff member, observations, etc.
•Submit a rationale for selecting the area of focus, your SMART
Goal, and the resources selected.
Homework Assignment
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