Improving
Mathematical Number
Sense & Technology
Integration
Teacher Quality Grant
Peyton Forest Elementary
Atlanta Public Schools
Atlanta, GA
July 22, 2013
Welcome!!
• Please be sure you have
completed an Entrance Card
and given that to one of the
leaders before we begin.
Grant Information
Meet your facilitators
University of West Georgia
Georgia State University
Continental Colony
Ithica Elementary
Goals for Today
• Understand rationale and history of this project
• Connect the AMC Assessments to the Common Core
State Standards for Mathematics, Georgia DOE materials
and RTI
• Determine the rationale for this type of assessment
• Learn to complete one assessment using the AMC
materials
• Begin to think about how the information gained from the
assessments could be used to make instructional
decisions.
Common
Vocabulary
•
CCSSM - Common Core State Standards in
Mathematics
•
AMC - Assessing Math Concepts
•
RTI - Response to Intervention
•
Assessment
•
Diagnostic
•
Formative
•
Summative
Think/Pair/Share
• What is meant when we
use the term “formative
assessment”?
Assessment
Informs Instruction
Assessment
Whole
Group
Small
Group
Reflective
Thinking
Independent
Work
Learning the Essential
Mathematics is What
Matters
We must know more than
• When children
only to are
whether
or notlearn
children
follow procedures without
able to get right answers.
understanding the underlying
We
must
uncover
the
mathematics, what they are
doing
is emptybehind
of mathematics.
thinking
the
answers.
How Do We Know
What They Know?
•
Importance of research-based, focused
assessments for diagnostic purposes
•
Universal Screener
•
Focused on Core Concepts
•
Probe for student thinking
•
Find the ‘edge of understanding’ (Richardson)
Assessments must be
developed to measure
student progress.
Overview of RTI
•
Universal Screener assessment is administered to
uncover student needs in a target area
•
Assessment is the beginning of the cycle
•
“Tiers” of instructional services are matched to
identified student needs
•
Continual progress monitoring
AMC and RTI
AMC and RTI
•
The Assessments:
•
target what a child knows and what the next step
for learning might be, whether Tier I, II or III
•
can be given informally on an ongoing basis to
progress monitor
•
indicate activities which meet a wide range of
needs and can be used with individual students
or in small groups
Common Core
How the Standards
were Initiated . . .
•
The Common Core State Standards Initiative
(CCSSI), coordinated by the National Governors
Association Center for Best Practices (NGA Center)
and the Council of Chief State School Officers
(CCSSO), committed to developing a common core
of state K-12 English-language arts (ELA) and
mathematics standards.
•
Governors and state commissioners of education
from 48 states, 2 territories and the District of
Columbia agreed to be a part of the development of
these standards.
How the Standards were
Constructed . . .
Lead Writers
Writing Teams
State Review
Teams
Validation
Team
State
Adoption
Process
Professional
Organizations
Developmental History of the
CCSS
•
July 2009: The development of the College and
Career Ready Standards draft, outlining topic
areas
•
October 2009: Public release of the College
and Career Ready Standards
•
January 2010: Public release of Draft 1
•
March 2010: Public release of Draft 2
•
June 2, 2010: Final release of Common Core
State Standards with approval of the Validation
Committee
Adoption means . . .
•
A state adopts 100% of the Common Core K‐12
standards in ELA and mathematics
•
•
Word for word
With option of adding up to an additional 15% of
standards on top of the core.
State participation
Standards Criteria
•
Fewer, clearer, and higher standards
•
Aligned with college and work expectations
•
Include rigorous content and application of knowledge
through high‐order skills
•
Build upon strengths and lessons of current state standards
•
Internationally benchmarked, so that all students are
prepared to succeed in our global economy and society
•
Based on evidence and research
• CCSSI 2010; www.corestandards.org
Important to
remember . . .
•“These Standards do not dictate
curriculum or teaching methods. For
example, just because Topic A appears
before Topic B in a given grade, it does
not mean that Topic A must be taught
before Topic B.”
•CCSS 2010, p. 5
Only a first step
•Along with standards:
•
Educators must be given resources, tools, and time to
adjust classroom practice.
•
Instructional materials needed that align to the
standards.
•
Assessments must be developed to measure student
progress.
•
Federal, state, and district policies will need to be
reexamined to ensure they support alignment of the
Common Core State Standards with student
achievement.
• CCSSI 2010; www.corestandards.org
Key Aspects in
Mathematics
•
Focus and coherence
•
•
•
Balance of concepts and skills
•
•
Content standards require both conceptual understanding and procedural
fluency
Mathematical practices
•
•
Focus on key topics at each grade level.
Coherent progressions across grade levels
Foster reasoning and sense‐making in mathematics.
College and career readiness
•
Level is ambitious but achievable.
•
CCSSI 2010; www.corestandards.org
In your groups . . .
•
Look at the description your group has been given.
•
Is your description a:
•
Mathematical Practice?
•
Literacy Practice?
•
What is meant by each description?
•
What is the importance of each description in a classroom
context.
When your group is done take a 10 minute break!
Mathematical
Practices
•
Make sense of problems and persevere in solving them.
•
Reason abstractly and quantitatively.
•
Construct viable arguments and critique the reasoning of
others.
•
Model with mathematics
•
Use appropriate tools strategically
•
Attend to precision
•
Look for and make use of structure
•
Look for and express regularity in repeated reasoning.
K-12 Literacy
Practices
•
Demonstrate independence.
•
Build strong content knowledge.
•
Respond to the varying demands of audience, task, purpose,
and discipline.
•
Comprehend as well as critique.
•
Value evidence.
•
Use technology and digital media strategically and capably.
•
Come to understand other perspectives and cultures.
Mathematical Practices & Understanding
Mathematics
•Students
•
Use it to make sense of and explain quantitative situations
•
•
"Construct viable arguments and critique the
reasoning of others”
Bring it to bear on the solutions to problems
•
•
“Model with Mathematics”
Incorporate it into their own arguments and use it to evaluate the arguments of others
•
•
who understand a concept can:
“Make sense of problems and persevere in solving them”
Make connections between it and related concepts
•
“Look for and make use of repeated reasoning”
K-5 Domains
Domains
Counting and Cardinality
Grade Level
K only
Operations and Algebraic Thinking
1-5
Number and Operations in Base Ten
1-5
Number and Operations – Fractions
3-5
Measurement and Data
1-5
Geometry
1-5
Critical Areas
•
In your notebook, find the Common
Core State Standards for Mathematics
•
Find your grade level standards
•
Where will you find the Critical Areas
for your grade level?
In Your Group
Common Core State Standards Mathematics
What Are The Critical
Areas . . .
How Do These Relate To How does the CCGPS
the Previous/Next Grade Frameworks support the
...
critical areas. . .
As you head to
Lunch...
•
During this time, please be sure to take a look at
your colleagues’ charts.
•
Use Post-It notes to ask questions of the
group.
•
What common ideas do you see?
•
What is one thing you saw from another
group that you would add to your chart?
When You Return
from
Lunch
.
.
.
•
Read pp. 3-8 in the Introduction to the Assessment
Series.
• Think about:
• What do children need to learn in mathematics?
• What are some of the obstacles that inhibit children’s
understanding of number?
• What is important to know about the development of
Number Concepts?
• What is meant by the term “illusion of learning”?
Lunch!!
Please be ready to get
back to work by
Welcome Back
From Lunch!!
• Read pp. 3-8 in the Introduction to the Assessment
Series.
• Think about:
• What do children need to learn in mathematics?
• What are some of the obstacles that inhibit children’s
understanding of number?
• What is important to know about the development of
Number Concepts?
• What is meant by the term “illusion of learning”?
AMC Core
Concepts
• Counting and Comparing
• Adding and Subtracting
• Place Value
Counting /Number
Relationships
Composing and
Decomposing Number
Place Value
Numbers as Tens & Ones
Developing Number
Concepts
Assessing Math
Concepts
•
A cohesive look at the development of children’s
understanding of core concepts.
•
NOT a random collection of questions focused on a
child’s ability to get right answers.
AMC: Based on Critical
Learning Phases
• Phase:
a particular moment or stage in a process,
especially one at which a significant change or
development occurs or a particular condition
reached.
•- Miriam Webster’s Dictionary
• The Critical Learning Phase that a child has
reached determines the way he or she is able to think
with numbers and to use numbers to solve problems.
•- Kathy Richardson
. . . determines the way he
or she is able to think with
numbers and to use
numbers to solve problems.
Critical Learning Phases
for Numbers to 100
•
Look at pp. 9 & 10 in any of the AMC Assessment
books
•
Discuss the information contained in the chart
•
What stood out for you?
•
What surprised you?
•
Which aspects do you need clarified?
• The assessments have
been carefully designed
so each question elicits
several levels of
thinking. This gives
teachers the most
information possible in
the shortest amount of
time.
Implications for
Instruction
•
The Assessments:
•
Pinpoint what each child knows and still needs to
learn.
•
Are not about “helping children be right,” but about
uncovering what they need regarding instruction.
The Assessments are the
Beginning, NOT the End
Assessment
Observation
Data
Instruction
The information you gets tells you what you
need to do for your students. What you learn
can truly guide your instruction.
Summarizing How
These Assessments
Help Us
• Assessments:
• guide instruction
• help us know what the child can do
• document growth
• guide us to what is coming into view as children
construct mathematical understandings
• let us know what children are learning and how they
are understanding it
• The assessment is a description, not
an evaluation.
• Children respond honestly when they
believe you are interested in what they
have to say, not in whether they are
right or wrong.
• Think of the assessment as a
conversation, not a quiz.
• When we help a child get the ‘right’
answer, it makes being right seem allimportant and being ‘wrong’ not okay.
• AND . . . it invalidates the results of
the assessment!
• (meaning we have just wasted our
student’s time as well as our own)
Assessing Math
Concepts
Counting Objects
Counting Objects
• “Counting is finding out how many.
Children learn the language and
patterns of counting long before they
understand what counting is all about,
so parents and teachers are often
unaware of the child’s lack of facility
with the central task of counting
objects.”
•
(Richardson, p.26)
Goal
• To determine if a child can
count and keep track of an
unorganized pile of up to 32
counters and can make a pile of
up to 18 counters.
Critical Learning
Phases
•
Gets a particular quantity
•
Keeps track when counting objects
•
Remembers “how many” after counting
•
Reacts to estimate while counting
•
Adjusts estimate and makes a closer estimate
•
Knows “one more” without counting
•
Knows “one less” without counting
•
Interprets and writes numerals to label quantities
Reading
•
Read The Challenges of Learning to Count
handout in your AMC Counting Objects
Assessment book
•
What surprises you about this information?
•
How does this relate to the article we read
this morning?
•
How might both of these readings impact
the way we work with our students?
View Videos of
Children Counting
•
Read p. 11-13 from the handout Assessment One:
Counting Objects.
•
As you watch, try to determine what each child
knows and what their next step should be.
•
Video 1
•
Video 2
Eavesdropping . . .
•
Think about what we have discussed this morning.
•
How does this help you as you observe my
conversation with a student?
•
Which aspects of the conversation stand out
for you?
•
What questions do you have as we move into
the afternoon?
Documenting The
Assessment
•
AMC Counting Objects Assessment in your Assessment Kit
•
Task One and Task Two
•
What you need
•
Goals
•
Procedure
•
Task One: Counting a Pile of Objects
•
Task Two: Counting Out a Particular Quantity
•
Summarizing Instructional Needs
Documenting The
Assessment
•
AMC Counting Objects Assessment in your Assessment
Kit
• Task Three
• What you need
• Goals
• Procedure
• Task Three: One More / One Less
• Summarizing Instructional Needs
The Indicators
•
For Task One
•
For Task Two
•
For Task Three
•
In general, 4 levels:
•
A - Ready to Apply
•
P - Needs Practice
•
I - Needs Instruction
•
X - Needs Prerequisite
Assessment Video
•
View Video 2 again
•
This time, using one of the Counting Objects online
assessment, record the student’s responses
Partner Practice
•
Choose a partner.
•
Using all the materials, conduct an assessment with
your partner. Be sure to record your partner’s
responses.
•
Switch roles.
More Video Practice
•
Watch and score the assessments of:
•
Video 3
•
Video 4
•
Video 5
•
Video 6
• Afterward, discuss in your group:
•
What thoughts came to you as a teacher while you
watched the interviews?
•
What kinds of information can you learn as an
interviewer?
Why is counting so
hard for young
children?
•
Words and symbols have no mathematical meaning
- the meaning is in the quantity
•
Practicing the symbol and words does not help me
understand what they represent
Homework
•
Read
•
Too Easy for Kindergarten and Just Right for First Grade
•
Teaching Number in the Early Elementary Years
•
Promoting Meaningful Mastery of Addition and Subtraction
• What Is the Question
•
Consider the following as you read:
•
What implications does this article have for students at your
grade level?
•
In what ways might this article help you think differently
about the number choices in Math Expressions?
• Be ready to share your thoughts.
•
Take a look at the Grouping Tens information in your notebook