Transcript Common Core State Standards

Common Core State Standards
Instruction, K-5
Mathematics
Anthony Quan—Consultant II, STEM
Belinda Lister—Math Consultant
Division of Curriculum and Instructional Services
commoncore.lacoe.edu
Agenda
• Effective Instruction
• Rigor/Relevance Framework
• Mathematics
– Standards for Mathematical Practice
– Research-Informed Instructional Practices
– Model Task
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Fraction Models
Area Model
Sharing Model
Linear Model
Rates Model
Set Model
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Effective Instruction
“A long line of students has established that the
single most important school influence on student
learning is the quality of the teacher.”
as presented by Linda Darling-Hammond (2007)
How would you describe a classroom where
effective instruction and learning is taking
place?
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California Standards
for the Teaching Profession
• Engaging and supporting all students
–
–
–
–
–
Connect to students’ prior knowledge
Use a variety of instructional strategies
Promote autonomy, interaction, and choice
Engage students in critical thinking/problem solving
Engage students in reflecting on their learning
• Understanding and organizing content
– Organize curriculum to support understanding
– Interrelate ideas and information
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California Standards
for the Teaching Profession
• Planning instruction
– Establish clear goals for student learning
– Design short- and long-term plans
– Modify plans according to student needs
• Assessing student learning
– Collect and use multiple sources of information
– Use results to guide instruction
– Involve students in assessing their own learning
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Learning Pyramid
Passive
Learning
Active
Learning
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adapted from Ntl Institute for Applied Behavioral Science (n.d.)
Rigor/Relevance Framework®
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International Center for Leadership in Education (n.d.)
Rigor/Relevance Framework®
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Students gather
and store bits of
knowledge/infor
mation and are
expected to
remember or
understand this
acquired
knowledge.
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A
Application 3
Comprehension 2
Awareness
International Center for Leadership in Education (n.d.)
Quadrant A: Acquisition
Acquisition
1
1
2
Knowledge in
one discipline
Apply
knowledge in
discipline
Quadrant A
Verbs
name
label
define
select
identify
list
memorize
recite
locate
record
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Products
definition
worksheet
list
quiz
test
workbook
true-false
reproduction
recitation
B
Application 3
Students use
acquired
knowledge to
solve problems,
design
solutions, and
complete work.
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Comprehension 2
Awareness
International Center for Leadership in Education (n.d.)
Quadrant B: Application
Application
1
3
4
5
Apply
knowledge across
disciplines
Apply
to real-world
predictable
situation
Apply to
real-world
unpredictable
situation
Quadrant B
Verbs
apply
sequence
demonstrate
interview
construct
solve
calculate
dramatize
interpret
illustrate
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Products
scrapbook
summary
interpretation
collection
annotation
explanation
solution
demonstration
outline
Evaluation 6
Students extend
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and refine their Synthesis
knowledge so that
Analysis4
they can use it
automatically and Application
3
routinely to analyze
and solve problems
and create
solutions.
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C
Assimilation
1
2
Knowledge in
one discipline
Apply
Knowledge in
one discipline
International Center for Leadership in Education (n.d.)
Quadrant C: Assimilation
Quadrant C
Verbs
sequence
annotate
examine
report
criticize
paraphrase
calculate
expand
summarize
classify
diagram
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Products
essay
abstract
blueprint
inventory
report
plan
chart
questionnaire
classification
diagram
discussion
collection
annotation
Evaluation 6
Students think in
complex ways and
Synthesis
5
apply acquired
knowledge
Analysis4
and skills, even when
Adaptation
confronted with
Application
3
perplexing unknowns,
to find creative
solutions and take
3
4
action that further
Apply
Apply
develops their skills
knowledge across to real-world
and knowledge.
International Center for Leadership in Education (n.d.)
Quadrant D: Adaptation
D
disciplines
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predictable
situation
5
Apply to
real-world
unpredictable
situation
Quadrant D
Verbs
evaluate
validate
justify
rate
referee
infer
rank
dramatize
argue
conclude
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Products
evaluation
newspaper
estimation
trial
editorial
radio program
Play
collage
machine
adaptation
poem
debate
invention
Rigor/Relevance Framework®
C
R
I
G
O
R
High
D
Student
Think
A
Low
Student
Think & Work
B
Teacher
Work
Student
Work
Low
High
RELEVANCE
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International Center for Leadership in Education (n.d.)
Teacher/Student Roles
Instructional Model
Three-Part Lesson Format
• Before
• During
• Beyond
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Before Phase
• Introduce problem or task
• Be certain the problem is understood
• Activate useful prior knowledge
• Establish clear expectations
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Candy Store Problem
The local candy store purchased
candy in cartons holding 12 boxes
per carton. The price paid for one
carton was $42.50. Each box
contained 8 candy bars that the store
planned to sell individually. What was
the candy store’s cost for each candy
bar?
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During Phase
• Students work with partners or in
teams
• Teacher:
- listens as students work
- provide appropriate suggestions
- observes and accesses
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After Phase--Processing
• Encourage student dialogue
• Accept without evaluation
• Request explanations to accompany
answers
• Call on students for their ideas
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Graphic Organizer
Instruction
Instruction
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CCSS for Mathematics
Instructional Implications
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Dan Meyer
http://www.youtube.com/watch?v=BlvKWEvKSi8
CCSS for Mathematics
• Provide focus and coherence
• Organized around mathematical principles
• Stress conceptual understanding of key ideas as well
as skills
• Prepare students for college and career
What are the implications for instruction?
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Influence on Student Learning
“…teachers
need
to understand
the standards.
…teachersthemselves
themselves
need
to understand
the
Teachers
must
have deep
appropriate
content
standards.
Teachers
mustand
have
deep and
knowledge
to
reach
that
understanding;
they
must
be
appropriate content knowledge to reach that
adaptable, with enough mastery to teach students with a
understanding;
they
must
be
adaptable,
with
range of abilities; and they must have the ability to
enough
to of
teach
rangelevels
of
inspire atmastery
least some
their students
students towith
the ahighest
abilities;
and they
must have
of mathematical
achievement.
” the ability to inspire at
Ewingof
(n.d.)
least some of their students to the highest levels
The Common Core Math Standards
mathematical achiev
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Standards for Mathematical Practice
Seek to Develop in Students
NCTM Process Standards
• Problem Solving
• Reasoning and Proof
• Communication
• Representation
• Connections
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Strands of Math Proficiency
• Adaptive Reasoning
• Strategic Competence
• Conceptual Understanding
• Procedural Fluency
• Productive Disposition
Standards for
1. Make sense of problem and persevere in
solving them.
6. Attend to precision.
Mathematical Practice
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the
reasoning of others.
Reasoning and
explaining
4. Model with mathematics.
5. Use appropriate tools strategically.
Modeling and
using tools
7. Look for and make use of structure.
8. Look for and express regularity in repeated
reasoning
adapted from McCallum (2011)
Standards for Mathematical Practice
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Overarching
habits of mind
of a productive
mathematical thinker
Seeing structure and
generalizing
Create a Frayer Model Poster
Essential
Characteristics
Examples
of What
Students Will
Be Doing
•
•
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Teaching
Methods
Standards for
Mathematical
Practice
Non-examples
of What
Students Will
Be Doing
Work with a table group on one of the
Standards for Mathematical Practice.
Create a Frayer Model Poster connecting
student actions and teacher actions.
Frayer Model Poster Carousel
• Display your poster.
• Examine the poster to the right of your
group’s poster.
• Look for evidence of the “processes and
proficiencies.”
• Rotate to the right and continue until you have
finished examining all posters.
• Be ready to share out any
questions or “ahas.”
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Research-Informed
•
•
•
•
•
•
Best Practices
Access prior knowledge and address
students’ misconceptions
• Provide
Access
prior knowledge and address
routines and structures that help
students’
misconceptions
struggling
learners
organize critical content
students
withand
challenging
tasks
that
• Engage
Provide
routines
structures
that
help
involve
activelearners
meaning making
struggling
organize critical content
Use formative assessment and provide timely, specific feedback
• Engage students with challenging tasks that
Provide on-going cumulative distributed practice
involve active meaning making
Promote learners’ beliefs about their own intelligence (growth
• mindset
Use formative
assessment and provide timely,
vs. fixed mindset)
specific feedback
adapted from Briars (2011)
Intensified Algebra
• Provide on-go
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Cognitively-Guided
Instruction Process
Start the study of a new
concept with a rich problem or
hypothesis
Use your understanding of
student thinking to guide further
instruction
Question, justify, and
critique thinking
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Invite your students to
engage in the problem
Communicate multiple
representations of
solutions.
Gendron (2011)
So, What’s New in the Common Core State Standards?
Debrief the CGI Process
Start the study of a new
concept with a rich problem
or hypothesis
Use
results
to plan
next
steps
Use your understanding of
student thinking to guide
further instruction
Question, justify, and
critique thinking
Asked questions to check for
understanding during and
after the task
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Table
Pattern
Task
Invite your students to
engage in the problem
Asked
questions to
unpack the
problem
Communicate multiple
representations of solutions.
Asked questions about
strategies and
relationships
Gendron (2011)
So, What’s New in the Common Core State Standards?
Students’ Beliefs
About Their Intelligence
• Fixed Mindset
– Avoid learning situations if they might make mistakes
– Try to hide, rather than fix, mistakes or deficiencies
• Growth Mindset
– Work to correct mistakes and deficiencies
– View effort as positive; increase effort when challenged
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Briars (2011)
Implementing the More Challenging Aspects of Common Core State Standards
Students Can
Develop Growth Mindsets
• Explicit instruction about the brain, its function, and that
intellectual development is the result of effort and learning
has increased students’ achievement in middle school
mathematics.
• Teacher praise influences mindsets:
– Fixed: Praise refers to intelligence
– Growth: Praise refers to effort,
engagement, perseverance
Briars (2011)
Implementing the More Challenging Aspects of Common Core StateStandards
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Expectancy: Can I Do This?
• Attribute successes to high effort or
effective strategy
• Attribute failures to low effort or ineffective strategy
• Avoid saying, “You’re smart”
• Discuss the different views of intelligence
• Be explicit about what sorts of effort lead to success
• Design instruction to support successful
learning experiences
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Dweck (2006)
Presentation on Intelligence Theory
Value: Is This Important?
“How many of us have used the
“it’s on the
test” to emphasize the importance of a skill or
assignment?”
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Value: Is This Important?
• Connect classroom activities to personal shortterm goals.
• Connect classroom activities to personal longterm goals.
• Place classroom activities in personally
meaningful contexts.
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Growth Mindset and
Productive Disposition
“Just as students must develop a productive
disposition toward’s mathematics such that they
believe that mathematics makes sense and that they
can figure it out, so too must teachers develop a similar
productive disposition.”
National Research Council (2005)
Adding It Up
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What about Technology?
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• Proficiency with technology allows
students to succeed in college and
careers. The Common Core
Standards include basic technology
skills to help them succeed; but in
the bigger picture, they call for
students to use technology to help
them learn in all areas.
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•
Whether it be using tools to
solve math problems, to
access information, or to
promote literacy and
communication skills,
technology is part of the
learning solution. It needs to
be viewed that way rather than
a separate competency.
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Closing
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Best Practices for the
Common Core
• Engage students with challenging tasks that involve active
meaning making
– Quadrant B, C, and D learning opportunities
– Cognitively-Guided Instruction with a focus on the Standards for
Mathematical Practice
– Questioning to facilitate thinking and learning
• Promote learners’ beliefs about their own intelligence
(growth mindset vs. fixed mindset)
– Design instruction to support student success
– Explicitly reinforce high effort and students’ use of effective strategies
– Repackage content using real-world connections,
puzzles, and games
– Model a productive disposition
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Your Task
• Upon your return to your school site, try to
incorporate some of the lessons, activities or
learnings into your practice.
•Bring back work samples of things you have tried.
•Bring your textbook or other instructional materials.
Reflection
• Think about what you learned today.
• Decide on one thing you will do differently to start
transitioning to the Common Core State
Standards.
• Share your ideas with a partner.
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For Further Investigation
• California’s Common Core State Standards
http://www.cde.ca.gov/ci/cc
• Common Core State Standards Initiative
http://www.corestandards.org
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