Transcript Document

Common Core State
Standards in Mathematics
Overview
Tere Hirsch
Contract Consultant, Mathematics
Division of Curriculum and Instructional Services
Los Angeles County Office of Education
[email protected]
Objectives for today:
EXAMINE
ANALYZE
FOCUS
THINK
“Math Class needs a
Makeover”
with Dan Meyer
http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html
CCSS Math Note Taking Guide
Reflection #1 :
ÒMath Class Needs a
MakeoverÓ
Reflection
#2 :
Reflection #2: “Implications for the classroom
teacher”
Re fle ction #3:
Standar ds of
Mathe m atical Pr actice
(SM P)
Reflection #4 :
Grade Level Standards
Reflection #5 :
WhatÕs Next?
Reflection #1
What similarities or differences did
you see in the video compared to
your classroom or those that you
have observed?
Race To the Top
2009
Common Core State Standard
(CCSS) Initiative sponsored by NGA
and CCSSO
Committee convened to develop…
1. CCSS
2. Nationwide assessment
3. Timeline for state adoption
California Timeline
Jan 2010: ACSC (Academic Content Standards
Commission) is created and members are chosen
June 2010 : ACSC studies CCSS
July 2010 : ACSC recommends adoption with some
additions
August 2, 2010: SBE adopts ACSC’s
recommendations
Materials: Implementation
Timeline 1
Milestone
Math
ELA
Completed
1/2012
Field review of framework
9/2012
9/2013
SBE action on framework
5/2013
5/2014
2014–15
2014–15
Materials submission
3/2016
3/2018
SBE approves materials
11/2016
11/2018
Curriculum Commission approves plan,
timeline and criteria committee
application
Common core assessments
Assumes the passage of Assembly Bill 250 (Brownley), which partially lifts
the suspension under EC Section 60200.7, and Curriculum Commission
funding for 2011 and subsequent years.
8
Assessment
SBAC (Smarter Balance Assessment
Consortium)
http://www.k12.wa.us/smarter/
Reflection #2
What are the implications for the
classroom teacher?
You
can
always
count
on
Peter…
Mathematical Proficiency
As defined by the California Framework
“WHERE”
THE
MATHEMATICS
WORK
Problem
Solving
Computational
& Procedural
Skills
DOING
MATH
Conceptual
Understanding
“WHY”
THE
MATHEMATICS
WORK
“HOW”
THE
MATHEMATICS
WORK
Big Picture in Mathematics
CCSS
Standards of Mathematical
Practice
Grade Level Standards
Grades K-5
Grades 6-8
High School Math
8th Grade Options
Algebra 1
Core Standards to
prepare for Algebra 1
How do we achieve understanding?
How do we foster mathematically
proficient students?
The Standards for
Mathematical Practice
Standards for
Mathematical
Practice
1
Make sense of
problems
and
persevere in
solving them
4
Model with
mathematics
6
Look for and
make use of
structure
2
Reason
abstractly and
quantitatively
3 Construct
viable
arguments and
critique the
reasoning of
others
5
Standards for
Mathematical
Practice
7
Attend to
precision
Use
appropriate tools
strategically.
8 Look for
and express
regularity in
repeated
reasoning
Grouping the Standards of Mathematical Practice
1. Make sense
of problems
and persevere
in solving
them.
6. Attend to
precision.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and
critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
Overarching habits of
mind of a productive
mathematical thinker.
Reasoning and
explaining
Modeling and
using tools.
7. Look for and make use of structure.
8. Look for and express regularity in
repeated reasoning.
William McCallum University of Arizona- April 1, 2011
Seeing structure
and generalizing.
1. Make sense of problems and persevere in solving
Do students:
• EXPLAIN?
• ANALYZE?
• Make CONJECTURES?
• PLAN a solution pathway?
• MULTIPLE representations?
• Use DIFFERENT METHODS to check?
• Check that it all makes sense?
• Understand other approaches?
• See connections among different approaches?
2. Reason abstractly and quantitatively
Do students:
• Make sense of quantities & their relationships?
• Decontextualize?
• Contextualize?
• Create a coherent representation?
• Consider units involved?
• Deal with the meaning of the quantities?
3. Construct viable arguments and critique the reasoning
of others.
Do students:
• Understand & use stated assumptions, definitions, and previous
results?
• Analyze situations, recognize & use counterexamples?
• Justify conclusions, communicate to others & respond to
arguments?
• Compare the effectiveness of 2 plausible arguments?
• Distinguish correct logical reasoning from flawed & articulate the
flaw?
• Look at an argument, decide if it makes sense,& ask useful
questions to clarify or improve it?
• Make conjectures& build a logical progression?
• Use mathematical induction as technique for proof?
• Write geometric proofs, including proofs of contradiction?
4. Model with mathematics
Do students:
• Apply the mathematics they know everyday?
• Analyze relationships mathematically to draw conclusions?
• Initially use what they know to simplify the problem?
• Identify important qualities in a practical situation?
• Interpret results In the context of the situation?
• Reflect on whether the results make sense?
5. Use appropriate tools strategically.
Do students:
• Consider available tools?
• Know the tools appropriate for their grade or course?
• Make sound decisions about when tools are helpful?
• Identify & use relevant external math Sources?
• Use technology tools to explore & deepen understanding
of concepts?
6. Attend to precision.
Do students:
• Communicate precisely with others?
• Use clear definitions?
• Use the equal sign consistently & appropriately?
• Calculate accurately & efficiently?
7. Look for and make use of structure.
Do students:
• Look closely to determine a pattern or structure?
• Use properties?
• Decompose & recombine numbers & expressions?
• Have the facility to shift perspectives?
8. Look for and express regularity in repeated reasoning.
Do students:
• Notice if calculations are repeated?
• Look for general methods & shortcuts?
• Maintain process while attending to details?
• Evaluate the reasonableness of intermediate results?
Reflection #3
What is the intent of the SMPs
– in the teacher’s case ?
– in the student’s case?
CA Common Core
Grade Level
Standards in
Mathematics
Focus of the Common Core State Standards
Ratios &
Proportional
Relationships
Counting
&
Cardinality
The Number System
Operations & Algebraic Thinking
Number & Operations in Base Ten
Expressions & Equations
Fractions
Functions
Measurement and Data
Geometry
Geometry
Statistics & Probability
K
1
2
3
4
5
From William McCallum, Arizona, (one of the writers of CCSS)
6
7
8
CCSS Domains K-5
Domain
K
1
2
3
4
5
Counting and Cardinality
(CC)

Operations and Algebraic
Thinking (OA)
     
Number and Operations in
Base Ten (NBT)
     
Measurement and Data
(MD)
     
Geometry (G)
     
Number and Operations –
Fractions (NF)
  
In grades K-5, students develop a solid foundation in whole numbers,
addition, subtraction, multiplication, division, fractions, and decimals.
CCSS Domains 6-8
6
7
Ratios and Proportional
Relationships (RP)


The Number System (NS)



Expressions and Equations
(EE)



Geometry (G)



Statistics and Probability (SP)



Domain
Functions (F)
8

With a strong foundation of content knowledge from grades K-5,
middle school students are prepared for robust learning in geometry
and statistics and probability
California Grade 8 Options
The goal for 8th grade students is Algebra 1
Two options for grade 8 that prepare students
for college and career:
• Algebra 1: Grade 8 Common Core and
the high school Algebra content cluster
• Grade 8 Common Core: goal of grade 8
Common Core is to finalize preparation
for students to take Algebra I in high school.
Grade Level Overviews
Standards for Mathematical Content



Content standards define what students should
understand and be able to do.
Clusters are groups of related content standards.
Domains are larger groups of related content standards
that progress across grade levels.
Domain
Code
Standard
from
Grade 3
Standard
Cluster
Fractions, Grades 3-6
Gr. 3: Develop an understanding of fractions as numbers
Gr. 4: Extend understanding of fraction equivalence and ordering
Gr. 4: Build fractions from unit fractions by applying and extending
previous understandings of operations on whole numbers
Gr. 4: Understand decimal notation for fractions, and compare
decimal fractions
Gr. 5: Use equivalent fractions as a strategy to add and subtract
fractions
Gr. 5: Apply and extend previous understandings of multiplication
and division to multiply and divide fractions
Gr. 6: Apply and extend previous understandings of multiplication
and division to divide fractions by fractions
Phil Daro
High School Standards: Conceptual Categories
Are arranged by conceptual cluster, not by course.
• number and quantity
• algebra
• functions
• Modeling*
• Geometry
• Statistics and Probability
Eighth grade Algebra 1 standards are organized around these themes as well.
*Modeling Standard for Mathematical Practice
is emphasized at the high school level. Students are expected to
use mathematics to analyze situations, understand them more fully,
and make decisions related to their everyday lives. (pp.60-61)
Theme
Domain
Cluster of
Standards
High School
Conceptual Theme
Notation
Reflection #4
At first glance, how are the CCSS
grade level standards different from
or similar to our current standards?
Next Steps
What will we do?
Remember:
– Testing begins in 2014/15
Some ideas
– websites & resources
Reflection #5
What else do you need to know
about CCSS?
What are your next steps in this
learning process?
REMEMBER…..
DEEP
DOWN
INSIDE,
WE
ALL
LOVE
MATH