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Common Core State Standards for Mathematics

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Title: Common Core State Standards for Mathematics


1
Common Core State Standards for Mathematics
  • Christine Downing, CCSS Consultant NH DOE
  • Patty Ewen, Office of Early Childhood Education,
    NH DOE

2
Whos in the room?
  • Name, position, school/district
  • Tell me something you already know about the CCSS
    for Mathematics?
  • Now tell me something you hope to learn more
    about in terms of CCSS for Mathematics?

3
Goals of Presentation
  • Dig into the Common Core State Standards for
    Mathematics
  • 2. Get down and dirty with SBAC
  • Content Specifications, Assessment Claims, Item
    Specifications
  • Throughout we will sift through and mix the
    resources!

4
Instructional Shifts
  • Focus
  • Coherence
  • Fluency
  • Deep Understanding
  • Application
  • Dual Intensity

5
Dig Into CCSS Mathematics
1
6
Context for Treasure Hunt
  • As you complete the treasure hunt, consider the
    following Common Core Message.
  • CCSS Solve Three Specific Problems
  • Increased Skills Demand and Competition
  • Students Not College/Career Ready
  • Variance Across the Country in Standards/Expectati
    ons
  • Is there evidence in CCSS for Mathematics to
    support this?

7
Treasure Hunt
  • Form Small Groups that represent the grade ranges
    from K through 12
  • As a group complete the Treasurer Hunt for
    Mathematics
  • As you complete the Treasurer Hunt, keep track of
    what intrigues you? What do you want to
    investigate deeper? Also, what surprised you?

8
Lets Do a Quick Overview of Mathematics
  • Here are some common, key messages that can be
    used to begin the discussion
  • Hang onits going to be quite a ride!

9
Criteria for New Standards
  • Fewer, clearer, and higher (Consistent, rigorous,
    and shared aligned with college and work
    expectations)
  • 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 (think DNA of education)
  • Internationally benchmarked, so that all students
    are prepared to succeed in our global economy and
    society
  • Based on evidence and research

10
Mathematics
  • Focus and coherence
  • Focus on key topics at each grade level.
  • Coherent progressions across grade levels.
  • Balance of concepts and skills
  • Content standards require both conceptual
    understanding and procedural fluency.
  • Mathematical practices (8 practices)
  • Foster reasoning and sense making in mathematics.
  • College and career readiness
  • Level is ambitious but achievable.

11
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12
Topic Placement in Top Achieving Countries
13
Topic Placement in the U.S.
14
International Comparison
15
CCSS Distribution of Emphasis
CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression
Domains K 1 2 3 4 5 6 7 8
Counting and Cardinality
Operations and Algebraic Thinking
Number and Operations in Base Ten
Number and Operations Fraction
Ratios and Proportional Reasoning
The Number System
Expressions and Equations
Functions
Measurement and Data
Geometry
Statistics and Probability
16
CCSS versus GLE/GSE emphasis In NECAP
CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression CCSS K 8 Domains Progression
Domains K 1 2 3 4 5 6 7 8
Counting and Cardinality
Operations and Algebraic Thinking
Number and Operations in Base Ten
Number and Operations Fraction
Ratios and Proportional Reasoning
The Number System
Expressions and Equations
Functions
Measurement and Data
Geometry
Statistics and Probability
17
NECAP Assessment Changes in Mathematics
Test Grade GLEs NOT Assessed in Fall 2013
NECAP Mathematics 3 DSP 2-4 Combinations
NECAP Mathematics 4 DSP 3-5 Probability
NECAP Mathematics 5 DSP 4-4, DSP 4-5, and GM 4-5 Combinations/Permutations Theoretical Probability Similarity
NECAP Mathematics 6 DSP 5-5 Experimental Theoretical Probability
NECAP Mathematics 7 DSP 6-4, DSP 6-5, FA 6-2, and GM 6-5 Combinations/Permutations Experimental Theoretical Probability Slope Similarity
NECAP Mathematics 8 FA 7-2 Slope Constant/Varying Rates of Change
18
CCSS Mathematics-High School
The high school standards are listed in
conceptual categories Number and Quantity
Algebra Functions Modeling Geometry
Statistics and Probability
19
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20
Lets Pause for a Bit
  • Lets Jigsaw the strands of mathematical
    proficiency.
  • Please form groups of 5.
  • All read pages 115 to 118 and 133 to 135
  • Person 1 reads conceptual understanding
  • Person 2 reads procedural fluency
  • Person 3 reads strategic competence
  • Person 4 reads adaptive reasoning
  • Person 5 reads productive disposition

21
  • How do the strands of mathematical proficiency
    relate to the 8 mathematical habits of mind?

22
National Council of Teachers of Mathematics NCTM
  • Mathematical Process Standards
  • Communication
  • Connections
  • Representations
  • Problem Solving
  • Reasoning
  • Proof
  • www.nctm.org

23
New Hampshire Connection to 8 Mathematical
Practices
PreK-16 Numeracy Action Plan for the 21st
Century http//www.education.nh.gov/innovations/pr
e_k_num/index.htm
24
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25
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26
Lets Dig a Little Deeper
  • The new standards support improved curriculum and
    instruction due to increased
  • FOCUS, via critical areas at each grade level
  • COHERENCE, through carefully developed
    connections within and across grades
  • CLARITY, with precisely worded standards that
    cannot be treated as a checklist
  • RIGOR, including a focus on College and Career
    Readiness and Standards for Mathematical Practice
    throughout Pre-K-12

27
Structure of Knowledge
28
Structure of Knowledge in CCSS
  • Critical Areas
  • Domains
  • Clusters
  • Standards

Top Level
Similar to STRANDS from GLEs and GSEs
Middle Level
Similar to STEMS from GLEs and GSEs
Bottom Level
29
Critical Areas
  • There are typically two to four Critical Areas
    for instruction in the introduction for each
    grade level or course.
  • They bring focus to the standards at each grade
    by grouping and summarizing the big ideas that
    educators can use to build their curriculum and
    to guide instruction.

30
Example of a Critical Area
  • __________________________________________________
    _____________________________________
  • Kindergarten
  • __________________________________________________
    _____________________________________
  • In Kindergarten, instructional time should focus
    on two critical areas (1) representing,
    relating, and operating on
  • whole numbers, initially with sets of objects
    and (2) describing shapes and space. More
    learning time in
  • Kindergarten should be devoted to number than to
    other topics.
  • (1) Students use numbers, including written
    numerals, to represent quantities and to solve
    quantitative problems, such as counting objects
    in a set counting out a given number of objects
    comparing sets or numerals and modeling simple
    joining and separating situations with sets of
    objects, or eventually with equations such as 5
    2 7 and 7 2 5. (Kindergarten students
    should see addition and subtraction equations,
    and student writing of equations in Kindergarten
    is encouraged, but it is not required.) Students
    choose, combine, and apply effective strategies
    for answering quantitative questions, including
    quickly recognizing the cardinalities of small
    sets of objects, counting and producing sets of
    given sizes, counting the number of objects in
    combined sets, or counting the number of objects
    that remain in a set after some are taken away.
  • (2) Students describe their physical world using
    geometric ideas (e.g., shape, orientation,
    spatial relations) and vocabulary. They identify,
    name, and describe basic two-dimensional shapes,
    such as squares, triangles, circles, rectangles,
    and hexagons, presented in a variety of ways
    (e.g., with different sizes and orientations), as
    well as three-dimensional shapes such as cubes,
    cones, cylinders, and spheres. They use basic
    shapes and spatial reasoning to model objects in
    their environment and to construct more complex
    shapes.
  • The Standards for Mathematical Practice
    complement the content standards at each grade
    level so that students
  • increasingly engage with the subject matter as
    they grow in mathematical maturity and expertise.

31
How do critical areas promote focus?
  • What is the number of critical areas per grade
    level/course?
  • How will/could it improve teaching and learning
    in our school/district when each grade focuses on
    a few Critical Areas?

Grade level K 1 2 3 4 5 6 7 8
of Critical Areas 2 4 4 4 3 3 4 4 3
Course Alg I Geo Alg II Math I Math II Math III
of Critical Areas 5 6 4 6 6 4
32
Main Activity Focusing on the Critical Areas
  • In small groups, read the Critical Areas for a
    grade level including the description.
  • Read each content standard, marking the recording
    sheet with a
  • v when a standard strongly matches or supports
    your Critical Area and
  • ? when you are not sure
  • Leave blank if the standard does not match or
    support the Critical Area

33
  • Did every standard fall within a Critical Area?
  • Are there standards that fall within more than
    one Critical Area?
  • Do all the standards within a cluster fall within
    the same Critical Area?

34
  • How do the Critical Areas help organize and bring
    focus to your grade level standards?
  • How should we as a school (or district) use what
    we have learned today about Critical Areas in
    planning for the implementation of the new
    standards?
  • How could this work be linked to existing
    curriculum built on GLEs/GSEs?

35
Down and Dirty with SBAC
2
  • Content Specifications
  • Assessment Claims
  • Item Specifications

36
SMARTER Balanced
  • Computer Adaptive
  • Multiple Choice, Constructed Response, Technology
    Enhanced
  • Performance Tasks
  • Writing, listening and speaking
  • Emphasis of mathematical practices

37
Components of SBAC System
  • Summative Assessments
  • Grades 3-8 and 11 in ELA and Mathematics
  • Computer Adaptive Testing
  • Performance Tasks
  • Interim Assessments
  • Optional
  • Progress of Students
  • Linked to content clusters in CCSS
  • Formative Tools and Processes
  • Evidence of progress toward learning goals

38
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39
Mathematics Content Specs
  • Claim 1 Conceptual Understanding and Procedural
    Fluency Students can explain and apply
    mathematical concepts and interpret and carry out
    mathematical procedures with precision and
    fluency.
  • Claim 2 Problem Solving Students can solve a
    range of complex well-posed problems in pure and
    applied mathematics, making productive use of
    knowledge and problem solving strategies.

40
Mathematics Content Specs
  • Claim 3 Communicating Reasoning Students can
    clearly and precisely construct viable arguments
    to support their own reasoning and to critique
    the reasoning of others.
  • Claim 4 Modeling and Data Analysis Students can
    analyze complex, real-world scenarios and can
    construct and use mathematical models to
    interpret and solve problems.

41
Lets look at SBAC Resources
  • Assessment Claims and Target Standards
  • Claim 1 of the Content Specifications
  • Design of Performance Tasks
  • Sample Items from Showcase 2 and 3

42
Where do you find all this for SBAC?
  • www.smarterbalanced.org
  • Now explore on your own!

43
Share
  • So what ahas did you have as you explored the
    wealth of information on SBAC?
  • What concerns do you have?
  • What will you do next?

44
Other Math Resources
  • MASS DOE presentation materials
  • NCSM Alignment Tool for CCSS resources
  • NCTM Reasoning and Sense Making Tools
  • Indiana Resources new??
  • North Carolina Unpacking

45
Questions/Comments
  • Thank you!
  • Christine Downing
  • Christine.downing_at_nh.gov
  • Patty Ewen
  • Patricia.ewen_at_doe.nh.gov
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