math shifts focuscoherencerigor. what are the shifts? focus: focus strongly where the standards...
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Math ShiftsFocus
CoherenceRigor
What are the Shifts?• Focus:
focus strongly where the standards focus
Instructional Shift: What does focus mean for our
instruction?
GRADE FOCUS (and expectation of FLUENCY and CONCEPTUAL UNDERSTANDING)
K-2 Addition and subtraction – concept, skills and problem solving
3-5 Multiplication of whole numbers and fractions – concepts, skills and problem solving
6 Ratios and proportional relationships; early expressions and equations
7 Ratios and proportional relationships; arithmetic of rational numbers
8 Linear Algebra
What are the Shifts?• Focus:
focus strongly where the standards focus • Coherence:
think across grades, and link to major topics in each grade
Instructional Shift:
What does coherence mean for our instruction?
PreK K 1 2 3 4 5 6 7 8 HS
Mathematical Practices
Counting & Cardinality
Number & Operations in Base TenRatios &
Proportional Relationships
Number &
QuantityNumber & Operations - Fractions
The Number System
Operations & Algebraic Thinking Expressions & Equations Algebra
Functions
Geometry
Measurement & Data Statistics & Probability
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Next Generation Mathematics Content Standards and Objectives
What are the Shifts?• Focus:
focus strongly where the standards focus • Coherence:
think across grades, and link to major topics in each grade
• Rigor: in major topics, pursue with equal intensity
— conceptual understanding— procedural skill and fluency— applications
Instructional Shift:
What does rigor mean for our instruction?
Center of the Classroom Culture
Standards for Mathematical Practice
Overview of session
Eight Standards for
Mathematical Practice
1. Make sense of problems & persevere in solving them.2. Reason abstractly & quantitatively.3. Construct viable arguments & critique the reasoning of
others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for & make use of structure.8. Look for & express regularity in repeated reasoning.
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Standards for Mathematical Practice
The Importance of the Standards for Mathematical Practices
Video clip
r
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Connecting the Standard for Mathematical Practice with the
Content Standards
Standards that begin with “understand” are good
opportunities to connect the Practices to the Content!
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Content & Practices
“A lack of understanding (of the content) effectively prevents a student from engaging in the Mathematical Practices.”
Skip Fennell, former NCTM president
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Content & Practices
Great Tasks Matter!
1.What is a great task?2.Why is it important to use
great tasks?
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“If we want students to develop the capacity to think, reason, and problem solve then we need to start with high-level, cognitively complex tasks.”
Stein & Lane, 1996
Tasks Matter
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“Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.”
Stein, Smith, Henningsen, & Silber, 2000
Thinkmath.edc.org
Tasks Matter
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Dan Meyer Math class needs a makeover - YouTube.mp4
Dan Meyer: Math Class Needs a Makeover
TED Talk
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What is a Great Task?
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Why use a Great Task?
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Center of the Classroom Culture
Standards for Mathematical Practice
Phil Daro Video clip
Getting Into the Grade Level Content Standards
Day Two
Grade Level Emphasis
Other Resources for Understanding the Grade Level Standards
Learning Progressiondocuments for the Common Core State Standards found
online at http://ime.math.arizona.edu/progressions/
Smarter Balanced Assessment ConsortiumAn Assessment System to Support Teaching and Learning
Item and Task Specifications and Sample Items
Sample assessment items and tasks areincluded in item/task specifications:www.smarterbalanced.org/itemspecs
Live sample items and tasks:www.sampleitems.smarterbalanced.org
Go to the Smarter Website
1. http://www.smarterbalanced.org2. Click on Smarter Balanced Assessment (top
of page)3. In drop down, scroll to Sample Items and
Performance Tasks4. In task bar, click on View More Sample Items5. In drop down, click on Choose 6-8 or High
School
ADE is inside ABCD. Point E is halfway between points B and C on the rectangle. Side AB is 8 cm and side AD is 7 cm.
Part A: What is the area of ADE?Part B: What is the ratio of the area of ABE to the area of ADE?Part C: What is the ratio of the area of DCE to the area of ABCD?
A 20-gallon container is filled with 6 gallons of gasoline. What fractions of the container is filled with gasoline?
.
Which equation is represented by the graph?
A.2y + x = 10B. y - 2x = -5C. -2y = 10x – 4D.2y = - 4x - 10
The three different linear functions below are represented in three different ways, as shown.
2y + 3 = 3x X f(x)
-3 -9 3 3 6 9
(I) (II)(III)
Which function has the greatest rate of change? Does any pair of functions have the same rate of change? Justify your answer.
The diagram on the right shows a pillow Chris wants to cover with fabric.
•What is the total surface area of the pillow? Round your answer to the nearest hundredth.
Show your work:
Answer _________ square inches
•If Chris shortens the length of the pillow from 15 in to 12 in, how much less fabric will she need? Round your answer to the nearest hundredth.
Show your work:
Answer _______square inches
Calculator Use on the SmarterBalanced Math Assessments
How will Smarter Balanced decide whenand how to allow calculators?
Grades 6-HS
• Calculators are available for a small proportion of grade 6 items and gradually increase in availability as students progress toward high school.
• Calculators will be available for most or all of the high school math items.
Powerful Collaboration
PLCs at Work
Teacher collaboration is the key to improving instruction and reaching all students.
Education Trust, 2005; Kersaint, 2007
Critical Questions of Learning
1. What is it we expect them to learn?2. How will we know when they have
learned it?3. How will we respond when they don’t
learn?4. How will we respond when they already
know it?
Rebecca DuFour4 Critical Questions of a PLC
Video Clip
There is such a
thing as group IQ.
What is Collaboration?
What is a Professional
Learning Community?
Remember the URN!
What should you expectas you begin collaboration
within your PLC?
Solution-Tree.com
Working Together to Analyze Instruction
Peer Review and Discussion
What does instruction for mathematical practices look like?
http://www.insidemathematics.org/index.php/standard-3
“…collaboration is a means to an end, not
the end itself.” (Learning by Doing, Solution Tree 2006)
Resources• Common Core State Standards Initiative
http://www.corestandards.org/Math
• Achieve the Core http://www.achievethecore.org/
• Illustrative Mathematics http://www.illustrativemathematics.org/
• The Hunt Institute Videos http://www.youtube.com/user/TheHuntInstitute?feature=watch
• WVDE Office of Instruction http://wvde.state.wv.us/instruction/math.html
Resources• National Science Digital Library – Serving STEM Education
http://nsdl.org/search/standards/D10003FB
• University of Arizona – Progressions Documents for the CCSS – M http://ime.math.arizona.edu/progressions/
• Hawaii State Department of Education – Standards Database http://wetserver.net/hcpsv3_staging/cc/common-core.jsp
• Council of Chief State School Officers http://spaces.ccsso.org/CCSSO/Home
• iTunes Preview – CCSS Apps https://itunes.apple.com/us/app/common-core-standards/id439424555