Transcript Slide 0

Moving Ahead with the
Common Core Learning
Standards
for Mathematics
Professional Development | February 9, 2012
RONALD SCHWARZ
Math Specialist, America’s Choice,| Pearson School Achievement
Services
Slide 0
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CFN 609
Block Stack
Math Olympiad for Elementary and Middle Schools
Slide 1
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25 layers of blocks are
stacked; the top four
layers are shown.
Each layer has two
fewer blocks than the
layer below it. How
many blocks are in all
25 layers?
AGENDA
Slide 2
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• Standards for Math Content:
Conceptual Shifts
• Standards for Math Practice
• What’s Different
• Impact on Instruction
• Math Performance Tasks
• Resources
2
What are Standards?
•Standards define what students should
understand and be able to do.
•Any country’s standards are subject to
periodic revision.
•But math is more than a list of topics.
3
Slide 3
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•The US has been a jumble of 50
different state standards. Race to the
bottom or the top?
DESPITE GAINS, ONLY 39% OF NYC 4TH GRADERS AND 26% OF
8TH GRADERS ARE PROFICIENT ON NATIONAL MATH TESTS
NAEP & NY STATE TEST RESULTS
NYC MATH PERFORMANCE
PERCENT AT OR ABOVE PROFICIENT
4th Grade
2009
NAEP
2003
2009
2003
NY State Test
2009
NAEP
Slide 4
2003
2009
NY State Test
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2003
8th Grade
What Does “Higher Standards”
Mean?
•More Topics? But the U.S. curriculum
is already cluttered with too many
topics.
5
Slide 5
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•Earlier grades? But this does not follow
from the evidence. In Singapore, division
of fractions: grade 6 whereas in the U.S.:
grade 5 (or 4)
Lessons Learned
Slide 6
6
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• TIMSS: math performance is being compromised
by a lack of focus and coherence in the “mile
wide. Inch deep” curriculum
• Hong Kong students outscore US students in the
grade 4 TIMSS, even though Hong Kong only
teaches about half the tested topics. US covers
over 80% of the tested topics.
• High-performing countries spend more time on
mathematically central concepts: greater
depth and coherence. Singapore: “Teach less,
learn more.”
Common Core State Standards Evidence Base
For example: Standards from individual highperforming countries and provinces were used
to inform content, structure, and language.
Mathematics
English language arts
1.Belgium
1.Australia
(Flemish)
2.Canada (Alberta)
3.China
4.Chinese Taipei
5.England
6.Finland
7.Hong Kong
8.India
9.Ireland
10.Japan
11.Korea
12.Singapore
New South Wales
•
Victoria
2.Canada
•
Alberta
•
British Columbia
•
Ontario
3.England
4.Finland
5.Hong Kong
6.Ireland
7.Singapore
•
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Slide 7
Why do students have to
do math problems?
Slide 8
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1.To get answers because
Homeland Security needs
them, pronto
2.I had to, why shouldn’t
they?
3.So they will listen in class
4.To learn mathematics
Answer Getting vs. Learning Mathematics
United States
How can I teach my kids to get the
answer to this problem?
Use mathematics they already know. Easy,
reliable, works with bottom half, good for
classroom management.
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Japan
How can I use this problem to teach
mathematics they don’t already
know?
Slide 9
9
Three Responses to a Math
Problem
Slide 10
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1. Answer getting
2. Making sense of the problem
situation
3. Making sense of the
mathematics you can learn
from working on the problem
Answer Getting
Slide 11
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Getting the answer one way or
another and then stopping
Learning a specific method for
solving a specific kind of problem
(100 kinds a year)
Butterfly method
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Slide 12
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Slide 13
Use butterflies on this TIMSS item
1/2 + 1/3 +1/4 =
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Slide 14
Answers are a black hole:
hard to escape the pull
Slide 15
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• Answer getting short circuits
mathematics, especially making
mathematical sense
• Very habituated in US teachers
versus Japanese teachers
• High-achieving countries devise
methods for slowing down,
postponing answer getting
Posing the problem
Slide 16
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• Whole class: pose problem, make sure
students understand the language, no
hints at solution
• Focus students on the problem
situation, not the question/answer
game. Hide question and ask them to
formulate questions that make situation
into a word problem
• Ask 3-6 questions about the same
problem situation; ramp questions up
toward key mathematics that transfers
to other problems
What problem to use?
Slide 17
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• Problems that draw thinking toward the
mathematics you want to teach. NOT too
routine, right after learning how to solve
• Ask about a chapter: what is the most
important mathematics students should
take with them? Find problems that draw
attention to this math
• Begin chapter with this problem (from
lesson 5 thru 10, or chapter test). This has
diagnostic power. Also shows you where
time has to go.
• Near end of chapter, external problems
needed, e.g. Shell Centre
What do we mean by
conceptual coherence?
Apply one important concept in 100 situations
rather than memorizing 100 procedures that
do not transfer to other situations:
Slide 18
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– Typical practice is to opt for short-term
efficiencies, rather than teach for general
application throughout mathematics.
– Result: typical students can get 80s on chapter
tests, but don’t remember what they ‘learned’
later when they need to learn more mathematics
– Use basic “rules of arithmetic” (same as algebra)
instead of clutter of specific named methods
– Curriculum is a ‘mile deep’ instead of a ‘mile
wide’
Teaching against the test
3+ 5 =[ ]
3+[ ]=8
[ ]+5=8
Slide 19
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8-3 =5
8-5 =3
Write a word problem that could be
modeled by a + b = c
Slide 20
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• Result or total unknown; e.g. 5 + 3 = ?
– Mike has 5 pennies. Sam gives him 3 more. How
many does Mike have now?
• Change or part unknown; e.g., 5 + ? = 8
– Mike has 5 pennies. Sam gives him some more.
Now he has 8. How many did he get from Sam?
• Start unknown; e.g., ? + 3 = 8
– Mike has some pennies. He gets 3 more. Now he
has 8. How many did he have at the beginning?
Some Addition and Subtraction
Situations
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21
Slide 21
Some More Addition and Subtraction
Situations
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22
Slide 22
Some Multiplication and Division
Situations
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23
Slide 23
Anna bought 3 bags of red gumballs and
5 bags of white gumballs. Each bag of
gumballs had 7 pieces in it. Which
expression could Anna use to find the
total number of gumballs she bought?
(7 × 3) + 5 =
(7 × 5) + 3 =
7 × (5 + 3) =
7 + (5 × 3) =
Slide 24
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A.
B.
C.
D.
Math Standards
Mathematical Practice: varieties of expertise
that math educators should seek to
develop in their students.
Mathematical Content:
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Mathematical Performance: what kids
should be able to do.
Mathematical Understanding: what kids
need to understand.
Slide 25
25
Standards for Mathematical Content
Organization by Grade Bands and Domains
K–5
6–8
Counting and Cardinality
Ratios and Proportional
Relationships
Operations and
Algebraic Thinking
The Number System
Expressions and
Equations
Number and
Operations—Fractions
Geometry
Measurement and Data
Statistics and Probability
Number and Quantity
Algebra
Functions
Modeling
Geometry
Statistics and Probability
Functions
Geometry
(Common Core State Standards Initiative 2010)
Slide 26
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Number and Operations
in Base Ten
High School
Progressions within and across
Domains
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Slide 27
Daro, 2010
2
7
Math Content
Slide 28
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Greater focus – in elementary school, on
whole number operations and the
quantities they measure, specifically:
Grades K-2 Addition and subtraction
Grades 3-5 Multiplication and division and
manipulation and understanding of
fractions (best predictor algebraic
performance)
Grades 6-8 Proportional reasoning,
geometric measurement and introducing
expressions, equations, linear algebra
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29
Slide 29
Why begin with
unit fractions?
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30
Slide 30
Unit Fractions
31
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Slide 31
Units are things that you count
Daro, 2010
32
Slide 32
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•Objects
•Groups of objects
•1
•10
•100
•¼ unit fractions
•Numbers represented as
expressions
Units add up
3 pennies + 5 pennies = 8 pennies
3 ones + 5 ones = 8 ones
3 tens + 5 tens = 8 tens
3 inches + 5 inches = 8 inches
3 ¼ inches + 5 ¼ inches = 8 ¼ inches
3(1/4) + 5(1/4) = 8(1/4)
3(x + 1) + 5(x+1) = 8(x+1)
Daro, 2010
33
Slide 33
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•
•
•
•
•
•
•
How CCLS support change
The new standards support improved
curriculum and instruction due to increased:
– FOCUS, via critical areas at each grade
level
– RIGOR, including a focus on College and
Career Readiness and Standards for
Mathematical Practice throughout Pre-K
through 12
(Massachusetts State Education Department)
Slide 34
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– COHERENCE, through carefully developed
connections within and across grades
Critical Areas
Grade
level
PK
K
1
2
3
4
5
6
7
8
# of
Critical
Areas
2
2
4
4
4
3
3
4
4
3
Slide 35
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• There are two to four critical areas for
instruction in the introduction for each grade
level, model course or integrated pathway.
• They bring focus to the standards at each
grade by providing the big ideas that
educators can use to build their curriculum
and to guide instruction.
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Slide 36
Critical Areas: Kindergarten
Slide 37
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• Whole numbers: comparing, joining,
separating, counting objects that
remain or in combined sets
• Shapes: shape, orientation, spatial
relationships
• Two-dimensional: square, triangle,
circle, rectangle, hexagon
• Three-dimensional: cube, cone,
cylinder, sphere
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Slide 38
Critical Areas: Grade 1
Slide 39
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• Addition and subtraction fluency to
20: model add-on, take-from, puttogether, take-apart, compare
• Place value: beginning of grouping by
10s and 1s
• Measurement of length: concept of
equal-sized units, transitivity
• Figures: compose and decompose
plane and solid shapes, understand
part-whole relationships
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Slide 40
Critical Areas: Grade 2
Slide 41
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• Base ten: place value of 1000s, 100s,
10s and 1s; counting by 5s, 10s,
100s
• Addition and subtraction fluency
within 100; problems within 1000
• Rulers: recognize and use inches and
centimeters
• Shapes: describe and analyze by
sides and angles; begin foundation
for later area, volume, congruence,
similarity, symmetry
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Slide 42
Critical Areas: Grade 3
Slide 43
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• Multiplication and division: using
equal-sized groups, arrays, area
models; finding unknown number of
groups or unknown group size;
solving problems involving single-digit
factors
• Fractions: built out of unit fractions,
use to represent part of a whole, is
relative to size of the whole, use to
represent numbers equal to greater
than, less than one
Critical Areas: Grade 3
Slide 44
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• Area of a shape: square units; since
rectangular arrays can be
decomposed into identical rows or
columns, area is connected to
multiplication
• Shapes: classified by sides and
angles; area of part of a shape
expressed as a unit fraction of the
whole
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45
Slide 45
Critical Areas: Grade 4
Slide 46
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• Base ten: place value to 1,000,000,
distributive property, multi-digit
multiplication, estimate or mentally calculate
products, quotients with multi-digit dividends,
interpret remainders based on context
• Fractions: equivalence, addition and
subtraction with like denominators, multiply
fraction by whole number
• Geometric figures analyzed and classified by
properties: parallel or perpendicular sides,
angle measures, symmetry
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Slide 47
Critical Areas: Grade 5
Slide 48
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• Fractions: fluency in addition and
subtraction with unlike
denominators, multiplication, division
in special cases (unit fractions by
whole numbers and vice-versa)
• Base ten: two-digit divisors
Critical Areas: Grade 5
Slide 49
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• Decimals: place value, operations to
hundredths with estimation,
relationship between decimals and
whole numbers (e.g., when
multiplied by a power of ten can
become a whole number)
• Volume: use cubic units, estimating
and measuring, finding volume of
right rectangular prism
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50
Slide 50
How CCLS support change
The new standards support improved
curriculum and instruction due to increased:
– FOCUS, via critical areas at each grade
level
– RIGOR, including a focus on College and
Career Readiness and Standards for
Mathematical Practice throughout Pre-K
through 12
(Massachusetts State Education Department)
Slide 51
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– COHERENCE, through carefully developed
connections within and across grades
A Coherent Curriculum
Slide 52
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• Is organized around the big
ideas of mathematics
• Clearly shows how standards
are connected within each
grade
• Builds concepts through logical
progressions across grades that
reflect the discipline itself.
International
Comparison
Charts in the next three slides are taken from:
Schmidt, W.H., Houang, R., & Cougan, L. (2002). A coherent
curriculum: The case of Mathematics. American educator, 26(2),
10-26, 47-48.
As cited by Massachusetts State Education Department
Slide 53
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The mathematics curriculum of
top-achieving countries on
international assessments
looks different from the U.S.
in terms of topic placement
Topic Placement in
Top Achieving Countries
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Slide 54
Topic Placement in
the U.S.
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Slide 55
International Comparison
In what ways do the curricula of the topachieving countries exhibit coherence?
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Slide 56
Domain Progression in the New
Standards
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Slide 57
(Massachusetts State Education Department)
How CCLS support change
The new standards support improved
curriculum and instruction due to increased:
– FOCUS, via critical areas at each grade
level
– RIGOR, including a focus on College and
Career Readiness and Standards for
Mathematical Practice throughout Pre-K
through 12
(Massachusetts State Education Department)
Slide 58
Copyright © 2010 Pearson Education, Inc.or its affiliate(s). All rights reserved.
– COHERENCE, through carefully developed
connections within and across grades
Standards for Mathematical Practice
Slide 59
Copyright © 2010 Pearson Education, Inc.or its affiliate(s). All rights reserved.
1 Make sense of problems and persevere in
solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the
reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically.
6 Attend to precision.
7 Look for and make use of structure.
8 Look for and express regularity in repeated
reasoning.
59
NCTM process standards
Slide 60
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• Problem Solving
• Reasoning and Proof
• Communication
• Representation
• Connections
60
Adding It Up
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Slide 61
National Research Council’s report
Adding It Up:
Slide 62
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• Conceptual Understanding (comprehension of
mathematical concepts, operations and
relations)
• Procedural Fluency (skill in carrying out
procedures flexibly, accurately, efficiently and
appropriately)
• Adaptive Reasoning
• Strategic Competence
• Productive Disposition (habitual inclination to
see mathematics as sensible, useful, and
worthwhile, coupled with a belief in diligence
and one’s own efficacy)
62
Text Rendering
•Read your assigned mathematical practice
description from the Common Core Learning
Standards.
•Describe the standard in your own words. Find
sentences, phrases, and words that are particularly
significant.
Slide 63
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•Discuss your selections with your group. What
does this Practice mean for classroom practice and
student understanding? Think about and describe
what it may look like, sound like and/or feel like in
the classroom.
Standards for Mathematical
Practice
Slide 64
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1. Make sense of problems and persevere in solving
them.
• Mathematically proficient students start by explaining to
themselves the meaning of a problem and looking for
entry points to its solution.
• They analyze givens, constraints, relationships, and
goals.
• They plan a solution pathway rather than simply
jumping into a solution attempt.
• They monitor and evaluate their progress and change
course if necessary.
• Mathematically proficient students check their answers
to problems using a different method, and they
continually ask themselves, “Does this make sense?”
There are 125 sheep
and
5 dogs in a flock.
Slide 65
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How old is the shepherd?
A Student’s Response
There are 125 sheep and 5 dogs in a flock.
How old is the shepherd?
125 x 5 = 625 extremely big
125 - 5 = 120 still big
125  5 = 25
That works!
Slide 66
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125 + 5 = 130 too big
Standards for Mathematical
Practice
2. Reason abstractly and quantitatively.
Slide 67
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• Mathematically proficient students make sense of quantities
and their relationships in problem situations.
• They bring two complementary abilities to bear on problems
involving quantitative relationships:
– the ability to decontextualize—to abstract a given situation
and represent it symbolically and manipulate the
representing symbols as if they have a life of their own,
without necessarily attending to their referents
– and the ability to contextualize, to pause as needed during
the manipulation process in order to probe into the
referents for the symbols involved.
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Slide 68
Standards for Mathematical
Practice
Slide 69
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3. Construct viable arguments and critique the
reasoning of others.
• Mathematically proficient students understand and use
stated assumptions, definitions, and previously
established results in constructing arguments.
• They make conjectures and build a logical progression
of statements to explore the truth of their conjectures.
• They justify their conclusions, communicate them to
others, and respond to the arguments of others.
• Mathematically proficient students are also able to
compare the effectiveness of two plausible arguments,
distinguish correct logic or reasoning from that which is
flawed, and—if there is a flaw in an argument—explain
what it is.
Take the number apart?
Slide 70
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Tina, Emma and Jen discuss this
expression:
6 × 5⅓
Tina: I know a way to multiply with a
mixed number that is different from
what we learned in class. I call my way
‘take the number apart.’ I’ll show you.
First, I multiply the 5 by the 6 and get
30. Then I multiply the ⅓ by the 6 and
get 2. Finally, I add the 30 and the 2 to
get my answer, which is 32.
70
Take the number apart?
Slide 71
71
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Tina: It works whenever I have to multiply a
mixed number by a whole number.
Emma: Sorry Tina, but that answer is wrong!
Jan: No, Tina’s answer is right for this one
problem, but ‘take the number apart’
doesn’t work for other fraction problems.
Which of the three girls do you think is right?
Justify your answer mathematically.
Distributive Property
5⅓ = 5 + ⅓
6 × 5⅓ = 6(5 + ⅓)
6(5 + ⅓)= 6 × 5 + 6 × ⅓
Since a(b + c) = ab + ac
Could illustrate with area of rectangle 6
by 5⅓
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Slide 72
72
Standards for Mathematical
Practice
Slide 73
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4. Model with mathematics.
• Mathematically proficient students can apply the
mathematics they know to solve problems arising in
everyday life, society, and the workplace.
• They are able to identify important quantities in a
practical situation and map their relationships using
such tools as diagrams, two-way tables, graphs,
flowcharts and formulas.
• They can analyze those relationships mathematically to
draw conclusions.
• They routinely interpret their mathematical results in
the context of the situation and reflect on whether the
results make sense, possibly improving the model if it
has not served its purpose.
Standards for Mathematical
Practice
Slide 74
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5. Use appropriate tools strategically.
• Mathematically proficient students consider the
available tools when solving a mathematical problem.
• These tools might include pencil and paper, concrete
models, a ruler, a protractor, a calculator, a
spreadsheet, a computer algebra system, a statistical
package, or dynamic geometry software.
• Proficient students are sufficiently familiar with tools
appropriate for their grade or course to make sound
decisions about when each of these tools might be
helpful, recognizing both the insight to be gained and
their limitations.
• They are able to use technological tools to explore and
deepen their understanding of concepts.
Standards for Mathematical
Practice
Slide 75
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6. Attend to precision.
• Mathematically proficient students try to communicate
precisely to others. They try to use clear definitions in
discussion with others and in their own reasoning.
• They state the meaning of the symbols they choose,
including using the equal sign consistently and
appropriately.
• They are careful about specifying units of measure, and
labeling axes to clarify the correspondence with
quantities in a problem.
• They calculate accurately and efficiently, express
numerical answers with a degree of precision
appropriate for the problem context.
Using the equal sign consistently
and appropriately
8
8 + 9 = 17 – 7 = 10 ÷ 2 = 5 + 3 = 8
Slide 76
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8+9=8
http://www.mathsisfun.com/definitions
/index.html
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Slide 77
Standards for Mathematical
Practice
Slide 78
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7. Look for and make use of structure.
• Mathematically proficient students look closely to
discern a pattern or structure.
• Young students, for example, might notice that three
and seven more is the same amount as seven and three
more, or they may sort a collection of shapes according
to how many sides the shapes have.
• They recognize the significance of an existing line in a
geometric figure and can use the strategy of drawing an
auxiliary line for solving problems. They also can step
back for an overview and shift perspective.
• They can see complicated things, such as some
algebraic expressions, as single objects or as being
composed of several objects.
Standards for Mathematical
Practice
Slide 79
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8. Look for and express regularity in
repeated reasoning.
• Mathematically proficient students notice if
calculations are repeated, and look both for
general methods and for shortcuts.
• As they work to solve a problem,
mathematically proficient students maintain
oversight of the process, while attending to
the details.
What is the value of
17 × 13 + 61 × 13 + 22 × 13?
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80
Slide 80
Slide 81
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“Proficient students of all ages expect
mathematics to make sense. They take an
active stance in solving mathematical
problems. When faced with a non-routine
problem, they have the courage to plunge in
and try something, and they have the
procedural and conceptual tools to continue.
They are experimenters and inventors, and
can adapt known strategies to new problems.
They think strategically.”
Common Core State Standards
Slide 82
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“Students who engage in these practices
individually and with their classmates,
discover ideas and gain insights that spur
them to pursue mathematics beyond the
classroom walls. They learn that effort
counts in mathematical achievement.
Encouraging these practices in students of all
ages should be as much a goal of the
mathematics curriculum as the learning of
specific content”
Common Core State Standards
Break
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Instructional Expectations
2011-12
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• Strengthening student work
Curriculum
Assessment
Classroom instruction
• Strengthening teacher
practice
Feedback
Instructional Expectations
2011-12: Core Documents
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Framework for Teaching, Charlotte
Danielson
Depth of Knowledge, Norman Webb
Understanding by Design, Grant
Wiggins
Universal Design for Learning
Curriculum Mapping, Heidi Hayes
Jacobs
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86
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Instructional Expectations:
Teachers
Look closely at current student work
Engage all students in at least one
cognitively-demanding
mathematics task which
demonstrates their ability to model
with mathematics and/or construct
viable arguments
Look closely at the resulting student
work
Spring 2012 Task – Domains
Chosen
Grade
Number and Operations in Base Ten
Operations and Algebraic Thinking
Number and Operations—Fraction
Ratios and Proportional Relationships
Expressions and Equations
Reasoning with Equations and Inequalities
Congruence
88
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1-2
3
4-5
6-7
8
Algebra
Geometry
Domain
89
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Math
Tasks
Some Criteria for Choice of Tasks
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Level of challenge – The Goldilocks
standard
Multiple points of entry
Identifying the math concept
involved with, and strengthened
by, working on the task
Opportunities to bring out student
misconceptions, which can be
identified and addressed
90
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91
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Research on Retention of Learning: Shell
Center: Swan et al
Misconception Learning verses Remedial Learning:
Test Scores
25
20
19.1
17.8
15.8
15
10
Students who were
taught using remedial
measures
10.4
7.9
5
0
Pre-test
Post-test
Delayed Test
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12.7
Students who were
taught by addressing
misconceptions
Pedagogy
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Make conceptions and misconceptions
visible to the student
Design problems that elicit
misconceptions so they can be dealt
with
Students need to be listened to and
responded to
Partner work
Revise conceptions
Debug processes
Meta-cognitive skills
A Problem (DO NOT SOLVE)
What questions do you ask yourself
as you encounter this problem?
How do these questions help you to
develop a solution approach?
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Make as many rectangles as you can
with an area of 24 square units. Use
only whole numbers for the length
and width. Sketch the rectangles,
and write the dimensions on the
diagrams. Write the perimeter of
each one next to the sketch.
Meta-Cognition
• Thinking about thinking.
• The unconscious process of
cognition.
• Meaning-making
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It is hard to articulate how you
think about thinking. It is even
harder to model
Meta-cognition implications for lessons.
•
•
•
•
•
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Make thinking public
Use multiple representations
Offer different approaches to solution
Ask questions about the problem posed.
Set a context, define the why of the
problem
• Focus students on their thinking, not the
solution
• Solve problems with partners
• Prepare to present strategies
Analysis of
Tasks
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Levels of Cognitive Demand
Lower-level
• Memorization
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• Procedures without
connections
Higher-level
• Procedures with connections
• Doing mathematics
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98
Norman Webb’s Depth of
Knowledge
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99
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• Level 1: Recall and
Reproduction
• Level 2: Skills and Concepts
• Level 3: Strategic Thinking
• Level 4: Extended Thinking
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100
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Standards for Mathematical Practice
“Not all tasks are created equal,
and different tasks will
provoke different levels and
kinds of student thinking.”
Stein, Smith, Henningsen, & Silver, 2000
1
0
Hiebert, Carpenter, Fennema, Fuson, Wearne,
Murray, Oliver, & Human, 1997
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“The level and kind of thinking
in which students engage
determines what they will
learn.”
Standards for Mathematical Practice
1
0
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The eight Standards for
Mathematical Practice – place an
emphasis on student
demonstrations of learning…
Equity begins with an
understanding of how the
selection of tasks, the
assessment of tasks, the student
learning environment create
great inequity in our schools…
Opportunities for all students to
engage in challenging tasks?
• Examine tasks in your instructional
0
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materials:
– Higher cognitive demand?
– Lower cognitive demand?
• Where are the challenging tasks?
• Do all students have the opportunity
to grapple with challenging tasks?
• Examine the tasks in your
assessments:
– Higher cognitive demand?
– Lower cognitive demand?
1
Students’ beliefs about their intelligence
• Fixed mindset:
Dweck, 2007
1
0
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– Avoid learning situations if they might
make mistakes
– Try to hide, rather than fix, mistakes or
deficiencies
– Decrease effort when confronted with
challenge
• Growth mindset:
– Work to correct mistakes and deficiencies
– View effort as positive; increase effort
when challenged
Students can develop growth mindsets
• Explicit instruction about the brain, its
NCSM Position Paper #7
Promoting Positive Self-Beliefs
1
0
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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
Timeline
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New York State Assessment Transition Plan
Revised October 20, 2011
ELA & Math
Assessment –
Grade / Subject
ELA
Grades 3-8
2011-12
2012-13
DRAFT
2013-14
2014-15
Aligned to 2005 Standards
1
Aligned to the Common Core
Grade 9
Grade 10
Grade 11
Regents
PARCC2
1
Aligned to 2005 Standards
Math
Grades 3-8
3
Algebra I
Aligned to 2005 Standards
Aligned to the Common Core
Aligned to 2005 Standards
3
Aligned to 2005 Standards
3
Aligned to 2005 Standards
Geometry
Algebra II
Aligned to the Common Core
Aligned to the Common Core
4
PARCC2
NYSAA
NYSESLAT
Aligned to the Common Core
Aligned to 2005 Standards
NCSC5
Aligned to the Common Core
1 New ELA assessments in grades 9 and 10 will begin during the 2012-13 school year and will be aligned to the Common Core, pending funding.
2 The PARCC assessments are scheduled to be operational in 2014-15 and are subject to adoption by the New York State Board of Regents. The
PARCC assessments are still in development and the role of PARCC assessments as Regents assessments will be determined. All PARCC assessments
will be aligned to the Common Core.
3 The names of New York State’s Mathematics Regents exams are expected to change to reflect the new alignment of these assessments to the Common
Core. For additional information about the upper-level mathematics course sequence and related standards, see the “Traditional Pathway” section of
Common Core Mathematics Appendix A.
4 The timeline for Regents Math roll-out is under discussion.
5 New York State is a member of the NCSC national alternate assessments consortium that is engaged in research and development of new alternate
assessments for alternate achievement standards. The NCSC assessments are scheduled to be operational in 2014-15 and are subject to adoption by
the New York State Board of Regents.
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107
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Additional State Assessments
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108
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Resources
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110
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Web Links
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11
1
Common Core State Standards:
http://www.corestandards.org/
Common Core Tools:
http://commoncoretools.wordpress.com/
New York State Site for Teaching and Learning
Resources
http://www.engageny.org/
PARCC:
http://www.parcconline.org/
Inside Mathematics:
http://www.insidemathematics.org/index.php/home
Mathematics Assessment Project:
http://map.mathshell.org/materials/index.php
Common Core Library:
http://schools.nyc.gov/Academics/CommonCoreLibr
ary/default.htm
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1
1
Pearson Professional Development
pearsonpd.com
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RONALD SCHWARZ, facilitator
[email protected]
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