Common Core: Shifts, Practices,
RigorCathy BattlesConsultantUMKC-Regional Professional Development [email protected]
Starter ProblemUsing each of the digits 1 through 9 only once, find two 3-digit numbers whose sum uses the remaining three digits
Some Answers
Partner TimeTurn to your partner and tell them what you
know about the common core and what you or your district has done.
About the Common Core StandardsClarity: The standards are focused, coherent, and
clear. Clearer standards help students (and parents and teachers) understand what is expected of them.
•Collaboration: The standards create a foundation to work collaboratively across states and districts, pooling resources and expertise, to create curricular tools, professional development, common assessments and other materials.
Source: Adapted From Student Achievement Partners
Education Week: COMMON STANDARDS www.edweek.org/go/standardsreport
4/25/12
Common Core Standards ShiftsSignificantly narrow the scope of content and
deepen how time and energy is spent in the classroom
Focus deeply on what is emphasized in the standards, so students gain strong foundations
Equity: Expectations are consistent for all – and not dependent on a student’s zip code. Level the playing field for students across the country…
CCSS Domain ProgressionK 1 2 3 4 5 6 7 8 HS
Counting & Cardinality
Number and Operations in Base Ten Ratios and Proportional Relationships Number &
QuantityNumber and Operations – Fractions The Number System
Operations and Algebraic Thinking
Expressions and Equations Algebra
Functions Functions
Geometry Geometry
Measurement and Data Statistics and Probability Statistics & Probability
2.
Reason abstractly
and quantitatively.
1. Make sense of problems
and persevere in solving them.
3.Construct viable argum
ents and critique the reasoning of others.
4.Model with
mathematics.
5.Use appropriate tools
strategically.
6. Attend to
precision.
7.Lo
ok fo
r and
mak
eus
e of
stru
ctur
e.
8.
Look f
or and exp
ress regu
larity
in repeated re
asoning. Counting
andCardinalit
yKindergarten
Numbers and
Operations in Base
TenGrades K-5
Operations and Algebraic
ThinkingGrades K-5
Measurement and Data
Grades K-5
Geometry
Grades K-5
Fractions
Grades 3-5
Kathy Andersonhttp://northstartechnologyguide.com/wp-content/uploads/2010/07/apple-core-250x238.jpg
2.
Reason abstractly
and quantitatively.
1. Make sense of problems
and persevere in solving them.
3.Construct viable argum
ents and critique the reasoning of others.
4.Model with
mathematics.
5.Use appropriate tools
strategically.
6. Attend to
precision.
7.Lo
ok fo
r and
mak
eus
e of
stru
ctur
e.
8.
Look f
or and exp
ress regu
larity i
n
repeated reaso
ning. Ratios andProportional Relationships
Grades 6-7
Expressions
and EquationsGrades 6-8
Statistics andProbability
Grades 6-8
GeometryGrades 6-8
The Number System
Grades 6-8
Functions
Grade 8
Kathy Andersonhttp://northstartechnologyguide.com/wp-content/uploads/2010/07/apple-core-250x238.jpg
2.
Reason abstractly
and quantitatively.
1. Make sense of problems
and persevere in solving them.
3.Construct viable argum
ents and critique the reasoning of others.
4.Model with
mathematics.
5.Use appropriate tools
strategically.
6. Attend to
precision.
7.Lo
ok fo
r and
mak
eus
e of
stru
ctur
e.
8.
Look f
or and exp
ress regu
larity i
n
repeated reaso
ning.
Kathy Anderson
Number and Quantity
Algebra
Functions
Statistics and
Probability
Geometry
Modeling
http://northstartechnologyguide.com/wp-content/uploads/2010/07/apple-core-250x238.jpg
Mathematical Practices are Not:
A checklistDisconnected from content standardsGrade specificNewRestricted to mathTaught in isolationSequentialA Friday problem solving activity
CORE ACADEMIC STANDARDS(CAS)
Missouri’s Core Academic Standards are the same as the Common Core Standards for Math and ELA but also include Social Studies and Science
RIGORA balance of :
A.Conceptual UnderstandingB.FluencyC.Application
Of all pre-college curricula, the highest level of mathematics in secondary school has the strongest continuing influence on bachelor’s degree completion. Finishing a course beyond Algebra 2 more than doubles the odds that a student who enters post-secondary education will complete a bachelor’s degree.
National Mathematics Advisory Panel
Adams, C. (2006). Answers in the toolbox: academic intensity, attendance patterns, and bachelor’s degree attainment. (Office of Educational Research and Improvement Publication.) http://www.ed.gov/pubs/Toolbox/Title.htm.
National Mathematics Advisory PanelRecommendations
1. A focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula; the most important topics underlying success in school algebra.
National Mathematics Advisory Panel Recommendations
2. A major goal of K – 8 mathematics education should be proficiency with fractions (including decimals, percent, and negative fractions), for such proficiency is foundational for algebra and seems to be severely underdeveloped. In addition, the Panel identified Critical Foundations of Algebra (p 17).
FractionsTurn to your neighbor and share one thing that you know about the Common Core and changes with fractions
18
“It is possible to have good number sense for whole numbers, but not for fractions.”Sowder, J. and Schappelle, Eds.
1989
Problem: 7/8 – 1/8 = ? Fraction Sense?
Interviewer: Melanie these two circles represent pies that were each cut into eight pieces for a party. This pie on the left had seven pieces eaten from it. How much pie is left there?Melanie: One-eighth, writes 1/8
Interviewer: The pie on the right had three pieces eaten from it. How much is left of that pie? Melanie: Five-eighths, writes 5/8
• Interviewer: If you put those two together, how much of a pie is left? • Melanie: Six-eighths, writes 6/8.
Interviewer: Could you write a number sentence to show what you just did? Melanie: Writes 1/8 + 5/8 = 6/16.
Interviewer: That’s not the same as you told me before. Is that OK? Melanie: Yes, this is the
answer you get when you add.
American students’ weak understanding of fractions
2004 NAEP - 50% of 8th-graders could not order three fractions from least to greatest (NCTM, 2007)
American students’ weak understanding of fractions
2004 NAEP, Fewer than 30% of 17-year-olds correctly translated 0.029 as 29/1000 (Kloosterman, 2010)
American students’ weak understanding of fractions
One-on-one controlled experiment tests - when asked which of two decimals, 0.274 and 0.83 is greater, most 5th- and 6th-graders choose 0.274 (Rittle-Johnson, Siegler, and Alibali, 2001)
American students’ weak understanding of fractions
Knowledge of fractions differs even more between students in the U.S. and students in East Asia than does knowledge of whole numbers (Mullis, et al., 1997)
• Not viewing fractions as numbers at all, but rather as meaningless symbols that need to be manipulated in arbitrary ways to produce answers that satisfy a teacher
• Focusing on numerators and denominators as separate numbers rather than thinking of the fraction as a single number.
• Confusing properties of fractions with those of whole numbers
FractionsFacets of the lack of student conceptual understanding:
3rd Grade Number and Operations Fractions(3.NF)Develop understanding of fractions as
numbers.Understand a fraction 1/b as the quantity formed
by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
3rd Grade Fractions (Cont)Understand a fraction as a number on the number line; represent fractions on a number line diagram.Represent a fraction 1/b on a number line diagram by
defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
Build fraction understanding from whole number understanding.
28
Build fraction understanding from whole number understanding.
29
Build fraction understanding from whole number understanding.
30
Fraction equivalence on the number line. number line.