common core: shifts, practices, rigor cathy battles consultant umkc-regional professional...

Common Core: Shifts, Practices,

Rigor

Cathy 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

http://www.edweek.org/go/standardsreport

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 TenRatios and Proportional

Relationships Number & QuantityNumber and Operations –

FractionsThe Number System

Operations and Algebraic Thinking

Expressions and Equations Algebra

Functions Functions

Geometry Geometry

Measurement and Data Statistics and ProbabilityStatistics & Probability

2.

Reason abstractly

and quantitatively.

1. Make sense of problems

and persevere in solving them.

3.

Construct viable arguments and

critique the reasoning of others.

4.M

odel with

mathematics.

5.Use appropriate tools

strategically.

6. Attend to

precision.

7.

Look

for a

nd m

ake

use

of st

ruct

ure.

8.

Look f

or and exp

ress regu

larity

in repeated re

asoning.

Counting and

Cardinality

Kindergarten

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.



3.



4.M

odel with

mathematics.


strategically.

6. Attend to

precision.

7.

Look

for a

nd m

ake

use

of st

ruct

ure.

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.



3.



4.M

odel with

mathematics.


strategically.

6. Attend to

precision.

7.

Look

for a

nd m

ake

use

of st

ruct

ure.

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 checklist

Disconnected from content standards

Grade specific

New

Restricted to math

Taught in isolation

Sequential

A 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)


2004 NAEP, Fewer than 30% of 17-year-olds correctly translated 0.029 as 29/1000 (Kloosterman, 2010)


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)


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

Fractions

Facets 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


29


30

Fraction equivalence on the number line. number line.

common core: shifts, practices, rigor cathy battles consultant umkc-regional professional...

Documents