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Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards Do not worry if you have built your castles in the air. They are where they should be. Now put the foundations under them. - Henry David Thoreau

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Do not worry if you have built your castles in the air. They are where they should be. Now put the foundations under them. - Henry David Thoreau. Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards. Icebreaker. - PowerPoint PPT Presentation

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Page 1: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Building Stronger Math StudentsBy Building a Stronger FoundationMCPS Adoption of New Internationally-driven Standards

Do not worry if you have built your castles in the air. They are where they should be. Now put the foundations under them.

- Henry David Thoreau

Page 2: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Icebreaker Do you consider yourself

a “math person?” Do you consider yourself

a reader?

Page 3: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Goals of the

MCPS

Mathem

atics Program

Develop students who love math and see it as sensible and useful to solving problems and making sense of the world.

All students will reach proficiency in math – Understanding, Computing, Applying, Reasoning, and Engaging (UCARE).

Page 4: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Building a Strong Foundation

Proficiency in Number Concepts

Success in Advanced Math

Page 5: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Rankings are for the 26 OECD countries participating in PISA in 2000, 2003, and 2006.

Programme of International Student Assessment (PISA) Results

Subject

2000 Rank

(out of 26)

Math 17th

Science 13th

Reading 14th

Slide Credit: EdTrust.orgData Source: Organization for Economic Cooperation and Development (OECD), PISA 2006 Results , http://www.oecd.org/

2003 Rank

(out of 26)

22nd

Tied for 17th

14th

2006 Rank

(out of 26)

2009 Rank(out of 26)

22nd Tied 20th

19th 13th

n/a Tied 10th

Why internationally-driven standards?

Page 6: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Slide Credit: EdTrust.orgData Source: Organization for Economic Cooperation and Development (OECD), PISA 2006 Results , http://www.oecd.org/

Why internationally-driven standards?

Finlan

dKo

rea

Neth

erlan

dsJa

pan

Cana

daBe

lgium

Switz

erlan

dNe

w Ze

aland

Aust

ralia

Czec

h Re

publ

icIce

land

Denm

ark

Fran

ceSw

eden

Aust

riaGe

rman

yIre

land

OECD

Ave

rage

Slova

ck R

epub

licNo

rway

Luxe

mbo

urg

Polan

dHu

ngar

ySp

ainUn

ited

Stat

esPo

rtuga

lIta

lyGr

eece

Turk

eyM

exico

300

350

400

450

500

5502003 PISA - Math

Aver

age

Scal

e Sc

ore

U.S.A.OECD Average

Page 7: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

What nations are consistently near the top in math?

Finland KoreaNetherlandsSwitzerlandCanadaJapanNew ZealandBelgiumAustralia

Why internationally-driven standards?

China has not taken PISA as a nation. Certain cities such as Shanghai have joined and are ranking near the top.

Page 8: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

What are the Internationally-driven Standards?The Common Core State Standards:

Include rigorous content and application of knowledge through high-order skills

Build upon strengths and lessons of current state standards

Internationally benchmarked so that all students are prepared to succeed in our global economy and society

Based on evidence and research

Learn more: http://www.corestandards.org/

Page 9: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Building a Strong Foundation

2001 MCPS

CCSS/EIC

Rigor ✔ ✔Coherence

✔ ✔

Focus ✔

What is needed in curriculum and instructionto help build a strong foundation?

Page 10: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

2001 MCPS

CCSS/EIC

Rigor ✔ ✔Coherence

✔ ✔

Focus ✔

Rigor, Coherence, and Focus Source: Achieve – CCSS

Rigor refers to the degree that sets of standards address key content that prepare students for success beyond high school.

Page 11: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Rigor, Coherence, and Focus Source: Achieve – CCSS

Focus refers to whether the standards create an appropriate balance among: conceptual understanding procedural skill problem solving with an emphasis

on application and modeling

Page 12: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

MCPS and CCS

Strand Comparison

Math K

Math 1

Math 2

Math 3

Math 4

Math 5

Math 6

Math 7

Math 8

Final Common Core StandardsNumberAlgebraGeometryMea-sure-mentStatisticsProbability

Perc

ent

of C

onte

nt

Math K

Math 1

Math 2

Math 3

Math 4

Math 5

Math 6

Math 7

Alg. Prep

2001 MCPS Curriculum NumberAlgebraGeometryMea-sure-mentStatisticsProbability

Perc

ent o

f Con

tent

Page 13: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Building a stronger foundation

The CCSS recommend that elementary schools focus on building a strong foundation in number concepts – before accelerating into advanced math.

MCPS Math teachers in advanced level courses in middle school and high school have requested a stronger foundation in number concepts for ALL students, even the most advanced.

So what does

this look

like?

Page 14: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Going Deep in Mathematics2001 Curriculum and CCSS

Understanding

ComputingApplying Reasoning

Engaging

Comprehending Concepts, Operations, & Relations

Carrying out procedures

Formulating and solving mathematical problems

Using logic to explain a solution

Seeing math as sensible, useful, and doable

Page 15: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

3 2 32 1

1½ ÷ ½ =

a. ½ b. ¾c. 3d. 1

Write this problemas a questionusing words and

not symbols.

How many halves are in one and one half?

MATHEMATICAL PROFICIENCY: LEARNING A CONCEPT IN

DEPTH

COMPUTING

UNDERSTANDING

REASONING

Page 16: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

1½ ÷ ½ = 3

Describe a situation

requiring use of this

concept.

You have a yard and

a half of ribbon to make bows. Each bow requires ½

yard. How many bows

can you make?

MATHEMATICAL PROFICIENCY: LEARNING A CONCEPT IN

DEPTH

APPLYING REASONING

Page 17: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Complete the number sentence with <, >, or =

352 360

114 113

MATHEMATICAL PROFICIENCY: LEARNING A CONCEPT IN

DEPTH

COMPUTING<

>

Same Problems, but requiring Understanding, Computing, Application,

and Reasoning

Page 18: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

MATHEMATICAL PROFICIENCY: LEARNING A CONCEPT IN

DEPTHENGAGEMENTWhen might we need to compare three digit

numbers?Which type of milk will give you the most energy

per serving? Reduced Fat Milk Chocolate Milk Whole Milk Fat Free Milk

Page 19: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Building a Stronger Foundation

MCPS 2001 Curriculum Framework

EIC / Internationally-driven

standards“Spiral” Curriculum – concepts introduced and mastered over several grade levels

Concept introduced and mastered in one grade level

Grade level standards not sufficiently challenging for most students

Many standards are “pulled down” from upper grades.

Language of standards was general and not specific – resulting in teaching to test.

Fewer, higher, clearer standards provide direction for teaching and learning – not testing.

Curriculum developed independently of all other subjects

Curriculum integrated with other content areas and thinking and academic skills

What Makes The EIC Foundation Stronger?

Page 20: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Building a Stronger Foundation

MCPS 2001 Curriculum

EIC / Internationally-driven standards

• Add and subtract two- and three-digit numbers using alternative strategies.

• Add two- and three-digit numbers with regrouping.

• Subtract two-and three-digit numbers with regrouping. *

• Model and use the identity and commutative properties for addition…to solve problems. *

* From a higher grade level

• Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

• Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.

• Explain why addition and subtraction strategies work, using place value and the properties of operations.

Comparing Standards on One Topic in Grade 2: Using Place Value to Add and Subtract

Page 21: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Building a Stronger Foundation

Critical Questions For Instructional Planning

1. What do students need to know and be able to do?

2. How will we know they have learned it?

3. What will we do when they haven’t?4. What will we do when they already

know it?

How Do We Plan To Reach ALL Students?

Page 22: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Building a Stronger Foundation

Enriched and Accelerated Instruction in Elementary Math

- Who consistently demonstrate strong mastery in all five strands for an indicator

All Students – In the grade level EIC/CCSS Curriculum• Grade level

expectations are at a higher level

• Fewer topics per grade level

• Enrichment–mastery of the 5 UCARE strands requires greater depth for all students

Few Students – grade level

advancement

Page 23: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Building a Stronger Foundation

Enrichment and Acceleration Implementation PlanSchool Year

Kindergarten, Grade 1, Grade 2

Grade 3, Grade 4, Grade 5

2011-2012 Common Core State Standards/ Elementary Integrated CurriculumGrade Level Math Curriculum with enrichment and acceleration

MCPS 2001 CurriculumContinue acceleration within grade level and next grade level up

School Year

Kindergarten, Grade 1, Grade 2, Grade 3

Grade 4, Grade 5

2012-2013 Common Core State Standards/ Elementary Integrated CurriculumGrade Level Math Curriculum with enrichment and acceleration

MCPS 2001 CurriculumContinue acceleration within grade level and next grade level up

Page 24: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Learning Progressions Enrichment and Acceleration in

Kindergarten

Building a Strong Number Foundation - Kindergarten:Learning progressions are the basis for deeper enrichment and acceleration beyond the marking period or grade level

Know number names and the count

sequence to 100(KMP1)

Count to tell the number of objectsCompare numbers

(KMP2)

Count forward from a given number

Compare numbers(KMP4)Co

untin

g & Ca

rdin

alit

y

Num

ber &

Op

erat

ion

s Bas

e Te

n

Learning Progression Enrichment

Learning Progression Acceleration

UCARE Enrichment

Decompose numbers less

than or equal to 10 into pairs in more than one way (KMP2)

Decompose numbers less

than or equal to 10 into more

than two parts (KMP2)

Decompose numbers less

than or equal to 20 into pairs in more than one

way (KMP2)

Fluency within 5(KMP4)Op

erat

ions

an

d Al

gebr

aic

Thin

king

Addition – putting together and adding to problems within 10. Subtraction – taking apart and taking from problems within 10

(KMP4)

Addition and subtraction problems unknowns in all positions within 10

(G1MP1)

Foundations for place value:

numbers 11-19 are ten ones and some more ones (KMP4)

Foundations for place value: Ten ones is a unit called a “ten”

Tens can be counted (G1MP1)

Apply place value concepts: Extend

counting sequence to 120 starting at

any number (G1MP1)

Page 25: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Opportunities for Enrichment/Acceleration (Grade K)

1 1 1 1

2 2 2 2

3 3 3 3

4 4 4 4

5 5 5 5

6 6 6 6

7 7 7 7

8 8 8 8

9 9 9 9

Enrichment:Geometry

Accel.: Counting

and Cardinality

Marking Period 3Opportunities for Enrichment/Acceleration (Kindergarten)

Marking Period 1

Wee

ks

Wee

ks

Wee

ks

Wee

ksEnrich/ Accel.:

Oper. and Alg.

Thinking

Accel.:Number

and Operations in Base Ten

Accel.:Operations

and Algebraic Thinking

Marking Period 4

Accel.: Counting

and Cardinality

Acceleration: Counting and Cardinality

Accel.: Counting

and Cardinality

Marking Period 2

Enrichment:Meas. and

Data

Page 26: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Foundations for place value: 10 ones is a unit called a “ten”

Tens can be counted (G1MP1)

Count to 120 starting at any

number Compare 2-digit

numbers(G1MP1)

Compare relative positions of three 2-

digit numbers(G1MP1)Nu

mbe

r &

Oper

atio

ns B

ase

Ten

Num

ber &

Op

erat

ion

s Bas

e Te

n Concrete Models: Add 2-digit to 1-

digit, 2-digit to multiple

of 10Subtract multiples

of 10(G1MP3)

Written Methods: Add 2-digit to 1-digit, 2-digit to multiple of

10Subtract multiples of

10(G1MP4)

Written Methods:Add 2-digit numbers

(G2MP2)

Building a Strong Number Foundation – Grade 1:Learning progressions are the basis for deeper enrichment and acceleration beyond the marking period or grade level

Learning Progression Enrichment

Learning Progression Acceleration

UCARE Enrichment

Add and subtract within 10(G1MP1)

Add and subtract within 20(G1MP2)

Fluently add and subtract within 10(G1MP3)

Fluently add and subtract within 20(G2MP1)

Oper

atio

ns

and

Alge

brai

c Th

inki

ng

Addition and subtraction problems

unknowns in all positions within 10

(G1MP1)

Addition and subtraction problems

unknowns in all positions within 20

(G1MP2)

Addition and subtraction

problems with 3 addends(G1MP2)Add 3

whole numbers within 10(G1MP1)

Page 27: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Opportunities for Enrichment/Acceleration (Grade 1)

* moves students to Number and Operations in Base Ten

Marking Period 2 Marking Period 3 Marking Period 4

1 1 1 1

2 2 2 2

3 3 3 3

4 4 4 4

5 5 5 5

6 6 6 6

7 7 7 7

8 8 8 8

9 9 9 9

Acceleration:Number and Operations

in Base Ten

Acceleration:Operations and Algebraic

Thinking/ Number and Operations in Base Ten

Enrichment:Geometry

Enrichment: Number and Operations

in Base Ten

Marking Period 1

Enrichment: Operations and

Algebraic Thinking

Acceleration:Operations and

Algebraic Thinking

Wee

ks

Acceleration: Number and Operations

in Base Ten

Enrichment: Number and Operations

in Base Ten

Enrichment/Acceleration: Operations and

Algebraic Thinking

Wee

ks

Wee

ks

Wee

ks

Enrichment:Measurement and Data

Acceleration:Operations and

Algebraic Thinking*

Page 28: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Meaning of a “hundred”

Count by 1s, 10s, 100s to 1000

Numerals and expanded form

(G2MP1)

Mentally add & subtract 10 or 100

Compare using symbols(G2MP1)

Count by 5s to 1000 from a given

number(G2MP1)Nu

mbe

r &

Oper

atio

ns B

ase

Ten

Num

ber &

Op

erat

ions

Ba

se Te

n

Learning Progressions Enrichment and Acceleration in

Kindergarten

Add & subtract 2-digit numbers

models- drawings- number lines – place

value strategies(G2MP2)

Fluently add & subtract 2-digit numbers

(G2MP2)

Mentally add & subtract within 100

Add four 2-digit numbers within 100(G2MP2)

Learning Progressions Enrichment and Acceleration in

Kindergarten

Add & subtract 3-digit numbersmodels- drawings- number lines – place value

strategies(G2MP4)

Fluently add & subtract 3-digit

numbers(G3)

Oper

atio

ns

and

Alge

brai

c Th

inki

ng Add & subtract

within 20 – mental

strategies(G2MP1)

Add 1-digit addends

from memory(G2MP3)

Repeated addition & rectangula

r arrays(G2MP3)

Repeated addition &

multiple representat

ions(G2MP3)

Fluently add and subtract within 20(G2MP2)

One step +/- word problems

(G2MP1)Include

compare problems (G2MP2)

Two step +/- word problems – 1-digit addends (G2MP2)Two digit addends

(G2MP3)

More complex two step

+/- problem types

(G2MP3)

Generate compare problems(G2MP2)

Enrichment AccelerationUCARE Enrichment

Building a Strong Number Foundation – Grade 2:Learning progressions are the basis for deeper enrichment and acceleration beyond the marking period or grade level

Page 29: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Opportunities for Enrichment/Acceleration (Grade 2)

Marking Period 3 Marking Period 4

1 1 1 1

2 2 2 2

3 3 3 3

4 4 4 4

5 5 5Enrichment:

Oper. and Algebraic Thinking

5

6 6 6 6

7 7 7 7

8 8 8 Enrichment:Geometry

8

9 9 9Enrichment:

Oper. and Algebraic Thinking

9

Opportunities for Enrichment/Acceleration (Grade 2)Marking Period 1

Wee

ks

Acceleration: Number and Operations

in Base Ten

Enrichment:Measurement and Data

Wee

ks

Wee

ks

Acceleration:Number and Operationsin Base Ten

Enrichment:Number and Operations

in Base Ten

Acceleration:Oper. and Algebraic

Thinking

Marking Period 2

Enrich.: Number

and Op. in Base Ten

Enrich.: Oper. and

Algebraic Thinking

Accel.: Oper. and

Algebraic Thinking

Accel.: Num. & Op. in

Base Ten

Enrich.: Num. & Op. in

Base Ten

Acceleration:Oper. and

Alg. Thinking W

eeks

Accel.: Oper. and Algebraic Thinking

Page 30: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

But is it fair to compare the U.S. to less diverse nations?

Why internationally-driven standards?

Page 31: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

Source: OECD, PISA 2006 Results, table 4.2c, http://www.oecd.org/

U.S.A.

Immigrants? The U.S. does have a larger percentage of immigrants and children of immigrants than most OECD countries

Why internationally-driven standards?

These four nations are in the top ten

Page 32: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

But, isn’t U.S. performance skewed by the high amount of poverty in the U.S.?

Why internationally-driven standards?

Page 33: Building Stronger Math Students By Building a Stronger Foundation MCPS Adoption of New Internationally-driven Standards

300350400450500550600

Source: Organization for Economic Cooperation and Development (OECD), PISA 2003 Results, data available at http://www.oecd.org/

Why internationally-driven standards?

Math Performance of Wealthiest Students (2003 PISA)U.S.A.