Building A Stronger Math Program By Building a Stronger

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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


Do you consider yourself a
“math person?”
Do you consider yourself a
reader?

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).
2000 Rank 2003 Rank 2006 Rank
(out of 26)
(out of 26)
(out of 26)
2009 Rank
(out of 26)
Math
17th
22nd
22nd
Tied 20th
Science
13th
Tied for 17th
19th
13th
n/a
Tied
10th
Subject
Reading
14th
14th
Rankings are for the 26 OECD countries participating in PISA in 2000, 2003, and 2006.
Slide Credit: EdTrust.org
Data Source: Organization for Economic Cooperation and Development (OECD), PISA 2006 Results, http://www.oecd.org/
550
2003 PISA - Math
OECD Average
U.S.A.
500
450
400
350
300
Slide Credit: EdTrust.org
Data Source: Organization for Economic Cooperation and Development (OECD), PISA 2006 Results, http://www.oecd.org/
China has not taken PISA as a nation.
Certain cities such as Shanghai have
joined and are ranking near the top.
Finland
Korea
Netherlands
Switzerland
Canada
Japan
New Zealand
Belgium
Australia
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/
2001 MCPS
CCSS/EIC
Rigor
✔
✔
Coherence
✔
✔
Focus
✔
refers to the degree that sets of
standards address key content that prepare
students for success beyond high school.
2001 MCPS
CCSS/EIC
Rigor
✔
✔
Coherence
✔
✔
Focus
✔
refers to whether the standards
create an appropriate balance among:
 conceptual understanding
 procedural skill
 problem solving with an emphasis on
application and modeling
Percent of Content
2001 MCPS Curriculum
Number
Algebra
Geometry
Measurement
Statistics
Math Math Math Math Math Math Math Math Alg.
K
1
2
3
4
5
6
7
Prep
Probability
Percent of Content
Final Common Core Standards
Math Math Math Math Math Math Math Math Math
K
1
2
3
4
5
6
7
8
Number
Algebra
Geometry
Measurement
Statistics
Probability
 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.
Going Deep in Mathematics
2001 Curriculum and CCSS
Comprehending
Concepts, Operations,
& Relations
Understanding
Seeing math as
sensible, useful, and
doable
Carrying out
procedures
Computing
Engaging
Applying
Reasoning
Formulating and solving mathematical problems
Using logic to explain a solution
1½ ÷ ½ =
a.
b.
c.
d.
½
¾
3
1
Write this problem
as a question
using words and not
symbols.
3
2

3
2
1
How many halves are in
one and one half?
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?
Complete the number sentence with <, >, or =
352 <
360
114 >
113
When 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
What Makes The EIC Foundation Stronger?
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
Comparing Standards on One Topic in Grade 2:
Using Place Value to Add and Subtract
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.
Critical Questions For Instructional Planning
1.
2.
3.
4.
What do students need to know and be able
to do?
How will we know they have learned it?
What will we do when they haven’t?
What will we do when they already know it?
Enriched and Accelerated Instruction in Elementary Math
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
Many Students – who consistently
master all five
• Additional - Who consistently
UCARE strands
Enrichment demonstrate
strong
for a topic
• MCPS
mastery in all five
Acceleration strands for an indicator
in mastered
Few Students – grade
topics
level advancement
Enrichment and Acceleration Implementation Plan
School Year
2011-2012
School Year
2012-2013
Kindergarten, Grade 1, Grade 2
Grade 3, Grade 4, Grade 5
Common Core State Standards/
Elementary Integrated Curriculum
Grade Level Math Curriculum with
enrichment and acceleration
MCPS 2001 Curriculum
Continue acceleration
within grade level and next
grade level up
Kindergarten, Grade 1,
Grade 2, Grade 3
Common Core State Standards/
Elementary Integrated Curriculum
Grade Level Math Curriculum with
enrichment and acceleration
Grade 4, Grade 5
MCPS 2001 Curriculum
Continue acceleration
within grade level and next
grade level up
Number &
Counting & Operations and
Operations
Cardinality Algebraic Thinking
Base Ten
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)
Addition – putting together and adding to
problems within 10. Subtraction – taking
apart and taking from problems within 10
(KMP4)
Decompose numbers
less than or equal to 10
into pairs in more than
one way (KMP2)
Addition and subtraction problems unknowns
in all positions within 10
(G1MP1)
Decompose numbers
less than or equal to
10 into more than
two parts (KMP2)
Know number names and the
count sequence to 100
(KMP1)
UCARE Enrichment
Apply place value
concepts: Extend counting
sequence to 120 starting at
any number (G1MP1)
Decompose numbers
less than or equal to
20 into pairs in more
than one way (KMP2)
Count to tell the number
of objects
Compare numbers
(KMP2)
Learning Progression
Enrichment
Fluency
within 5
(KMP4)
Count forward from a
given number
Compare numbers
(KMP4)
Learning Progression
Acceleration
1
2
2
2
3
3
3
4
4
4
5
5
Accel.:
Counting
6
and
Cardinality
5
6
Acceleration:
Counting and Cardinality
Enrich/
Accel.:
Oper. and
Alg.
Thinking
Accel.:
Counting
6
and
Cardinality
7
Marking Period 4
1
Accel.:
Accel.:
Operations
Counting
and
3
and
Cardinality Algebraic
4
Thinking
Enrichment:
Meas. and
Data
2
5
Weeks
1
Weeks
1
Weeks
Weeks
Marking Period 1
Opportunities for Enrichment/Acceleration (Kindergarten)
Marking Period 2
Marking Period 3
Enrichment:
Geometry
6
7
7
7
8
8
8
8
9
9
9
9
Accel.:
Number
and
Operations
in Base Ten
Number &
Number & Operations and
Operations Algebraic Thinking Operations
Base Ten
Base Ten
Concrete Models:
Add 2-digit to 1-digit,
2-digit to multiple of 10
Subtract multiples of 10
(G1MP3)
Addition and subtraction
problems unknowns in all
positions within 10
(G1MP1)
Add and
subtract
within 10
(G1MP1)
Add 3 whole
numbers
within 10
(G1MP1)
Foundations for place value:
10 ones is a unit called a “ten”
Tens can be counted (G1MP1)
UCARE Enrichment
Written Methods:
Add 2-digit to 1-digit,
2-digit to multiple of 10
Subtract multiples of 10
(G1MP4)
Written Methods:
Add 2-digit numbers
(G2MP2)
Addition and subtraction
problems unknowns in all
positions within 20
(G1MP2)
Add and
subtract
within 20
(G1MP2)
Addition and
subtraction problems
with 3 addends
(G1MP2)
Fluently add
and subtract
within 10
(G1MP3)
Count to 120 starting at
any number
Compare 2-digit numbers
(G1MP1)
Learning Progression
Enrichment
Fluently add
and subtract
within 20
(G2MP1)
Compare relative positions
of three 2-digit numbers
(G1MP1)
Learning Progression
Acceleration
Marking Period 2
Acceleration:
Number and Operations
2
in Base Ten
1
Enrichment:
Number and Operations
2
in Base Ten
1
Enrichment:
Number and Operations
4
in Base Ten
3
3
5
5
3
Weeks
Enrichment/Acceleration:
Operations and
6
Algebraic Thinking
4
6
7
7
8
8
9
9
Enrichment:
Operations and
Algebraic Thinking
Acceleration:
Operations and
Algebraic Thinking
Marking Period 4
Acceleration:
Operations and Algebraic
2
Thinking/ Number and
3 Operations in Base Ten
1
2
Enrichment:
Measurement and Data
4
Weeks
1
Weeks
Marking Period 3
5
6
4
Acceleration:
Operations and
Algebraic Thinking*
Weeks
Marking Period 1
5
6
7
7
8
8
Acceleration:
Number and Operations
in Base Ten
9
* moves students to
Number and
Operations in Base Ten
9
Enrichment:
Geometry
Number &
Operations
Base Ten
Number & Operations and
Operations Algebraic Thinking
Base Ten
Add & subtract 3-digit numbers
models- drawings- number lines – place value strategies
(G2MP4)
Add & subtract 2-digit numbers
models- drawings- number lines –
place value strategies
(G2MP2)
One step +/- word
problems (G2MP1)
Include compare
problems (G2MP2)
Add & subtract
within 20 –
mental
strategies
(G2MP1)
Generate
compare
problems
(G2MP2)
Fluently add
and subtract
within 20
(G2MP2)
Meaning of a “hundred”
Count by 1s, 10s, 100s to 1000
Numerals and expanded form
(G2MP1)
UCARE Enrichment
Fluently add &
subtract 2-digit
numbers
(G2MP2)
Fluently add & subtract
3-digit numbers
(G3)
Mentally add & subtract within 100
Add four 2-digit numbers
within 100
(G2MP2)
Two step +/- word problems –
1-digit addends (G2MP2)
Two digit addends (G2MP3)
Add 1-digit
addends from
memory
(G2MP3)
Mentally add & subtract
10 or 100
Compare using symbols
(G2MP1)
Enrichment
Repeated
addition &
rectangular
arrays
(G2MP3)
More complex
two step +/problem types
(G2MP3)
Repeated
addition &
multiple
representations
(G2MP3)
Count by 5s to 1000 from a
given number
(G2MP1)
Acceleration
Opportunities for Enrichment/Acceleration (Grade 2)
Marking Period 2
Marking Period 3
1 Acceleration:
1
5
Enrichment:
Number and Operations
in Base Ten
6
7
7
8
9
Weeks
Weeks
4
Accel.:
Oper. and
2
Algebraic Enrich.:
Number
3 Thinking
and Op. in
Base Ten
4
Enrich.:
Oper.
5
and
Accel.:
Algebraic
Oper.
Thinking
and
6
Algebraic
Thinking
Acceleration:
Oper. and Algebraic
Thinking
1
1
2
2
3
Accel.:
Num. &
Op. in
Base Ten
Enrich.:
Num. &
Op. in
Base Ten
Enrichment:
Measurement and Data
5
4
Enrichment:
Oper. and Algebraic
Thinking
5
6
6
7
7
8
8
9
9
Enrichment:
Geometry
Enrichment:
Oper. and Algebraic
Thinking
Marking Period 4
3
4
Weeks
Oper. and Acceleration:
2 Alg. Thinking Number and
Operations
3
in Base Ten
Weeks
Marking Period 1
8
9
Acceleration:
Number and Operations
in Base Ten
These four
nations are in
the top ten
U.S.A.
Source: OECD, PISA 2006 Results, table 4.2c, http://www.oecd.org/
600
550
500
450
400
350
300
Source: Organization for Economic Cooperation and Development (OECD), PISA 2003 Results, data available at
http://www.oecd.org/
U.S.A.

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