Transcript NH ALPS - Mathematics

Cecile Carlton
NH DOE Mathematics Coach
Goals for Math Session
 Math Content
 Development/refinement of the Learning
Progressions
 Levels: Emergent, Beginning, Transition,
Intermediate, Advanced
 Teaching Strategies/Teacher’s Role
 Student Performance
 Resources
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• Solving
Problems with
Operations
• 26 Levels
Equality
• Understanding
Rational
Numbers
• 23 Levels
Operations
Rational Numbers
Math Learning Progressions
• Connects to
Rational
Numbers and
Operations
• 27 Levels
3
• Measurement
with numbers to
make sense of
the world in
which they live
• 27 Levels
Data and Statistics
• Identify, extend
and generalize
• 22 Levels
Measurement
Patterns and Change
Math Learning Progressions
• Collecting,
organizing and
displaying data
(interpreting
and analyzing
information)
• 18 Levels
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Sample LP from
Understanding Rational Numbers
A] whole numbers 0-20, and
B] 1/2 as fair share
and
M:N&O:K:2 (A)
A1] compares two collections deciding how much bigger or smaller
and A2] demonstrates that to count a collection each object must be (5 SU's)
touched or 'included' exactly once as the numbers are said, A3] the
numbers must be said once and always in the conventional order, and
A4] the last number said tells 'how many' in the whole collection, it
does not describe the last object touched. (counting principles)
B1] shares a quantity (1-20) of objects evenly.
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A] whole numbers 0-12, and
B] 1/2 as fair share
and
A1] compares different collections based on magnitude (bigger,
smaller, same) and A2] indicates if a change to a quantity will make it
bigger, smaller, or stay the same. (A focus on quantity versus size. )
B1] shares a quantity (1-12) of objects evenly.
NCTM Focal Points K
M:N&O:K:1
NCTM Focal Points:
K Numbers & Operations
(A)
NCTM Research * (B)
(3 SU's)
NCTM Research * (A)
(2 SU's)
(
4
K
)
E
M
E
R
G
E
N
T
E
n
t
r
y
P
o
i
n
t
2
whole numbers 1-10
and
1] distinguishes numerals from other written symbols (e.g. ordinal
numbers), 2] uses number names to count, and 3] recalls the
sequence of number names
1
whole numbers 1-6
and
1] know at a glance [or at a touch] how many are in small collections
(subitize), and 2] attach correct number names to such collections.
(3 SU's)
Tower Stem -> Using models, explanations, or other representations student demonstrates conceptual understanding of …
Challenge
Level
Types of Rational Numbers
Comparisons and relationships of rational numbers
Coding Alignment
Math Learning Progression
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Defining Math Challenge Levels
 Emergent
 Beginning
 Transitional
 Intermediate
 Advanced
 Social understanding of
mathematics – i.e. they
count in order to please
 Active – construct,
modify, and integrate
math ideas
 Extend ability to
compute additively –
multiplicative reasoning
emerges – develops
fluency
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Challenge Levels
 Intermediate
 Advanced
 Conjectures and verifies –
comprehends cause and
effect, abstract reasoning
and generalizing increases
 More complex, algebraic
expressions, new
geometric perspectives,
new ways to analyze data.
Focus on using
understanding of
mathematics to solve
problems.
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Sample Teaching
Strategies For
Operations
Teaching Operations
Addition and
Subtraction Structures
•Join problems
•Separate problems
•Part-part-whole problems
•Compare problems
Problem difficulty
Computational and semantic
forms of equations
See K-12 Mathematics New
Hampshire Curriculum Framework
June 2006 ( p.41)
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Student
Performance
Observe Brandi – conceptual
understanding of numbers
developed through use of
manipulatives, written expressions
and explanations.
Is she demonstrating conceptual
understanding? What evidence
did you see?
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Using Video Evidence
• Have video focused on student’s interactions with materials
• Should be able to see/hear student in a pre-questioning exchange such as:
• How are you thinking about this problem?
• How would you solve this problem? What do you think you need to solve this
problem?
• Do you have an estimate? Does that estimate make sense – explain why?
• Show student engaged in solving the problem (Don’t say what the student
should say – have the student make the connections)
• Post questioning could include:
•
•
•
•
How did you solve/think through the problem at hand?
Does your answer make sense?
How close was your estimate/ (and or ideas about possible solution)?
Is there another way you can show/solve the problem? Why or why not?
• Watch for ways student responds to make connections and expand conceptual
understanding (are they connecting to previous learning?)
• Accuracy of solution as well as process is assessed.
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Suggested Resources
 First Steps in Mathematics Number Volumes 1 and 2.
ISBN 0-9759986-8-4 www.stepspd.org
 Elementary and Middle School Mathematics Teaching
Developmentally. 7th edition / John A. Van de Walle,
Karen S. Karp, Jennifer M. Bay-Williams ISBN-13: 9780-205-573523-3 www.pearsonhighered.com
 Doing What Works – Research-based education
practices online http://dww.ed.gov
 National Council of Mathematics Illuminations
http://illuminations.nctm.org/
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Contact Info
Alternate Assessment Coaches:
Allyson Vignola – 603-848-4850
[email protected]
Marie Cote – 603-689-8777
[email protected]
Cecile Carlton NH DOE Math Coach
[email protected]
NH Department of Education:
Gaye Fedorchak – 603-271-7383
[email protected]
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