Cecile CarltonNH DOE Mathematics Coach

Goals for Math SessionMath ContentDevelopment/refinement of the Learning

ProgressionsLevels: Emergent, Beginning, Transition,

Intermediate, Advanced Teaching Strategies/Teacher’s RoleStudent PerformanceResources

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Math Learning Progressions

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Math Learning Progressions

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Sample LP from Understanding Rational Numbers

Math Learning Progression

4 A] whole numbers 0-20, andB] 1/2 as fair share

and A1] compares two collections deciding how much bigger or smaller and A2] demonstrates that to count a collection each object must be 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.

M:N&O:K:2 (A)

(5 SU's)

3 A] whole numbers 0-12, andB] 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 KM:N&O:K:1

(3 SU's)

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

NCTM Focal Points: K Numbers & Operations (A)NCTM Research * (B)(3 SU's)

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.

NCTM Research * (A)(2 SU's)

Tower Stem ->

Challenge Level Types of Rational Numbers Comparisons and relationships of rational numbers Coding Alignment

EMERGENT

(

K

)

Entry Point

Using models, explanations, or other representations student demonstrates conceptual understanding of …

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Defining Math Challenge LevelsEmergent

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 LevelsIntermediate

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 OperationsAddition and Subtraction Structures

•Join problems•Separate problems•Part-part-whole problems•Compare problems

Problem difficultyComputational and semantic forms of equations

See K-12 Mathematics New Hampshire Curriculum Framework June 2006 ( p.41)

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Student PerformanceObserve 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 ResourcesFirst 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: 978-0-205-573523-3 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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Alternate Assessment Coaches:Allyson Vignola – 603-848-4850allysonvignola@hotmail.comMarie Cote – 603-689-8777marie.cote@comcast.netCecile Carlton NH DOE Math CoachCecile.carlton@ed.state.nh.us

NH Department of Education:Gaye Fedorchak – 603-271-7383Gfedorchak@ed.state.nh.us

Contact Info

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