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 2

Math Learning Progressions Rational Numbers Understanding Rational Numbers 23 Levels Operations Solving Problems with Operations 26 Levels Equality Connects to Rational Numbers and Operations 27 Levels 3

Math Learning Progressions Patterns and Change Identify, extend and generalize 22 Levels Measurement Measurement with numbers to make sense of the world in which they live 27 Levels Data and Statistics Collecting, organizing and displaying data (interpreting and analyzing information) 18 Levels 4

Sample LP from Understanding Rational Numbers Math Learning Progression 5

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 6

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. 7

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) 8

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? 9

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. 10

Suggested Resources First Steps in Mathematics Number Volumes 1 and 2. ISBN Elementary and Middle School Mathematics Teaching Developmentally. 7 th edition / John A. Van de Walle, Karen S. Karp, Jennifer M. Bay-Williams ISBN-13: Doing What Works – Research-based education practices online National Council of Mathematics Illuminations

Alternate Assessment Coaches: Allyson Vignola – Marie Cote – Cecile Carlton NH DOE Math Coach NH Department of Education: Gaye Fedorchak – Contact Info 12