Overview of Class #5 Introduction to beansticks (second material for modeling place value) Modeling conventional subtraction algorithm Mathematical proficiency Learning to see students through lens of mathematical proficiency Comments/questions about Project #1? Wrap Up

Important Steps when Modeling Algorithms Carefully model the numbers, paralleling the written form. Model the steps of the algorithm with the materials. Carefully map the modeling to the written form: Record the transformations with the materials in precise correspondence with how the steps are recorded in the conventional algorithm, making the meaning of the steps clear, one by one. Use the language of the materials.

Reflections on Small Group Work What things stood out to you about how this activity was structured? Why do you think I decided to structure this activity in this way?

Mathematical Proficiency for All Students Conceptual understanding - comprehension of mathematical concepts, operations, and relations Procedural fluency - skill in carrying out procedures flexibly, accurately, efficiently, and appropriately Strategic competence - ability to formulate, represent, and solve mathematical problems Adaptive reasoning - capacity for logical thought, reflection, explanation, and justification Productive disposition - habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy Kilpatrick, J., J. Swafford, and B. Findell. (2001). Adding It Up: How Children Learn Mathematics. Washington, DC: National Academy Press.

Video Clip: November 6, 1989 Early in unit on addition and subtraction computation Using beansticks, number line Students have already learned conventional algorithm, but few or none know it well yet Problem: Joshua ate 16 peas on Monday and 32 peas on Tuesday. How many more peas did he eat on Tuesday than he did on Monday? Students have already worked on problem, whole class discussion of solutions

Focal Students for Video Clip Analysis Shea Rania Bernadette Lin Christina Can you see anything more deeply about the students using the strands as a lens? What does this framework open up for thinking about children? Choose one of the students to focus on. Who picked each? As you watch, try to analyze your student using the strands of mathematical proficiency. Do you see examples of the different strands --- things they do or say, or don’t do or don’t say. Take notes on your transcript AFTER VIEWING: get in groups by student fill out chart think about questions Whole class discussion - share out from small groups

Wrapping Up Comments/questions about Project 1? Assignments Collect notebooks Comment cards?

Week #5 Assignment Readings (Erlwanger & Ma) Analysis of common student errors Subtraction with regrouping Bring notes, student work, and draft assertions from Project #1 to class next week