Number Talks

Mathematical literacy is not the ability to calculate; it is the ability to reason quantitatively. No matter how many computation algorithms they know, students become mathematically literate only when they can use numbers to solve problems, to clarify issues and to support or refute opinions. Marilyn Frankenstein

1Parent NightBethany Farmer, Curriculum CoordinatorAllison McCarthy, Teacher2

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Give it a try3Thoughts to ponderOur classrooms are filled with students and adults who think of mathematics as rules and procedures to memorize without understanding of numerical relationships that provide the foundations for these rules.

- Quote from 1919.4

5If teaching were the same as telling, wed all be so smart we could hardly stand it.. - Mark Twain

Tell me and I forgetShow me and I rememberInvolve me and I understand- Copernicus

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7Strands of Mathematical Proficiency

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 ones own efficacy.

8Standards for Mathematical PracticeMake sense of problems and persevere in solving them

Reason abstractly and quantitatively

Construct viable arguments and critique the reasoning of others

Model with mathematics

Use appropriate tools strategically

Attend to precision

Look for and make use of structure

Look for and express regularity in repeated reasoning

9Rigor10The CCSSM require a balance of:Solid conceptual understandingProcedural skill and fluencyApplication of skills in problem solving situationsPursuit of all three requires equal intensity in time, activities, and resources.

It is only when you build from within that you really understand something. If children dont build from within and you just try to explain it to a child then its not truly learned. It is only rote, and thats not really understanding.

Ann Badeau, second-grade teacher11Compare the Two TasksWork each task.Share solution strategies. Discuss: How are Marthas Carpeting Task and the Fencing Task the same and how are they different?A Numerically Powerful Child. . .Develops meaning for numbers and operations

Looks for relationships among numbers and operations

Understands computation strategies and uses them appropriately and efficiently

Makes sense of numerical and quantitative situations

Future Basics: Developing Numerical Power, A Monograph of the National Council of Supervisors of Mathematics, 1998RationaleStudent engagement/student centered

the best way for students to develop their mathematical confidence and understanding of mathematics is to create an environment in which students are trusted to solve problems and work together using their ideas to do so.- Van de Walle and Lovin

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