In primary grades students rate math as one of the subjects they like the most. They believe they have competence and hard work will yield success. By middle school, students believe success in math is due to innate ability and effort does not yield success (Sousa 2008)

To make Algebraic connections and to capitalize on students’ prior knowledge To highlight the importance of number sense formulated in the primary grades Everything I Needed for Algebra, I Learned in the First Grade Session Objectives: Leslie Byrd Allison Partner Linganore High School

What is our common goal? Mathematical Proficiency

Conceptual Understanding – the comprehension of math concepts, operations, and relations. Examples: Patterning, comparing quantities using a number line and other models, finding the missing number in a number sentence, using properties (commutative, identity, associative, distributive), composing/decomposing numbers The Five Strands of Mathematical Proficiency

-- a person’s ability to recognize that something has changed in a small collection when, without that person’s knowledge an object has been added or removed from the collection (Tobias Danzig 1967) -- the ability to compare the sizes of two collections shown simultaneously, and the ability to remember the number of objects presented successively in time (Keith Devlin 2000) Number Sense

Subitizing Perceptual Subitizing – instant recognition of a number without using a mathematical process. Conceptual Subitizing – to know the number of a collection by recognizing a familiar pattern. ACTIVITY: SUM WAR

Just as phonemic awareness is a prerequisite to learning phonics and becoming a successful reader, developing number sense is a prerequisite for succeeding in mathematics. Sousa 2008 Carl Dennis lives on Allen Brian Avenue Carl Gary lives on Brian Allen Avenue Gary Edward lives on Carl Edward Avenue 3 X 4 = 12 3 X 7 = 21 7 X 5 = 35

Procedural Fluency – skill in carrying out the procedures flexibly, accurately, efficiently, and appropriately. Examples: Estimation methods, algorithms for addition/subtraction, mental math computations, alternative algorithms with a focus on place value. The Five Strands of Mathematical Proficiency

It must be remembered that the purpose of education is not to fill the minds of students with facts… it is to teach them to think, if that is possible, and always to think for themselves. Robert Hutchins

The Five Strands of Mathematical Proficiency Strategic Competence – the ability to formulate, represent, and solve mathematical problems. Examples: Identify the question in a problem, select and apply a strategy (model/act it out, look for patterns, write an equation(L2), make a table(L3), guess and check), identify alternate ways to solve, explore/invent/use objectives.

Adaptive Reasoning – capacity for logical thought, reflection, explanation, and justification. Example: Connecting to prior knowledge (extend a solution to a new problem), identify mathematical concepts in relationships to other mathematical concepts, sort/classify problems, finding the most efficient way to solve a problem, support or refute mathematical statements or solutions(justify). The Five Strands of Mathematical Proficiency

Productive Disposition – the habitual inclination to see math as sensible, useful, and worthwhile, coupled with the belief in diligence and one’s own efficacy. Examples: engaging students mathematical intuition (explore, invent, use), write story problems that model a certain situation or number sentence, using multiple strategies.

And once I had a teacher who understood. He brought with him the beauty of mathematics. He made me create it for myself. He gave me nothing and it was more than any other teacher has ever dared to give me. (Cochran, 1991)