mathematics k-5 fdresa june 2013 supporting ccgps leadership academy
TRANSCRIPT
How can school leader familiarity with the Standards for Mathematical Practice, Standards for Mathematical Content, content emphases, and instructional shifts impact successful implementation of CCGPS?
Essential Question
“It is literally true that you can succeed best and quickest by helping others to succeed.”
Napoleon Hill American author 1883-1970
Monitoring Collaborating
A Partnership
Mathematics is the economy of information. The central idea of all mathematics is to
discover how knowing some things well, via reasoning, permits students to know much else…without having to commit the information to memory as a separate fact.
It is the connections…the reasoned, logical connections…that make mathematics manageable.
Common Core Georgia Performance Standards place a greater emphasis on problem solving, reasoning, representation, connections, and communication.
Theory
There is a shift toward the student applying mathematical concepts and skills in the context of authentic problems and understanding concepts rather than merely following a sequence of procedures.
In mathematics classrooms, students will learn to think critically in a mathematical way with an understanding that there are many different ways to a solution and sometimes more than one right answer in applied mathematics.
Theory
Those content standards which set an expectation of understanding are potential “points of intersection” between the Standards for Mathematical Content and the Standards for Mathematical Practice.
These points of intersection are weighted toward central and generative
concepts. merit the most time, resources, innovative
energies, and focus. qualitatively improve the curriculum,
instruction, assessment, professional development, and student achievement in mathematics.
Theory
The standards define what students should understand and be able to do in their study of mathematics.
Asking a student to understand something means asking a teacher to assess whether the student has understood it.
Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient rigor.
Assessment
The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by using manipulatives and a variety of
representations, working independently and cooperatively to solve
problems, estimating and computing efficiently, and conducting investigations and recording findings.
Engagement
Standards for Mathematical Practice Eight standards crossing all grade levels and
applied in conjunction with content standards
Standards for Mathematical Content Multiple standards categorized in domains
Six Shifts Teacher practices
Common Core GPS
K 1 2 3 4 5 6 7 8 9 - 12
Modeling
Geometry
Measurement and Data
The Number SystemNumber and Operations in Base Ten
Operations and Algebraic Thinking
Geometry
Number and Operations Fractions
Expressions and Equations
Statistics and Probability
Algebra
Number and Quantity
Functions
Statistics and Probability
Ratios & Proportional Relationships
FunctionsCounting
and Cardinality
© Copyright 2011 Institute for Mathematics and Education
Standards for Mathematical Content
Six Shifts
FOCUS: PrioritiesCOHERENCE: Vertical Scope
FLUENCY: Intensity/FrequencyDEEP UNDERSTANDING:
Variety/SMPAPPLICATION: Relevance
DUAL INTENSITY:Balance in Practice/Understanding
MCC5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.
MCC7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a+0.05a=1.05a means that “increase by 5%” is the same as “multiply by1.05.”
MCC9-12.A.SSE.1 Interpret expressions that represent a quantity in terms of its context.
MCC9-12.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients.
MCC9-12.A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity.
Coherence
Grade 3From Grade 2
Fluent addition and subtraction to 18; foundational ideas about addition and subtraction
Foundational place value understanding
Foundational ideas about shape and position in space
Ability to compare and categorize
Understanding of quantities to 1000
Measurement as unit iteration
Foundational data ideas
Later Deep understanding of
addition and subtraction, multiplication and division
Useful place value understanding
Understanding of defining attributes about shape, comparison of shape
Foundational fractional relationships
Continuation of fluency/algebraic thinking
Measurement, addition, subtraction relationships
Data analysis
Coherence
Where to look…Frameworks Concepts and Skills to Maintain
Enduring Understandings Previous Unit Current Unit
Evidence of Learning in Current Unit
Coherence / Focus
Grade Priorities in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding
K-2 Addition and subtraction; measurement using whole number quantities
3-5 Multiplication and division of whole numbers and fractions
6 Ratios and proportional reasoning; early expressions and equations
7 Ratios and proportional reasoning; arithmetic of rational numbers
8 Linear algebra
9-12 Modeling
Focus
Grade
Required Fluency
K Add/subtract within 5
1 Add/subtract within 10
2 Add/subtract within 20; add/subtract within 100 (pencil and paper)
3 Multiply/divide within 100 ; add/subtract within 1000
4 Add/subtract within 1,000,000
5 Multi-digit multiplication
6 Multi-digit division ; multi-digit decimal operations
7 Solve px + q = r, p(x + q) = r
8 Solve simple 2x2 systems by inspection
9-12 Algebraic manipulation in which to understand structure.Writing a rule to represent a relationship between two quantities.Seeing mathematics as a tool to model real-world situations.Understanding quantities and their relationships.
Fluency
Kindergarten
3+2=55-1=4
Grade 1
6+4=108-2=6
Grade 3
5X7=35 12÷4=3
132+256=388
675-38=637
Grade4
3,276+5,428=8,704
358,732-126,325=
232,407
Grade 5
2,378 X 42=
99,876
Grade 2
8+7=15 16-9=7 22+7=2
9 67-
18=49
Fluency
Write the equation of the line 3x+2y=7 so that it can easily be graphed
using the y-intercept and slope.
Write the rule to express the relationship
between the area of a square and
its inscribed circle.
Fluency
High School
FLEXIBILITY ACCURACY EFFICIENCY APPROPRIATENESS
Accuracy Appropriateness
Flexibility
Efficiency
FLUENTPROBLEMSOLVER
Fluency
Two Approaches Word problems: Assigned after explanation of
operations, algorithms, or rules; and students are expected to apply these procedures to the problems.
Problematic situations: Used at the beginning… for construction of understanding, for generation and exploration of mathematical ideas and strategies…offering multiple entry levels, and supportive of mathematization.
(Young Mathematicians at Work, Fosnot, 2002)
Application
A Delicate BalanceTeachers must…
…ritualize skills practice
…normalize productive
struggle
Dual Intensity
INSTRUCTION
Teacher-Focused
Content Delivery Strategies
HOMEWORK
Distributed Practice
PROCESSING
Student-Focused
Linked to Delivery Strategy
DRILL
Basic facts recall
Fluency
APPLICATION
Making content relevant,
purposeful, and meaningful
REVIEW/PREVIEW
Maintaining old learning
Building foundations for new learning
Six Elements
How can school leader familiarity with the Standards for Mathematical Practice, Standards for Mathematical Content, content emphases, and instructional shifts impact successful implementation of CCGPS?
Essential Question