Transcript communicate and reason mathematically

New York State
Mathematics
Core Curriculum
2005
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Curriculum, Instruction and
Instructional Technology
Anne Schiano
Assistant Director
[email protected]
(518) 474-5922
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Board of Regents Approves
NYS Learning Standard in
Mathematics
and
NYS Mathematics
Core Curriculum
2005
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Mathematics, Science, and Technology
Learning Standard 3: Mathematics
Students will:
•understand the concepts of and become
proficient with the skills of mathematics;
•communicate and reason mathematically;
•become problem solvers by using appropriate
tools and strategies;
through the integrated study of number sense and
operations, algebra, geometry, measurement, and
statistics and probability.
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Standard 3
The Three Components
•Conceptual Understanding consists of those
relationships constructed internally and connected to
already existing ideas.
•Procedural Fluency is the skill in carrying out
procedures flexibly, accurately, efficiently, and
appropriately.
•Problem Solving is the ability to formulate,
represent, and solve mathematical problems.
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Standard 3
Process and Content Strands
The Five Process Strands
The Five Content Strands
Problem Solving
Number Sense and
Operations
Reasoning and Proof
Algebra
Communication
Geometry
Connections
Measurement
Representation
Statistics and Probability
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The Five Content Strands
Performance Indicators which:
• define a broad range of content knowledge
that students must master
• are taught in an integrated manner
• engage students in construction of knowledge
• integrate conceptual understanding and
problem solving
• should not be viewed as a checklist of skills
void of understanding and application
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Number Sense and Operations
Strand
Students will:
•understand numbers, multiple ways of
representing numbers, relationships among
numbers, and number systems;
•understand meanings of operations and
procedures, and how they relate to one
another;
•compute accurately and make reasonable
estimates.
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Algebra Strand
Students will:
•represent and analyze algebraically a wide
variety of problem solving situations;
•perform algebraic procedures accurately;
•recognize, use, and represent algebraically
patterns, relations, and functions.
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Geometry Strand
Students will:
•use visualization and spatial reasoning to
analyze characteristics and properties of
geometric shapes;
•identify and justify geometric relationships,
formally and informally;
•apply transformations and symmetry to
analyze problem solving situations;
•apply coordinate geometry to analyze
problem solving situations.
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Measurement Strand
Students will:
•determine what can be measured and how,
using appropriate methods and formulas;
•use units to give meaning to measurements;
•understand that all measurement contains
error and be able to determine its significance;
•develop strategies for estimating
measurements.
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Statistics and Probability Strand
Students will:
•collect, organize, display, and analyze data;
•make predictions that are based upon data
analysis;
•understand and apply concepts of probability.
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The Five Process Strands
Performance Indicators which:
• highlight ways of acquiring and using content
knowledge
• give meaning to mathematics as a discipline
rather than a set of isolated skills
• engage students in mathematical content as
they solve problems, reason mathematically,
prove mathematical relationships, participate
in mathematical connections, and model and
represent mathematical ideas
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Problem Solving Strand
Students will:
•build new mathematical knowledge through
problem solving;
•solve problems that arise in mathematics and
in other contexts;
•apply and adapt a variety of appropriate
strategies to solve problems;
•monitor and reflect on the process of
mathematical problem solving.
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Reasoning and Proof Strand
Students will:
•recognize reasoning and proof as
fundamental aspects of mathematics;
•make and investigate mathematical
conjectures;
•develop and evaluate mathematical
arguments and proofs;
•select and use various types of reasoning and
methods of proof.
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Communication Strand
Students will:
•organize and consolidate their mathematical
thinking through communication;
•communicate their mathematical thinking
coherently and clearly to peers, teachers, and
others;
•analyze and evaluate the mathematical
thinking and strategies of others;
•use the language of mathematics to express
mathematical ideas precisely.
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Connections Strand
Students will:
•recognize and use connections among
mathematical ideas;
•understand how mathematical ideas
interconnect and build on one another to
produce a coherent whole;
•recognize and apply mathematics in contexts
outside of mathematics.
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Representation Strand
Students will:
•create and use representations to organize,
record, and communicate mathematical ideas;
•select, apply, and translate among
mathematical representations to solve
problems;
•use representations to model and interpret
physical, social, and mathematical
phenomena.
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Bands within the
Content Strands
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Number Sense and Operations
Bands
•Number Systems
•Number Theory
•Operations
•Estimation
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Algebra Bands
•Variables and Expressions
•Equations and Inequalities
•Patterns, Relations, and Functions
•Coordinate Geometry
•Trigonometric Functions
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Geometry Bands
•Shapes
•Geometric Relationships
•Transformational Geometry
•Coordinate Geometry
•Constructions
•Locus
•Informal Proofs
•Formal Proofs
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Measurement Bands
•Units of Measurement
•Tools and Methods
•Units
•Error and Magnitude
•Estimation
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Statistics and Probability Bands
•Collection of Data
•Organization and Display of Data
•Analysis of Data
•Predictions from Data
•Probability
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Guide to Reading
the Document
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Prekindergarten
Major
Understanding
Problem Solving
Strand
Students will build new mathematical knowledge
through problem solving.
Performance
Indicator
PK.PS.1 Explore, examine, and make
observations about a social
problem or mathematical
situation
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Prekindergarten
Number Sense and Operations
Major
Understanding
Strand
Students will understand numbers, multiple ways of
representing numbers, relationships among numbers,
and number systems.
Band
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Performance
Indicator
Number Systems PK.N.1 Count the items in a
collection and know the last
counting word tells how many
items are in the collection
(1 to 10)
Performance Indicator Guide
PK – Prekindergarten
K – Kindergarten
PS – Problem Solving
RP – Reasoning and Proof
CM – Communication
CN – Connections
R – Representation
N – Number Sense and Operations
A – Algebra
G – Geometry
M – Measurement
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S – Statistics and Probability