


STANDARD 1
The competent teacher of mathematics communicates mathematical content
and concepts.
Knowledge Indicators: The competent teacher of mathematics
1A. Understands the dynamics of working collaboratively
with others.
2B. Understands learning styles and learning
strategies.
Performance Indicators: The competent teacher of mathematics
1C. Communicates verbally and in written,
visual, and symbolic forms using appropriate technology.
1D. Creates effective learning environments
where students will be able to work collaboratively in onetoone,
small group, and large group contexts.
1E. Analyzes the thinking and learning strategies
of all students to extend mathematical knowledge.
STANDARD 2
The competent teacher of mathematics develops and utilizes a variety
of problemsolving techniques.
Knowledge Indicator: The competent teacher of mathematics
2A. Understands the many strategies for problem
solving.
Performance Indicators: The competent teacher of mathematics
2B. Uses problem explorations and modeling
to extend mathematical knowledge of all students.
2C. Generalizes results of problems and extends
them to other problem situations.
STANDARD 3
The competent teacher of mathematics recognizes a variety of reasoning
techniques and applies appropriate techniques to concepts, procedures,
and conjectures.
Knowledge Indicator: The competent teacher of mathematics
3A. Understands various ways of reasoning
with respect to concepts, procedures, and conjectures.
Performance Indicators: The competent teacher of mathematics
3B. Applies mathematical reasoning and appropriate
technologies in the development of concepts, procedures, and conjectures.
3C. Generalizes reasoning skills within the
study of mathematics and applies or extends them to other contexts.
STANDARD 4
The competent teacher of mathematics makes connections within and among
the various branches of mathematics and other disciplines.
Knowledge Indicators: The competent teacher of mathematics
4A. Understands the connections within the
mathematics curriculum.
4B. Understands mathematical connections to
school curriculums and to other disciplines.
4C. Has knowledge of the historical development
of mathematics that includes contributions of men and women from various
cultures.
Performance Indicators: The competent teacher of mathematics
4D. Develops the connections within and among
the various branches of mathematics.
4E. Connects mathematics to other disciplines.
STANDARD 5
The competent teacher of mathematics selects, integrates and uses appropriate
technologies.
Knowledge Indicators: The competent teacher of mathematics
5A. Becomes familiar with the capabilities
and benefits of current and emerging technologies.
5B. Understands the selection, integration
and utilization of appropriate technologies throughout the mathematics
curriculum.
Performance Indicators: The competent teacher of mathematics
5C. Selects appropriate technologies for instruction.
5D. Integrates current technology as appropriate
for instruction.
STANDARD 6
The competent teacher of mathematics demonstrates, applies, and explains
a knowledge and sense of number.
Knowledge Indicators: The competent teacher of mathematics
6A. Knows and understands the concepts of
number, number theory and numeration systems.
Early Childhood/Elementary School Teacher
6A1. Understands
number sense, including concepts of order, magnitude, mental
math, estimation, place value, and senses the reasonableness of results.
6A2. Understands
decimals, fractions, ratios, proportions, and percents as ways to
represent numbers and relationships.
6A3. Knows the
properties of prime and composite numbers.
Middle School Teacher knows and understands the above and
6A4. Has knowledge
of complex numbers, modular systems, and matrices.
Secondary School Mathematics Teacher knows and understands the
above and
6A5. Understands
polar and vector representations of complex numbers, algebraic structures,
and topics from discrete mathematics.
6B. Knows and understands algorithms of operations.
Early Childhood/Elementary School Teacher
6B1. Understands
composition, decomposition, and recomposition of numbers including place
value of any base, factors and multiples, prime and composite numbers,
inverses, and the application of these concepts.
Middle School Teacher knows and understands the above and
6B2. Understands
operations with algebraic expressions and has knowledge of symbolic manipulators.
Secondary School Mathematics Teacher understands the above and
6B3. Has knowledge
of iterative processes as they relate to fractals and other applications.
Performance Indicators: The competent teacher of mathematics
6C. Applies the concepts of number theory
and numeration systems.
Early Childhood/Elementary School Teacher
6C1. Uses number
sense to judge reasonableness of results.
6C2. Applies
proportional reasoning to solve problems.
6C3. Uses the
properties of prime and composite numbers to determine greatest common
factors and least common multiples to solve problems.
6C4. Performs
operations in any base and converts between bases.
Middle School Teacher demonstrates the above and
6C5. Computes
and interprets the results of computation using complex numbers, modular
systems, and matrices.
Secondary School Mathematics Teacher demonstrates the above
and
6C6. Computes
using polar and vector representations of complex numbers.
6D. Models, explains, develops and applies
algorithms of operations.
Early Childhood/Elementary School Teacher
6D1. Chooses
appropriately from mental math, paper and pencil, manipulative, and technology
to perform computations.
Middle School Teacher demonstrates the above and
6D2. Models,
develops, and applies algorithms with technology.
Secondary School Mathematics Teacher demonstrates the above
and
6D3. Uses numerical
approximations as a basis for numerical integration and numericalbased
proofs.
STANDARD 7
The competent teacher of mathematics understands and applies the process
of measurement.
Knowledge Indicators: The competent teacher of mathematics
7A. Knows customary, metric, and nonstandard
measurement.
Early Childhood/Elementary School Teacher
7A1. Knows how
to measure length, area, volume, capacity, time, temperature, angles, weight
and mass.
7A2. Has knowledge
of nonstandard and emerging units such as graphic screen pixels and font
size.
Middle School Teacher knows the above and
7A3. Understands
trigonometric ratios and relationships.
7A4. Understands
how changing one measure of a multidimensional object may affect other
measures.
7A5. Understands
conversion factors as they apply to dimensional analysis.
Secondary School Mathematics Teacher knows the above and
7A6. Understands
nonlinear scales.
Performance Indicators: The competent teacher of mathematics
7B. Selects and applies appropriate units
and tools for measuring, comparing, and ordering.
Early Childhood/Elementary School Teacher
7B1. Uses customary,
metric, and nonstandard measures.
7B2. Selects
and uses appropriate tools to perform above measurements.
7B3. Estimates
measurement.
7B4. Determines
acceptable measures of accuracy and calculates relative error.
Middle School Teacher demonstrates the above and
7B5. Uses trigonometric
ratios and their relationships to solve problems.
Secondary School Mathematics Teacher demonstrates the above
and
7B6. Applies
nonlinear scales (e.g. exponential and logarithmic).
7C. Uses formulas and other procedures for
computing or estimating the measure of multi dimensional objects.
Early Childhood/Elementary School Teacher
7C1. Measures
objects using both direct and indirect measurement.
7C2. Uses formulas
to aid in indirect measurement.
7C3. Applies
measurements and formulas to irregular shapes, regions, and solids.
7C4. Reads and
interprets scale drawings.
Middle School Teacher demonstrates the above and
7C5. Explains
how changing one measure of a multidimensional object impacts other measurements.
7C6. Reads and
interprets topographical maps and architectural drawings.
Secondary School Mathematics Teacher demonstrates the above
and
7C7. Applies
dimensional analysis.
7C8. Uses modeling
and visualization to hypothesize about and predict measurements.
STANDARD 8
The competent teacher of mathematics demonstrates, applies and explains
a knowledge and sense of algebra via patterns, functions, symbols, and
models.
Knowledge Indicators: The competent teacher of mathematics
8A. Knows and understands applications of
concepts, representations, and relationships of variables and patterns.
Early Childhood/Elementary School Teacher
8A1. Understands
the order of operations.
8A2. Understands
the concept of variables.
8A3. Understands
symbolic, numeric, and graphical representations of mathematical situations.
8A4. Understands
the properties and operations of real numbers in an algebraic context.
Middle School Teacher knows and understands the above and
8A5. Understands
a wide range of modeling applications involving graphs, tree charts, and
other visual representations of data with multiple dimensions.
Secondary School Mathematics Teacher knows and understands the
above and
8A6. Understands
variable relationships, logic, and concepts of discrete mathematics.
8B. Knows and
understands concepts and representations of relations and functions.
Early Childhood/Elementary School Teacher
8B1. Understands
the symbolic, numeric, graphical and verbal representations of relations
and functions and the relationships among them.
8B2. Understands
polynomial and exponential functions.
Middle School Teacher knows and understands the above and
8B3. Understands
logarithmic, parametric, trigonometric, rational, radical, absolute value
relations and their graphs.
Secondary School Mathematics Teacher knows and understands the
above and
8B4. Understands
linear algebra.
8C. Knows and understands the development
and applications of calculus.
Early Childhood/Elementary School Teacher
8C1. Understands
concepts of rates of change and patterns that lead to limits.
8C2. Understands
concepts of distance, area, volume, and shapes that lead to limits.
Middle School Teacher knows and understands the above and
8C3. Knows the
historical development of calculus.
8C4. Understands
the concept of limits.
8C5. Understands
the basic concepts of calculus and their applications.
Secondary School Mathematics Teacher knows and understands the
above and
8C6. Understands
the concepts of calculus and analytical geometry and their applications.
8D. Knows and understands algebraic structures.
Early Childhood/Elementary School Teacher
8D1. Understands
the properties of the real number systems.
8D2. Understands
the properties of sets and Venn diagrams.
Middle School Teacher knows and understands the above and
8D3. Understands
the properties of complex and modular systems and their applications.
Secondary School Mathematics Teacher knows and understands the
above and
8D4. Understands
groups, rings, integral domains, and fields.
Performance Indicators: The competent teacher of mathematics
8E. Applies concepts, representations, and
relationships of variables and patterns.
Early Childhood/Elementary School Teacher
8E1. Applies
the order of operations to numerical and algebraic expressions.
8E2. Identifies,
completes, and extends patterns and sequences.
8E3. Represents
mathematical situations symbolically, numerically, and graphically.
8E4. Applies
properties and operations of real numbers in an algebraic context.
8E5. Solves
number sentences involving variables.
8E6. Translates
word situations to algebraic sentences and solves them using algebra.
8E7. Uses equations
and inequalities as a means of solving practical applications.
Middle School Teacher demonstrates the above and
8E8. Uses a
wide range of modeling applications involving graphs and tree charts.
8E9. Solves systems of linear equations graphically
and algebraically (including matrices and determinants).
8E10. Solves
systems of nonlinear equations and inequalities algebraically and graphically.
Secondary School Mathematics Teacher demonstrates the above
and
8E11. Explains
and applies symbolic logic.
8E12. Explains
and applies induction and recursion.
8E13. Explains
and applies sequences and series.
8F. Uses concepts and representations of relations
and functions and their applications.
Early Childhood/Elementary School Teacher
8F1. Represents
functions and relations in symbolic, numeric, graphical, and verbal forms.
8F2. Finds and
uses slopes and intercepts to construct, analyze, and interpret graphs
of equations and inequalities.
Middle School Teacher demonstrates the above and
8F3. Finds and
uses slope, symmetry, roots, intercepts, critical points, and vertices,
to construct and interpret graphs of functions and relations.
8F4. Recognizes
and uses the equations of lines, hyperbolas, parabolas, circles, ellipses,
and nonlinear equations.
8F5. Formulates,
explains, and solves problems involving nonlinear equations such as variation
and exponential and logarithmic growth and decay.
Secondary School Mathematics Teacher demonstrates the above
and
8F6. Applies
principles and properties of linear algebra.
8G. Explains and uses the concepts of calculus
and applications.
Early Childhood/Elementary School Teacher
(There are no additional performance standards for elementary teachers
in this indicator.)
Middle School Teacher demonstrates the above and
8G1. Calculates
and interprets basic limits.
8G2. Illustrates
the basic concepts of calculus using concrete applications.
Secondary School Mathematics Teacher demonstrates the above
and
8G3. Uses differentiation,
integration, and other concepts of calculus to solve problems
and interpret results.
STANDARD 9
The competent teacher of mathematics knows and uses geometric methods
to analyze, categorize, and draw conclusions about points, lines, planes,
and space.
Knowledge Indicators: The competent teacher of mathematics
9A. Understands terminology, properties of
two and three dimensional shapes, and the relationships among them.
9B. Knows Euclidean and nonEuclidean geometry,
coordinates geometry, graph theory, and transformational geometry and the
relationships among them.
9C. Understands the process of conjecturing,
justifying, and proof.
Early Childhood/Elementary School Teacher
9C1. Understands
inductive and deductive reasoning.
Middle School Teacher knows the above and
9C2. Understands
the appropriate uses of different types of proof.
Secondary School Mathematics Teacher knows the above and
9C3. Extends
the understanding of proof to finite and nonEuclidean settings.
Performance Indicators: The competent teacher of mathematics
9D. Uses and applies the properties of geometry.
Early Childhood/Elementary School Teacher
9D1. Recognizes
relationships and patterns in geometric figures.
9D2. Uses characteristics
of geometric figures including symmetry, congruence, and similarity to
recognize, identify, build, draw, describe, analyze, and categorize two
and threedimensional figures and tessellation.
9D3. Applies
geometric concepts to solve practical applications.
9D4. Explains
the relationships between perimeter, area, and volume of similar figures.
Middle School Teacher demonstrates the above and
9D5. Uses trigonometry
to solve practical applications.
Secondary School Mathematics Teacher demonstrates the above.
9E. Identifies, analyzes, categorizes, and
applies multidimensional figures using spatial visualization skills and
modeling.
Early Childhood/Elementary School Teacher
9E1. Translates
between two and threedimensional representations of the same figure including
the use of coordinate geometry and graph theory.
9E2. Uses manipulative,
Euclidean geometry, coordinate geometry, transformational geometry, and
appropriate technology to model mathematical concepts and solve problems.
Middle School Teacher demonstrates the above and
9E3. Generates
solids of revolution from twodimensional figures.
9E4. Gives examples
of nonEuclidean geometry.
9E5. Applies
recursion and iteration geometrically.
9E6. Recognizes
and uses relationships that exist between algebra and geometry.
Secondary School Mathematics Teacher demonstrates the above
and
9E7. Describes
relationships of the planar sections of threedimensional objects.
9E8. Explains
relationships that exist between transformations (including matrix representations)
as a geometric equivalence of the function concept.
9F. Constructs convincing arguments and proofs.
Early Childhood/Elementary School Teacher
9F1. Makes and
identifies mathematical conjectures and provides justification to support
or refute conjectures using a. manipulatives; b. constructions; c.algebraic,
coordinate, and transformational methods; d. interactive technology; and
e. paragraph and twocolumn proofs.
Middle School Teacher demonstrates the above and
9F2. Constructs
inductive, deductive, and indirect arguments and explains the difference
among them.
Secondary School Mathematics Teacher demonstrates the above
and
9F3. Uses a
formal axiomatic system to construct and analyze proofs.
STANDARD 10
The competent teacher of mathematics demonstrates knowledge and application
of probability, descriptive and inferential statistics.
Knowledge Indicators: The competent teacher of mathematics
10A. Understands how to collect, organize
and represent data to answer questions.
Early Childhood/Elementary School Teacher
10A1. Understands
how to create tables, graphs, charts, pictures, and other visual representations
of a set of data.
10A2. Understands
simple random sampling and recognizes bias.
10A3. Understands
line of best fit.
Middle School Teacher knows the above and
10A4. Understands
data trends and curves of best fit.
Secondary School Mathematics Teacher knows and understands the
above.
10B. Understands summary statistics.
Early Childhood/Elementary School Teacher
10B1. Understands
measures of central tendency, variation, and position.
10B2. Understands
common distributions.
Middle School Teacher understands the above.
Secondary School Mathematics Teacher knows the above and
10B3. Understands
additional measures of central tendency and variation.
10C. Understands how to interpret and predict
the results of data analysis.
Early Childhood/Elementary School Teacher
10C1. Understands
the design of observations and experiments to answer questions.
10C2. Understands
the concept of reliability and validity.
Middle School Teacher knows the above and
10C3. Understands
correlation and regression techniques.
Secondary School Mathematics Teacher knows the above and
10C4. Understands
the design of experiments used in hypothesis testing.
10D. Understands counting techniques and probability.
Early Childhood/Elementary School Teacher
10D1. Understands
fundamental counting principles, combinations, and permutations.
10D2. Understands
probability and odds of events.
10D3. Understands
dependent and independent events.
Middle School Teacher knows and understands the above and
10D4. Understands
the use of random variables to solve problems.
Secondary School Mathematics Teacher knows and understands the
above and
10D5. Understands
the link between probability theory and inferential statistics.
Performance Indicators: The competent teacher of mathematics
10E. Poses questions and collects, organizes
and represents data to answer those questions.
Early Childhood/Elementary School Teacher
10E1. Creates
tables, graphs, charts, pictures, and other visual representations of a
set of data.
10E2. Collects
simple random samples and recognizes sample bias.
10E3. Uses visual
techniques for finding, interpreting, and applying the line of best fit.
Middle School Teacher demonstrates the above and
10E4. Finds
and applies appropriate curves of best fit using technology.
Secondary School Mathematics Teacher demonstrates the above.
10F. Calculates, explains, and interprets
summary statistics.
Early Childhood/Elementary and Middle School School Teacher
10F1. Uses measures
of central tendency and variation to describe a set of data.
10F2. Uses common
distributions as appropriate to solve problems.
Secondary School Mathematics Teacher demonstrates the above
and
10F3. Uses additional
measures of central tendency and variation to describe a set ofdata.
10G. Predicts, calculates, interprets, and
applies the results of data analysis.
Early Childhood/Elementary and Middle School Teacher
10G1. Develops
a hypothesis based on a question or problem of interest and devises a plan
for the collection of data.
10G2. Uses simple
survey and sampling techniques.
10G3. Collects,
records, organizes, displays, summarizes, and interprets data.
Secondary School Mathematics Teacher demonstrates the above
and
10G4. Chooses
an appropriate experimental design, selects and performs proper research
procedures, and interprets results.
10H. Demonstrates and uses counting techniques
and probability.
Early Childhood/Elementary School Teacher
10H1. Uses the
fundamental counting principles, combinations, and permutations.
10H2. Determines
the probability and odds of events.
10H3. Analyzes
problems situations (e.g. fairness of games, lotteries).
10H4. Creates
simulations to analyze simple theoretical or experimental probabilities.
10H5. Computes
probabilities for dependent and independent events.
Middle School Teacher demonstrates the above and
10H6. Determines
probabilities involving combinations and permutations.
10H7. Generates
and interprets probability distributions for random variables.
Secondary School Mathematics Teacher demonstrates the above
and
10H8. Links
probability to inferential statistics.
STANDARD 11
The competent teacher of mathematics understands the process of reading
and demonstrates instructional abilities to teach reading in the content
area of mathematics.
Knowledge Indicators: The competent teacher of mathematics
11A. Understands that the reading process
is the construction of meaning through the interactions of the readerís
background knowledge and experiences, the information in the text, and
the purpose of the reading situation.
11B. Recognizes the relationships among the
four language arts (reading, writing, listening, and speaking), and knows
how to provide opportunities to integrate these through instruction.
11C. Understands how to design, select, modify
and evaluate materials in terms of the reading needs of the learner.
11D. Understands the importance of and encourages
the use of adolescent literature in the curriculum and for independent
reading.
11E. Understands the relationship between
oral and silent reading.
11F. Understands the role of subject area
vocabulary in developing reading comprehension.
11G. Understands the importance of the unique
study strategies required of the specific content area in developing reading
comprehension.
11H. Understands the importance of the relationship
between assessment and instruction in planning.
Performance indicators: The competent teacher of mathematics
11I. Plans and teaches lessons for students
that develop comprehension of content area materials through instructional
practices that include analyzing critically, evaluating sources, synthesizing
and summarizing material.
11J. Plans and teaches lessons on how to monitor
comprehension and correct confusions in misunderstandings that arise during
reading.
11K. Plans and models use of comprehension
strategies before, during, and after reading of text.
11L. Provides opportunities for students to
develop content area vocabulary through instructional practices that develop
connections and relationships among words, use of context clues, and understanding
of connotative and denotative meaning of words.
11M. Plans and teaches lessons that encourage
students to write about the content read in order to improve understanding.
11N. Plans and teaches lessons for students
to develop study strategies that include previewing and preparing to read
text effectively, recognizing organizational patterns unique to informational
text, and using graphic organizers as an aid for recalling information.
11O. Plans and teaches units that require
students to carry out research or inquiry using multiple text, including
electronic resources.
11P. Provides continuous monitoring of student
progress through observations, work samples, and various informal reading
assessments.
11Q. Analyzes and evaluates the quality and
appropriateness of instructional materials in terms of readability, content,
length, format, illustrations, and other pertinent factors.
11R. Promotes the development of a literate
environment that includes classroom libraries that foster reading.