Mathematics Department

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  one-to-one, 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 problem-solving 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 numerical-based 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 non-standard 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 non-standard 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 multi-dimensional 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 non-standard 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 multi-dimensional 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 non-Euclidean 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 non-Euclidean 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 three-dimensional 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 multi-dimensional figures using spatial visualization skills and modeling.
Early Childhood/Elementary School Teacher
          9E1. Translates between two- and three-dimensional 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 two-dimensional figures.
          9E4. Gives examples of non-Euclidean 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 three-dimensional 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 two-column 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.