Knowledge, Skills and Abilities for Advanced Math Endorsement
(1) In addition to passing the required Commission-approved
subject-matter, examinations for advanced math and completing the required
practicum experience, the following requirements must be met to add an advanced
math endorsement onto any Initial or Continuing Teaching License. The
requirements to add an advanced math endorsement onto a Basic or Standard
Teaching License can be found at:
(2) Demonstrated Content Knowledge.
(a) For knowledge of numbers, operations and algebra, candidates will:
(A) Demonstrate knowledge of the properties of the natural, integer, rational, real and complex number systems and the interrelationships of these number systems
(B) Identify and apply the basic ideas, properties and results of number theory and algebraic structures that underlie numbers and algebraic expressions, operations, equations and inequalities;
(C) Use algebraic equations to describe lines, planes and conic sections and to find distances in the plane and space;
(D) Demonstrate the use of algebra to model, analyze, and solve problems from various areas of mathematics, science and the social sciences;
(E) Apply properties and operations of matrices and techniques of analytic geometry to analyze and solve systems of equations; and
(F) Use graphing calculators, computer algebra systems, and spreadsheets to explore algebraic ideas and algebraic representations of information and to solve problems.
(b) For knowledge of geometry, candidates will:
(A) Identify and apply the basic ideas, properties and results of number theory and algebraic structures that underlie numbers and algebraic expressions, operations, equations and inequalities;
(B) Use algebraic equations to describe lines, planes and conic sections and to find distances in the plane and space;
(C) Demonstrate the use of algebra to model, analyze, and solve problems from various areas of mathematics, science and the social sciences;
(D) Apply properties and operations of matrices and techniques of analytic geometry to analyze and solve systems of equations; and
(E) Use graphing calculators, computer algebra systems, and spreadsheets to explore algebraic ideas and algebraic representations of information, and to solve problems.
(c) For knowledge of functions, candidates will:
(A) Demonstrate knowledge of the concept of a function and the most important classes of functions, including polynomial, exponential and logarithmic, rational and trigonometric;
(B) Represent functions in multiple forms, such as graphs, tables, mappings, formulas, matrices and equations;
(C) Perform a variety of operations on functions, including addition, multiplication and composition of functions, and recognize related special functions such as identities and inverses and those operations that preserve the various properties;
(D) Use functions to model situations and solve problems in calculus, linear and abstract algebra, geometry, statistics and discrete mathematics;
(E) Explore various kinds of relations, including equivalence relations, and the differences between relations and functions;
(F) Use calculator and computer technology effectively to study functions and solve problems;
(G) Demonstrate specific knowledge of trigonometric functions, including properties of their graphs, special angles, identities and inequalities, and complex and polar forms; and
(H) Use analytic representations, measures, and properties to analyze transformation of two- and three-dimensional objects.
(d) For knowledge of discrete mathematics and computer science, candidates will:
(A) Demonstrate knowledge of discrete topics including graphs, trees, networks, enumerative combinatorics and finite difference equations, iteration and recursion, and the use of tools such as functions, diagrams and matrices to explore them;
(B) Build discrete mathematical models for social decision-making;
(C) Apply discrete structures such as: sets, logic, relations and functions, and their applications in design of data structures and programming;
(D) Use recursion and combinatorics in the design and analysis of algorithms; and
(E) Candidates employ linear and computer programming to solve problems.
(e) For knowledge of probability and statistics, candidates will:
(A) Explore data using a variety of standard techniques to organize and display data and detect and use measures of central tendency and dispersion;
(B) Use surveys to estimate population characteristics and design experiments to test conjectured relationships among variables;
(C) Use theory and simulations to study probability distributions and apply them as models of real phenomena;
(D) Demonstrate knowledge of statistical inference by using probability models to draw conclusions from data and measure the uncertainty of those conclusions;
(E) Employ calculators and computers effectively in statistical explorations and practice; and
(F) Demonstrate knowledge of basic concepts of probability such as conditional probability and independence, and develop skill in calculating probabilities associated with those concepts.
(f) For knowledge of calculus, candidates will:
(A) Demonstrate conceptual understanding of and procedural facility with basic calculus concepts such as limits, derivatives and integrals of functions of one and two variables;
(B) Use concepts of calculus to analyze the behavior of functions and solve problems; and
(C) Determine the limits of sequences and series and demonstrate the convergence or divergence of series.
(3) Demonstrated Competency in Following Process Standards.
(a) For competency in problem solving, candidates will engage in mathematical inquiry through understanding a problem, exploring, recognizing patterns, conjecturing, experimenting and justifying.
(b) For competency in reasoning and proof, candidates will select and use various types of reasoning and develop and evaluate mathematical arguments and proof in all the mathematics content knowledge areas.
(c) For competency in communication, candidates will:
(A) Organize and consolidate their mathematical thinking through communication;
(B) Communicate coherently and use the language of mathematics such as symbols and terminology to express ideas precisely; and
(C) Analyze the mathematical thinking of others.
(d) For competency in representation, candidates will:
(A) Use multiple forms of representation including concrete models, pictures, diagrams, tables and graphs; and
(B) Use invented and conventional terms and symbols to communicate reasoning and solve problems.
(e) For competency in connections, candidates will:
(A) Understand how mathematical ideas interconnect and build on one another to produce a coherent whole; and
(B) Recognize and apply mathematics in contexts outside of mathematics.
(4) Demonstrated Knowledge and Skill In Mathematics Pedagogy.
(a) For demonstrated knowledge and skill in the principles of equity, candidates will demonstrate high expectations and strong support for all students to learn mathematics,
(b) For demonstrated knowledge and skill in developing curriculum, candidates will:
(A) Map curriculum that is coherent, focused on important mathematics and carefully sequenced;
(B) Be familiar with curriculum both preceding and following the high school level; and
(C) Be able to discern the quality of learning opportunities for students when given a particular task, activity, educational software, etc., and are able to make adaptations to assure quality.
(c) For demonstrated knowledge and skill in developing a quality learning environment, candidates will foster a classroom environment conducive to mathematical learning through:
(A) Providing and structuring the time necessary to explore sound mathematics and grapple with significant ideas and problems;
(B) Using the physical space and materials in ways that facilitate students' learning of mathematics;
(C) Providing a context that encourages the development of mathematical skill and proficiency; and
(D) Respecting and valuing students' ideas, ways of thinking, and mathematical dispositions.
(d) For demonstrated knowledge and skill in teaching, candidates will:
(A) Understand what mathematics students know and need to learn and then challenge and support them to learn it well; and
(B) Orchestrate discourse by:
(i) Posing questions and tasks that elicit, engage and challenge each student's thinking;
(ii) Listening carefully to students' ideas; asking students to clarify and justify their ideas orally and in writing;
(iii) Deciding what to pursue in depth from among the ideas that students bring up during a discussion;
(iv) Deciding when and how to attach mathematical notation and language to students' ideas;
(v) Deciding when to provide information, when to clarify an issue, when to model, when to lead, and when to let a student struggle with a difficulty; and
(vi) Monitoring students' participation in discussions and deciding when and how to encourage each student to participate.
(e) For demonstrated knowledge and skill in learning, candidates will:
(A) Know that students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge; and
(B) Have the ability to recognize and move students from concrete to abstract levels of understanding.
(f) For demonstrated knowledge and skill in assessment, candidates will:
(A) Use a variety of formal and informal, formative and summative assessment techniques to support the learning of important mathematics;
(B) Understand how, why and when to use various assessment techniques and tools; as well as how these tools inform their understanding about student thinking and understanding; and
(C) Plan instruction based upon the information obtained through classroom and external assessments of each student’s developmental level.
(g) For demonstrated knowledge and skill in technology, candidates will:
(A) Understand that technology is an integral part of teaching and learning mathematics both influencing what is taught and enhancing how it is learned.
(B) Demonstrate effective and appropriate use of technology.
(h) For demonstrated knowledge and skill in mathematic historical development candidates will demonstrate knowledge of historical and cultural influences in mathematics including contributions of underrepresented groups.
(i) For demonstrated ability to differentiate instruction, candidates will demonstrate competencies in delivering differentiated instructional strategies that promote equitable learning opportunities and success for all students regardless of native language, socioeconomic background, ethnicity, gender, disability or other individual characteristics. Candidates will:
(A) Identify, select, and implement appropriate instruction that is sensitive to students’ strengths and weaknesses, multiple needs, learning styles, and prior experiences including but not limited to cultural, ethnic, personal, family and community influences; and
(B) Use appropriate services and resources in the delivery of differentiated instruction.
(5) This endorsement is valid to teach:
(a) Advanced Algebra;
(e) Statistics & Probability;
(g) Survey Geometry;
(h) Trigonometry Analysis; and
(i) Other math-related courses.
(6) This endorsement is required to teach any math course above the Algebra I level.
Stat. Auth.: ORS 342
Stats. Implemented: ORS 342.120 - ORS 342.143, ORS 342.153, ORS 342.165, & ORS 342.223 - ORS 342.232
 Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria, and is in particular concerned with "counting" the objects in those collections (enumerative combinatorics) and with deciding whether certain "optimal" objects exist (extremal combinatorics). One of the most prominent combinatorialists of recent times was Gian-Carlo Rota, who helped formalize the subject beginning in the 1960s. The prolific problem-solver Paul Erdős worked mainly on extremal questions. The study of how to count objects is sometimes thought of separately as the field of enumeration. From Wilipedia, the free encyclopedia.
 An expression, such as a polynomial, each term of which is determine by application of a formula to preceding terms; or a formula that generates the successive terms of a recursion.