Competencies For Secondary Teachers: 2020 Mathematics .
Competencies for Secondary Teachers:Mathematics Grades 7-122020In addition to the Arkansas Teaching Standards, the teacher of Mathematics, grades 7-12, shalldemonstrate knowledge and competencies in the following areas:1. Knowing andUnderstandingMathematicsNCTM/CAEP:Standard 1Praxis (5161): Sections I &IIAR Algebra I, II, & IIIStandardsAR Calculus StandardsAR Geometry StandardsAR Statistics StandardsAR Quantitative LiteracyStandardsNCTM/CAEP Standard 1: Demonstrate and apply understandings ofmajor mathematics concepts, procedures, knowledge, and applicationswithin and among mathematical domains of: Number; Algebra andFunctions; Calculus; Statistics and Probability; Geometry,Trigonometry and MeasurementArkansas teachers should exhibit knowledge and understanding of theessential concepts in each mathematical domain. Additional, specificcompetencies from Praxis content knowledge test specifications andArkansas Standards are included. The intention of this is to augment andprovide additional detail to the essential concepts.1.1 Essential Concepts in Number. Demonstrate and applyunderstandings of major mathematics concepts, procedures,knowledge, and applications of number including flexibly applyingprocedures, using real and rational numbers in contexts, developingsolution strategies, and evaluating the correctness of conclusion.Major mathematical concepts in Number include number systems(particularly rational numbers); algorithmic and recursive thinking;number and set theory; ratio, rate of change, and proportionalreasoning; and structure, relationships, operations, andrepresentationsAdditional specific competencies in Number required for Arkansasteachers include:a) Understand the structure of the natural, integer, rational,real, and complex number systems and how basic operationson numbers in these systems are performedb) Understand and apply the properties of exponents, includingworking with rational exponents and radicalsc) Reason quantitatively and use understanding of units tosolve problems (e.g., dimensional analysis, reasonablenessof solutions)d) Understand how to solve problems involving ratios,proportions, averages, percents, and metric and traditionalunit conversionse) Understand how to perform operations on matrices andapply matrices to solve problems, including in programmingapplicationsf) Represent and compare very large and very small numbers(e.g., scientific notation, orders of magnitude) and estimateand perform calculations on these numbersNCTM/CAEP National Council of Teachers of Mathematics/ Council for the Accreditation of Educator Preparation: 2020 Standards for the Preparation ofSecondary Mathematics Teachers. Praxis (5161) Praxis (5161) Mathematics: Content Knowledge. AR Algebra I, II, & III Standards 2016 Arkansas Algebra I,II, & III Content Standards AR Calculus Standards 2016 Arkansas Calculus Content Standards AR Geometry Standards 2016 Arkansas Geometry ContentStandards AR Statistics Standards 2016 Arkansas Statistics Content Standards AR Math Apps. & Algorithm Standards 2016 Arkansas MathematicalApplications and Algorithms Content Standards ARTMCC 2019 Arkansas Technical Math for College and Career Content Standards AMTE 2017 Standards forPreparing Teachers of Mathematics Teacher Educators NCTM-PA National Council of Teachers of Mathematics: Principles to Action NCTM-MP NationalCouncil of Teachers of Mathematics: What Do the Standards for Mathematical Practice Mean to You? Guide for Life 2019 Arkansas Department of EducationG.U.I.D.E for Life: 5 Skills for Personal Success AR Quantitative Literacy Standards 2016 Arkansas Quantitative Literacy Content StandardsRevised 12/3/2020
Competencies for Secondary Teachers:Mathematics Grades 7-122020g) Use number sense and proportional reasoning in real worldsettings to make and communicate decisions in quantitativeanalysish) Understand how to use counting techniques such as themultiplication principle, permutations, and combinationsi) Understand basic set theory (e.g., unions, differences, Venndiagrams)j) Understand the differences between discrete and continuousrepresentations (e.g., data, functions) and how each can beused to model various phenomena1.2 Essential Concepts in Algebra and Functions. Demonstrate andapply understandings of major mathematics concepts, procedures,knowledge, and applications of algebra and functions including howmathematics can be used systematically to represent patterns andrelationships including proportional reasoning, to analyze change,and to model everyday events and problems of life and society.Essential Concepts in Algebra and Functions include algebra thatconnects mathematical structure to symbolic, graphical, and tabulardescriptions; connecting algebra to functions; and developingfamilies of functions as a fundamental concept of mathematics.Advanced concepts should include algebra from a more theoreticalapproach including relationship between structures (e.g., groups,rings, and fields) as well as formal structures for number systemsand numerical and symbolic calculations.Rewrite algebraic expressions in equivalent forms and choose theappropriate form of an algebraic expression for a given purposeAdditional specific competencies in Algebra required for Arkansasteachers include:a) Understand how to perform arithmetic operations onpolynomials and rational expressionsb) Understand and utilize the relationship between zeros ofpolynomial functions (including non-real complex zeros andgraphical representations of real zeros) and factors of therelated polynomial expressionsc) Understand how to use polynomial identities (e.g.,difference of squares, sum and difference of cubes) to solveproblemsd) Use equations and inequalities to describe relationshipse) Justify the reasoning process used to solve equations,including analysis of potential extraneous solutionsf) Use varied techniques (e.g., graphical, algebraic) to solveequations and inequalities in one variableNCTM/CAEP National Council of Teachers of Mathematics/ Council for the Accreditation of Educator Preparation: 2020 Standards for the Preparation ofSecondary Mathematics Teachers. Praxis (5161) Praxis (5161) Mathematics: Content Knowledge. AR Algebra I, II, & III Standards 2016 Arkansas Algebra I,II, & III Content Standards AR Calculus Standards 2016 Arkansas Calculus Content Standards AR Geometry Standards 2016 Arkansas Geometry ContentStandards AR Statistics Standards 2016 Arkansas Statistics Content Standards AR Math Apps. & Algorithm Standards 2016 Arkansas MathematicalApplications and Algorithms Content Standards ARTMCC 2019 Arkansas Technical Math for College and Career Content Standards AMTE 2017 Standards forPreparing Teachers of Mathematics Teacher Educators NCTM-PA National Council of Teachers of Mathematics: Principles to Action NCTM-MP NationalCouncil of Teachers of Mathematics: What Do the Standards for Mathematical Practice Mean to You? Guide for Life 2019 Arkansas Department of EducationG.U.I.D.E for Life: 5 Skills for Personal Success AR Quantitative Literacy Standards 2016 Arkansas Quantitative Literacy Content StandardsRevised 12/3/2020
Competencies for Secondary Teachers:Mathematics Grades 7-122020g) Understand how varied techniques (e.g., graphical,algebraic, matrix) are used to solve systems of equations andinequalitiesh) Understand the concept of average rate of change over aninterval for nonlinear functions and utilize it in problemsolving contextsi) Recognize, extract, and interpret information about a linearequation presented in various forms (e.g., slope-intercept,point-slope, standard), including within a modeling contextj) Understand sequences and define them recursively (e.g.,arithmetic, geometric)Additional specific competencies in Functions required for Arkansasteachers include:a) Understand the function concept and the use of function notationb) Understand how to find the domain and range of a function anda relationc) Analyze function behavior using different representations (e.g.,graphs, mappings, tables, recursively-defined functions)d) Understand how to find and interpret the zero(s) of functionse) Understand how functions and relations are used to modelrelationships between quantitiesf) Understand how new functions are obtained from existingfunctions (e.g., compositions, transformations, inverses)g) Understand differences between linear, quadratic, andexponential models, including how their equations are createdand used to solve problemsh) Understand the relationship between points on the unit circleand the values of trigonometric functions for any given anglemeasurei) Understand how periodic phenomena are modeled usingtrigonometric functionsj) Understand the derivation and application of trigonometricidentities (e.g., Pythagorean, double angle, half angle, sum ofangles, difference of angles)k) Understand how to interpret representations of functions of twovariables (e.g., three-dimensional graphs, tables)l) Understand how to solve trigonometric, logarithmic, andexponential equationsm) Apply knowledge of functions and equations in programmingapplications1.3 Essential Concepts in Calculus. Demonstrate and applyunderstandings of major mathematics concepts, procedures,knowledge, and applications of calculus including the mathematicalNCTM/CAEP National Council of Teachers of Mathematics/ Council for the Accreditation of Educator Preparation: 2020 Standards for the Preparation ofSecondary Mathematics Teachers. Praxis (5161) Praxis (5161) Mathematics: Content Knowledge. AR Algebra I, II, & III Standards 2016 Arkansas Algebra I,II, & III Content Standards AR Calculus Standards 2016 Arkansas Calculus Content Standards AR Geometry Standards 2016 Arkansas Geometry ContentStandards AR Statistics Standards 2016 Arkansas Statistics Content Standards AR Math Apps. & Algorithm Standards 2016 Arkansas MathematicalApplications and Algorithms Content Standards ARTMCC 2019 Arkansas Technical Math for College and Career Content Standards AMTE 2017 Standards forPreparing Teachers of Mathematics Teacher Educators NCTM-PA National Council of Teachers of Mathematics: Principles to Action NCTM-MP NationalCouncil of Teachers of Mathematics: What Do the Standards for Mathematical Practice Mean to You? Guide for Life 2019 Arkansas Department of EducationG.U.I.D.E for Life: 5 Skills for Personal Success AR Quantitative Literacy Standards 2016 Arkansas Quantitative Literacy Content StandardsRevised 12/3/2020
Competencies for Secondary Teachers:Mathematics Grades 7-122020study of the calculation of instantaneous rates of change and thesummation of infinitely many small factors to determine somewhole. Essential Concepts in Calculus include limits, continuity, theFundamental Theorem of Calculus, and the meaning and techniquesof differentiation and integration.Additional specific competencies in Calculus required for Arkansasteachers include:a) Understand the meaning of a limit of a function and how tocalculate limits of functions, conditions when the limit doesnot exist, and solve problems using the properties of limitsb) Understand the derivative of a function as a limit, as theslope of a line tangent to a curve, and as a rate of changec) Understand what it means that a particular function iscontinuous at a given pointd) Know the relationship between continuity anddifferentiabilitye) Understand how and when to use standard differentiationand integration techniquesf) Understand how to analyze the behavior of a function (e.g.,extrema, concavity, symmetry)g) Understanding how to apply derivatives to solve problemsboth theoretically and in a real-world context (e.g., relatedrates, optimization)h) Understand the foundational theorems of calculus (e.g.,fundamental theorems of calculus, mean value theorem,intermediate value theorem)i) Understand integration as a limit of Riemann sums tocompute area, volume, distance, or other accumulationprocessesj) Know how to determine the limits of sequences, if they exist1.4 Essential Concepts in Statistics and Probability. Demonstrate andapply understandings of statistical thinking and the major concepts,procedures, knowledge, and applications of statistics and probability,including how statistical problem solving and decision making dependon understanding, explaining, and quantifying the variability in a set ofdata to make decisions and understanding the role of randomization andchance in determining the probability of events. Essential Concepts inStatistics and Probability include quantitative literacy, visualizing andsummarizing data, statistical inference, probability, and appliedproblemsAdditional specific competencies in Statistics and Probability requiredfor Arkansas teachers include:NCTM/CAEP National Council of Teachers of Mathematics/ Council for the Accreditation of Educator Preparation: 2020 Standards for the Preparation ofSecondary Mathematics Teachers. Praxis (5161) Praxis (5161) Mathematics: Content Knowledge. AR Algebra I, II, & III Standards 2016 Arkansas Algebra I,II, & III Content Standards AR Calculus Standards 2016 Arkansas Calculus Content Standards AR Geometry Standards 2016 Arkansas Geometry ContentStandards AR Statistics Standards 2016 Arkansas Statistics Content Standards AR Math Apps. & Algorithm Standards 2016 Arkansas MathematicalApplications and Algorithms Content Standards ARTMCC 2019 Arkansas Technical Math for College and Career Content Standards AMTE 2017 Standards forPreparing Teachers of Mathematics Teacher Educators NCTM-PA National Council of Teachers of Mathematics: Principles to Action NCTM-MP NationalCouncil of Teachers of Mathematics: What Do the Standards for Mathematical Practice Mean to You? Guide for Life 2019 Arkansas Department of EducationG.U.I.D.E for Life: 5 Skills for Personal Success AR Quantitative Literacy Standards 2016 Arkansas Quantitative Literacy Content StandardsRevised 12/3/2020
Competencies for Secondary Teachers:Mathematics Grades 7-122020a) Understand how to summarize, represent, and interpret datacollected from measurements on a single variable (e.g., boxplots, dot plots, normal distributions)b) Understand how to summarize, represent, and interpret datacollected from measurements on two variables, eithercategorical or quantitative (e.g., scatterplots, time series)c) Understand how to create and interpret linear regression models(e.g., rate of change, intercepts, correlation coefficient)d) Understand how to make inferences and justify conclusionsfrom samples, experiments, and observational studiese) Understand the concept of independence and understand how tocompute probabilities of simple events, probabilities ofcompound events, and conditional probabilitiesf) Know how to make informed decisions using probabilities andexpected valuesg) Understand how to find probabilities involving finite samplespaces and independent trials, including the use of the countingtechniques (e.g., fundamental counting principles, permutations,combinations)h) Understand normal distributionsi) Using statistical and probabilistic reasoning to drawconclusions, to make decisions, and to evaluate outcomes ofdecision1.5 Essential Concepts in Geometry, Trigonometry, andMeasurement. Demonstrate and apply understandings of majormathematics concepts, procedures, knowledge, and applications ofgeometry, including using visual representations for numericalfunctions and relations, data and statistics, and networks, to providea lens for solving problems in the physical world. EssentialConcepts in Geometry, Trigonometry, and Measurement includetransformations, geometric arguments, reasoning and proof, appliedproblems, and non-Euclidean geometriesAdditional specific competencies in Geometry required for Arkansasteachers include:a) Know the properties of lines (e.g., parallel, perpendicular,intersecting) and anglesb) Know and apply properties of triangles, quadrilaterals (e.g.,parallelogram, rectangle, rhombus) and other polygonsc) Understand and investigate transformations in the plane andapply their propertiesd) Understand congruence and similarity, including congruenceand similarity theorems and use of transformations to definecongruence and similarityNCTM/CAEP National Council of Teachers of Mathematics/ Council for the Accreditation of Educator Preparation: 2020 Standards for the Preparation ofSecondary Mathematics Teachers. Praxis (5161) Praxis (5161) Mathematics: Content Knowledge. AR Algebra I, II, & III Standards 2016 Arkansas Algebra I,II, & III Content Standards AR Calculus Standards 2016 Arkansas Calculus Content Standards AR Geometry Standards 2016 Arkansas Geometry ContentStandards AR Statistics Standards 2016 Arkansas Statistics Content Standards AR Math Apps. & Algorithm Standards 2016 Arkansas MathematicalApplications and Algorithms Content Standards ARTMCC 2019 Arkansas Technical Math for College and Career Content Standards AMTE 2017 Standards forPreparing Teachers of Mathematics Teacher Educators NCTM-PA National Council of Teachers of Mathematics: Principles to Action NCTM-MP NationalCouncil of Teachers of Mathematics: What Do the Standards for Mathematical Practice Mean to You? Guide for Life 2019 Arkansas Department of EducationG.U.I.D.E for Life: 5 Skills for Personal Success AR Quantitative Literacy Standards 2016 Arkansas Quantitative Literacy Content StandardsRevised 12/3/2020
Competencies for Secondary Teachers:Mathematics Grades 7-122020e) Know how to prove geometric theorems, such as those aboutlines and angles, triangles, and parallelogramsf) Understand how geometric constructions are made with avariety of tools and methodsg) Understanding how trigonometry is applied to triangles,including the definition of trigonometric functions in righttrianglesh) Understand and apply theorems about circlesi) Find arc length and area measurements of sectors of circlesj) Know how to translate between a geometric description (e.g.,focus, asymptotes, directrix) and an equation for a conic sectionk) Understand how to represent geometric objects incoordinategeometry to algebraically prove simple geometric theoremsl) Use perimeter, area, surface area, and volume formulas to solveproblemsm) Know how to visualize relationships (e.g., cross section, nets,rotations) between two-dimensional and three-dimensionalobjectsn) Apply geometric concepts in modeling and real world situations2. Knowing and UsingMathematical ProcessesNCTM/CAEP:Standard 2NCTM-MPNCTM/CAEP Standard 2: Demonstrate, within or across mathematicaldomains, their knowledge of and ability to apply the mathematicalprocesses of problem solving; reason and communicate mathematically;and engage in mathematical modeling. Apply technology appropriatelywithin these mathematical processes2.1 Demonstrate a range of mathematical problem-solving strategies tomake sense of and solve nonroutine problems (both contextual andnoncontextual) across mathematical domains2.2 Organize mathematical reasoning and use the language ofmathematics to express mathematical reasoning precisely, both orallyand in writing, to multiple audiences2.3 Understand the difference between the mathematical modelingprocess and models in mathematics; engage in the mathematicalmodeling process and demonstrate ability to model mathematicsNCTM-MP: The Standards for Mathematical Practices describevarieties of expertise that mathematics educators at all levels shouldseek to develop in their students. These practices rest on important“processes and proficiencies” with longstanding importance inmathematics education. Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and the critique the reasoning ofothers Model with mathematicsNCTM/CAEP National Council of Teachers of Mathematics/ Council for the Accreditation of Educator Preparation: 2020 Standards for the Preparation ofSecondary Mathematics Teachers. Praxis (5161) Praxis (5161
Competencies for Secondary Teachers: Mathematics Grades 7-12 2020 NCTM/CAEP National Council of Teachers of Mathematics/ Council for the Accreditation of Educator Preparation: 2020 Standards for the Preparation of Secondary Mathematics Teachers. Praxis (5161) Praxis (5161) Mathematics: Content Knowledge. AR Alg
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