Minnesota State University, Mankato s4

Minnesota State University, Mankato Professional Education Unit

INITIAL LICENSURE PROGRAM UNDER the LICENSURE RULES (LAWS OF MINNESOTA; 1993, CHAPTER 224, ARICLE 12, SECTION 34)

College: Science Engineering & Technology Department: Mathematics & Statistics

Submission Date to BOT: July 1, 2000

Studies Program: Mathematics Degree: BST

Licensure Standards: Minnesota Board of Teaching Standards Date: March 1999

Program Contact Person(s): Mary Ann Lee

Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles A. A teacher of mathematics MATH 121 Calculus I MATH 121 Calculus I MATH 121 Calculus I understands patterns, relations, MATH 122 Calculus II MATH 122 Calculus II MATH 122 Calculus II functions, algebra, and basic concepts MATH 223 Calculus III MATH 223 Calculus III MATH 223 Calculus III underlying calculus from both concrete MATH 247 Linear Algebra I MATH 247 Linear Algebra I MATH 247 Linear Algebra I and abstract perspectives and is able to MATH 290 Foundations of MATH 290 Foundations of MATH 290 Foundations of apply this understanding to represent Mathematics Mathematics Mathematics and solve real world problems. The MATH 316 Intermediate MATH 316 Intermediate MATH 316 Intermediate teacher of mathematics must Analysis Analysis Analysis demonstrate knowledge of the following MATH 332 College Geometry MATH 332 College Geometry MATH 332 College Geometry mathematical concepts and procedures MATH 345 Abstract Algebra I MATH 345 Abstract Algebra I MATH 345 Abstract Algebra I and the connections among them: MATH 354 Concepts of MATH 480 History of MATH 480 History of Probability and Mathematics Mathematics Statistics MATH 484 Technology in MATH 484 Technology in MATH 375 Introduction to Secondary School Secondary School Discrete Mathematics Mathematics Mathematics

1 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles MATH 480 History of MATH 485 Teaching Secondary MATH 485 Teaching Secondary Mathematics School Mathematics School Mathematics MATH 484 Technology in MATH 495 Selected Topics MATH 495 Selected Topics Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (1) recognize, describe, and generalize MATH 121 Calculus I patterns and build mathematical models to MATH 122 Calculus II describe situations, solve problems, and MATH 223 Calculus III make predictions; MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 316 Intermediate Analysis MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 480 History of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (2) analyze the interaction between MATH 121 Calculus I quantities and variables to model patterns MATH 122 Calculus II of change and use appropriate MATH 223 Calculus III representations including tables, graphs, MATH 247 Linear Algebra I matrices, words, ordered pairs, algebraic MATH 290 Foundations of

2 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles expressions, algebraic equations, and Mathematics verbal descriptions; MATH 316 Intermediate Analysis MATH 345 Abstract Algebra I MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 480 History of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (3) represent and solve problem MATH 121 Calculus I situations that involve variable quantities MATH 122 Calculus II and use appropriate technology; MATH 223 Calculus III MATH 247 Linear Algebra I MATH 316 Intermediate Analysis MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (4) understand patterns present in number MATH 122 Calculus II systems and apply these patterns to further MATH 290 Foundations of

3 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles investigations; Mathematics MATH 345 Abstract Algebra I MATH 375 Introduction to Discrete Mathematics (5) apply properties of boundedness and MATH 121 Calculus I limits to investigate problems involving MATH 122 Calculus II sequences and series; MATH 316 Intermediate Analysis MATH 354 Concepts of Probability and Statistics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics (6) apply concepts of derivatives to MATH 121 Calculus I investigate problems involving rates of MATH 122 Calculus II change; MATH 223 Calculus III MATH 316 Intermediate Analysis MATH 354 Concepts of Probability and Statistics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics (7) apply concepts and standard MATH 121 Calculus I mathematical representations from MATH 122 Calculus II differential, integral and multivariate MATH 223 Calculus III calculus; linear algebra, including vectors MATH 247 Linear Algebra I and vector spaces; and transformational MATH 316 Intermediate operations to solve problems; and Analysis MATH 354 Concepts of

4 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles Probability and Statistics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics (8) apply properties of group and field MATH 247 Linear Algebra I structures to mathematical investigations. MATH 290 Foundations of Mathematics MATH 345 Abstract Algebra I B. A teacher of mathematics MATH 121 Calculus I MATH 247 Linear Algebra I MATH 247 Linear Algebra I understands the discrete processes from MATH 122 Calculus II MATH 290 Foundations of MATH 290 Foundations of both concrete and abstract perspectives MATH 223 Calculus III Mathematics Mathematics and is able to identify real world MATH 247 Linear Algebra I MATH 354 Concepts of MATH 354 Concepts of applications; the differences between the MATH 290 Foundations of Probability and Probability and mathematics of continuous and discrete Mathematics Statistics Statistics phenomena; and the relationships MATH 345 Abstract Algebra I MATH 375 Introduction to MATH 375 Introduction to involved when discrete models or MATH 354 Concepts of Discrete Mathematics Discrete Mathematics processes are used to investigate Probability and MATH 484 Technology in continuous phenomena. The teacher of Statistics Secondary School mathematics must demonstrate MATH 375 Introduction to Mathematics knowledge of the following Discrete Mathematics MATH 485 Teaching Secondary mathematical concepts and procedures MATH 484 Technology in School Mathematics and the connections among them: Secondary School MATH 495 Selected Topics Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (1) the application of discrete models to MATH 247 Linear Algebra I problem situations using appropriate MATH 290 Foundations of representations such as sequences, vertex- Mathematics edge graphs and trees, matrices, and arrays; MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to

5 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles Discrete Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (2) application of systematic counting MATH 247 Linear Algebra I techniques to problem situations including MATH 290 Foundations of determination of the existence of a Mathematics solution, the determination of the number MATH 354 Concepts of of possible solutions, or the optimal Probability and solution; Statistics MATH 375 Introduction to Discrete Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (3) application of discrete mathematics MATH 247 Linear Algebra I strategies, for example, pattern searching, MATH 290 Foundations of organization of information, sorting, case- Mathematics by-case analysis, iteration and recursion, MATH 354 Concepts of and mathematical induction, to investigate, Probability and solve, and extend problems; Statistics MATH 375 Introduction to Discrete Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (4) exploration, development, analysis, MATH 121 Calculus I

6 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles and comparison of algorithms designed to MATH 122 Calculus II accomplish a task or solve a problem; MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 480 History of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (5) application of additional discrete MATH 247 Linear Algebra I strategies including symbolic logic and MATH 290 Foundations of linear programming; Mathematics MATH 375 Introduction to Discrete Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (6) matrices as a mathematical system MATH 247 Linear Algebra I and matrices and matrix operations as tools MATH 345 Abstract Algebra I to record information and find solutions of MATH 484 Technology in systems of equations; and Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics (7) analysis of iterative and recursive MATH 375 Introduction to

7 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles algorithms to estimate the time needed in Discrete Mathematics order to execute the algorithms for data MATH 484 Technology in likely to be encountered in problem Secondary School situations. Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics C. A teacher of mathematics MATH 121 Calculus I MATH 121 Calculus I MATH 121 Calculus I understands that number sense is the MATH 122 Calculus II MATH 122 Calculus II MATH 122 Calculus II underlying structure that ties MATH 247 Linear Algebra I MATH 247 Linear Algebra I MATH 247 Linear Algebra I mathematics into a coherent field of MATH 290 Foundations of MATH 290 Foundations of MATH 290 Foundations of study, rather than an isolated set of Mathematics Mathematics Mathematics rules, facts, and formulae. The teacher MATH 345 Abstract Algebra I MATH 345 Abstract Algebra I MATH 345 Abstract Algebra I of mathematics must demonstrate MATH 354 Concepts of MATH 354 Concepts of MATH 354 Concepts of knowledge of the following Probability and Probability and Probability and mathematical concepts and procedures Statistics Statistics Statistics and the connections among them: MATH 375 Introduction to MATH 375 Introduction to MATH 375 Introduction to Discrete Mathematics Discrete Mathematics Discrete Mathematics MATH 484 Technology in MATH 484 Technology in MATH 484 Technology in Secondary School Secondary School Secondary School Mathematics Mathematics Mathematics MATH 485 Teaching Secondary MATH 485 Teaching Secondary MATH 485 Teaching Secondary School Mathematics School Mathematics School Mathematics MATH 495 Selected Topics MATH 495 Selected Topics MATH 495 Selected Topics (1) an intuitive sense of numbers MATH 121 Calculus I including a sense of magnitude, mental MATH 247 Linear Algebra I mathematics, place value, and a sense MATH 484 Technology in of reasonableness of results; Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (2) an understanding of number systems, MATH 121 Calculus I their properties and relations including MATH 122 Calculus II whole numbers, integers, rational numbers, MATH 247 Linear Algebra I real numbers, and complex numbers; MATH 290 Foundations of

8 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles Mathematics MATH 345 Abstract Algebra I MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (3) translation among equivalent forms of MATH 121 Calculus I numbers to facilitate problem solving; MATH 122 Calculus II MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 345 Abstract Algebra I MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (4) application of appropriate methods of MATH 121 Calculus I estimation of quantities and evaluation of MATH 247 Linear Algebra I the reasonableness of estimates; MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (5) a knowledge of elementary MATH 121 Calculus I operations, application of properties of MATH 247 Linear Algebra I operations, and the estimation of results; MATH 290 Foundations of

9 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles Mathematics MATH 345 Abstract Algebra I MATH 354 Concepts of Probability and Statistics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (6) geometric and polar representation of MATH 121 Calculus I complex numbers and the interpretation of MATH 122 Calculus II complex solutions to equations; MATH 223 Calculus III MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics (7) algebraic and transcendental MATH 121 Calculus I numbers; MATH 122 Calculus II MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics (8) numerical approximation techniques MATH 121 Calculus I as a basis for numerical integration, MATH 122 Calculus II numerical-based proofs, and MATH 247 Linear Algebra I investigation of fractals; and MATH 290 Foundations of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics

10 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles MATH 495 Selected Topics (9) number theory divisibility, properties MATH 290 Foundations of of prime and composite numbers, and the Mathematics Euclidean algorithm. MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics D. A teacher of mathematics MATH 121 Calculus I MATH 121 Calculus I MATH 121 Calculus I understands geometry and MATH 122 Calculus II MATH 122 Calculus II MATH 122 Calculus II measurement from both abstract and MATH 223 Calculus III MATH 223 Calculus III MATH 223 Calculus III concrete perspectives and is able to MATH 247 Linear Algebra I MATH 247 Linear Algebra I MATH 247 Linear Algebra I identify real world applications and to MATH 290 Foundations of MATH 290 Foundations of MATH 290 Foundations of use geometric learning tools and models, Mathematics Mathematics Mathematics including geoboards, compass and MATH 316 Intermediate MATH 332 College Geometry MATH 332 College Geometry straight edge, rules and protractor, Analysis MATH 316 Intermediate MATH 345 Abstract Algebra I patty paper, reflection tools, spheres, MATH 332 College Geometry Analysis MATH 484 Technology in and platonic solids. The teacher of MATH 345 Abstract Algebra I MATH 484 Technology in Secondary School mathematics must demonstrate MATH 375 Introduction to Secondary School Mathematics knowledge of the following Discrete Mathematics Mathematics MATH 485 Teaching Secondary mathematical concepts and procedures MATH 480 History of MATH 485 Teaching Secondary School Mathematics and the connections among them: Mathematics School Mathematics MATH 495 Selected Topics MATH 484 Technology in MATH 495 Selected Topics Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (1) shapes and the ways shapes can be MATH 122 Calculus II derived and described in terms of MATH 223 Calculus III dimension, direction, orientation, MATH 247 Linear Algebra I perspective, and relationships among these MATH 290 Foundations of properties; Mathematics MATH 332 College Geometry MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary

11 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles School Mathematics MATH 495 Selected Topics (2) spatial sense and the ways shapes can MATH 121 Calculus I be visualized, combined, subdivided, and MATH 122 Calculus II changed to illustrate concepts, properties, MATH 223 Calculus III and relationships; MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 332 College Geometry MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (3) spatial reasoning and the use of MATH 121 Calculus I geometric models to represent, visualize, MATH 122 Calculus II and solve problems; MATH 223 Calculus III MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 332 College Geometry MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary

12 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles School Mathematics MATH 495 Selected Topics (4) motion and the ways in which MATH 121 Calculus I rotation, reflection, and translation of MATH 122 Calculus II shapes can illustrate concepts, properties, MATH 223 Calculus III and relationships; MATH 247 Linear Algebra I MATH 332 College Geometry MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (5) formal and informal argument, MATH 121 Calculus I including the MATH 122 Calculus II processes of making assumptions; MATH 223 Calculus III formulating, testing, and reformulating MATH 247 Linear Algebra I conjectures; justifying arguments based on MATH 290 Foundations of geometric figures; and evaluating the Mathematics arguments of others; MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 375 Introduction to Discrete Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (6) plane, solid, and coordinate geometry MATH 122 Calculus II systems MATH 223 Calculus III including relations between coordinate and MATH 247 Linear Algebra I synthetic geometry, and generalizing MATH 332 College Geometry geometric principles from a two- MATH 484 Technology in dimensional system to a three-dimensional Secondary School system; Mathematics

13 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (7) attributes of shapes and objects that MATH 121 Calculus I can be measured, including length, area, MATH 122 Calculus II volume, capacity, size of angles, weight, MATH 223 Calculus III and mass; MATH 247 Linear Algebra I MATH 354 Concepts of Probability and Statistics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (8) the structure of systems of MATH 121 Calculus I measurement, including the development MATH 122 Calculus II and use of measurement systems and the MATH 223 Calculus III relationships among different systems; MATH 247 Linear Algebra I MATH 354 Concepts of Probability and Statistics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (9) measuring, estimating, and using MATH 121 Calculus I measurements to describe and compare MATH 122 Calculus II geometric phenomena; MATH 223 Calculus III MATH 247 Linear Algebra I MATH 354 Concepts of Probability and Statistics

14 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (10) systems of geometry, including MATH 122 Calculus II Euclidean, non-Euclidean, coordinate, MATH 223 Calculus III transformational, and projective geometry; MATH 332 College Geometry MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics 11) transformations, coordinates, and MATH 122 Calculus II vectors, including polar and parametric MATH 223 Calculus III equations, and the use of these in problem MATH 247 Linear Algebra I solving; MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (12) three-dimensional geometry and its MATH 122 Calculus II generalization to other dimensions; MATH 223 Calculus III MATH 247 Linear Algebra I MATH 332 College Geometry MATH 485 Teaching Secondary School Mathematics (13) topology, including topological MATH 121 Calculus I properties and transformations; MATH 122 Calculus II MATH 223 Calculus III MATH 316 Intermediate Analysis MATH 332 College Geometry

15 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (14) extend informal argument to include MATH 121 Calculus I more rigorous proofs; and MATH 122 Calculus II MATH 223 Calculus III MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 316 Intermediate Analysis MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 375 Introduction to Discrete Mathematics MATH 480 History of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics (15) extend work with two-dimensional MATH 121 Calculus I right triangles including unit circle MATH 122 Calculus II trigonometry. MATH 485 Teaching Secondary School Mathematics E. A teacher of mathematics uses a MATH 354 Concepts of MATH 354 Concepts of MATH 354 Concepts of variety of conceptual and procedural Probability and Probability and Probability and tools for collecting, organizing, and Statistics Statistics Statistics reasoning about data; applies numerical MATH 484 Technology in MATH 484 Technology in MATH 484 Technology in and graphical techniques for Secondary School Secondary School Secondary School representing and summarizing data; and Mathematics Mathematics Mathematics interprets and draws inferences from MATH 485 Teaching Secondary MATH 485 Teaching Secondary MATH 485 Teaching Secondary these data and makes decisions in a wide School Mathematics School Mathematics School Mathematics range of applied problem situations. MATH 495 Selected Topics MATH 495 Selected Topics MATH 495 Selected Topics The teacher of mathematics must

16 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles demonstrate knowledge of the following mathematical concepts and procedures and the connections among them: (1) data and its power as a way to explore MATH 354 Concepts of questions and issues in our world; Probability and Statistics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (2) investigation through data including MATH 495 Selected Topics formulating a problem; devising a plan to collect data; and systematically collecting, recording, and organizing data; (3) data representation to describe data MATH 354 Concepts of distributions, central tendency, and Probability and variance through appropriate use of graphs, Statistics tables, and summary statistics; MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (4) analysis and interpretation of data, MATH 354 Concepts of including summarizing data, and making or Probability and evaluating arguments, Statistics predictions, recommendations, or decisions MATH 484 Technology in based on an analysis of the data; and Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (5) descriptive and inferential statistics, MATH 354 Concepts of including validity and reliability. Probability and

17 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles Statistics F. A teacher of mathematics MATH 354 Concepts of MATH 354 Concepts of MATH 354 Concepts of understands how to reduce the Probability and Probability and Probability and uncertainties through predictions based Statistics Statistics Statistics on empirical or theoretical probabilities. MATH 484 Technology in MATH 484 Technology in MATH 484 Technology in The teacher of mathematics must Secondary School Secondary School Secondary School demonstrate knowledge of the following Mathematics Mathematics Mathematics mathematical concepts and procedures MATH 485 Teaching Secondary MATH 485 Teaching Secondary MATH 485 Teaching Secondary and the connections among them: School Mathematics School Mathematics School Mathematics MATH 495 Selected Topics MATH 495 Selected Topics MATH 495 Selected Topics (1) inference, and the role of randomness MATH 354 Concepts of and sampling in statistical claims about Probability and populations; Statistics MATH 485 Teaching Secondary School Mathematics (2) probability as a way to describe MATH 354 Concepts of chance or risk in simple and compound Probability and events; Statistics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (3) predicting outcomes based on MATH 354 Concepts of exploration of probability through data Probability and collection, experiments, and simulations; Statistics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (4) predicting outcomes based on MATH 354 Concepts of theoretical probabilities, and comparing Probability and mathematical expectations with Statistics

18 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles experimental results; MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (5) random variable and the application MATH 354 Concepts of of random variable to generate and Probability and interpret probability distributions; Statistics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (6) probability theory and the link of MATH 354 Concepts of probability theory to inferential statistics; Probability and and Statistics (7) discrete and continuous probability MATH 354 Concepts of distributions as a basis for making Probability and inferences about population. Statistics G. A teacher of mathematics is able to MATH 121 Calculus I MATH 121 Calculus I MATH 121 Calculus I reason mathematically, solve problems MATH 122 Calculus II MATH 122 Calculus II MATH 122 Calculus II mathematically, and communicate in MATH 223 Calculus III MATH 223 Calculus III MATH 223 Calculus III mathematics effectively at different MATH 247 Linear Algebra I MATH 247 Linear Algebra I MATH 247 Linear Algebra I levels of formality and knows the MATH 290 Foundations of MATH 290 Foundations of MATH 290 Foundations of connections among mathematical Mathematics Mathematics Mathematics concepts and procedures as well as their MATH 316 Intermediate MATH 316 Intermediate MATH 316 Intermediate application to the real world. The Analysis Analysis Analysis teacher of mathematics must be able to: MATH 332 College Geometry MATH 332 College Geometry MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 345 Abstract Algebra I MATH 345 Abstract Algebra I MATH 354 Concepts of MATH 354 Concepts of MATH 354 Concepts of Probability and Probability and Probability and Statistics Statistics Statistics MATH 375 Introduction to MATH 375 Introduction to MATH 375 Introduction to Discrete Mathematics Discrete Mathematics Discrete Mathematics

19 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles MATH 480 History of MATH 480 History of MATH 480 History of Mathematics Mathematics Mathematics MATH 484 Technology in MATH 484 Technology in MATH 484 Technology in Secondary School Secondary School Secondary School Mathematics Mathematics Mathematics MATH 485 Teaching Secondary MATH 485 Teaching Secondary MATH 485 Teaching Secondary School Mathematics School Mathematics School Mathematics MATH 495 Selected Topics MATH 495 Selected Topics MATH 495 Selected Topics (1) solve problems in mathematics by: MATH 121 Calculus I MATH 122 Calculus II MATH 223 Calculus III MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 332 College Geometry MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (a) formulating and posing problems; MATH 121 Calculus I MATH 122 Calculus II MATH 223 Calculus III MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 332 College Geometry MATH 354 Concepts of Probability and Statistics

20 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles MATH 375 Introduction to Discrete Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (b) solving problems using different MATH 121 Calculus I strategies, verifying and interpreting MATH 122 Calculus II results, and generalizing the solution; MATH 223 Calculus III MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 332 College Geometry MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (c) using problem solving approaches MATH 121 Calculus I to investigate and understand mathematics; MATH 122 Calculus II and MATH 223 Calculus III MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 332 College Geometry MATH 354 Concepts of Probability and Statistics

21 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles MATH 375 Introduction to Discrete Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (d) applying mathematical modeling to MATH 121 Calculus I real world situations; MATH 122 Calculus II MATH 223 Calculus III MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 332 College Geometry MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (2) reason in mathematics by: MATH 121 Calculus I MATH 122 Calculus II MATH 223 Calculus III MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 316 Intermediate Analysis MATH 332 College Geometry MATH 345 Abstract Algebra I

22 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 480 History of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (a) examining patterns, abstracting and MATH 121 Calculus I generalizing based on the examination, and MATH 122 Calculus II making convincing mathematical MATH 223 Calculus III arguments; MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 316 Intermediate Analysis MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 480 History of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics

23 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles (b) framing mathematical questions and MATH 121 Calculus I conjectures, formulating counter-examples, MATH 122 Calculus II and constructing and MATH 223 Calculus III evaluating arguments; and MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 316 Intermediate Analysis MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 480 History of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (c) using intuitive, informal MATH 121 Calculus I exploration, and formal proof. MATH 122 Calculus II MATH 223 Calculus III MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 316 Intermediate Analysis MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 354 Concepts of Probability and Statistics

24 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles MATH 375 Introduction to Discrete Mathematics MATH 480 History of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (3) communicate in mathematics by: MATH 121 Calculus I MATH 122 Calculus II MATH 223 Calculus III MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 316 Intermediate Analysis MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 480 History of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (a) expressing mathematical ideas MATH 121 Calculus I orally, visually, and in writing; MATH 122 Calculus II MATH 223 Calculus III

25 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 316 Intermediate Analysis MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 480 History of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (b) using the power of mathematical MATH 121 Calculus I language, notation, and symbolism; and MATH 122 Calculus II MATH 223 Calculus III MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 316 Intermediate Analysis MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 480 History of

26 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (c) translating mathematical ideas into MATH 121 Calculus I mathematical language, notations, and MATH 122 Calculus II symbols; and MATH 223 Calculus III MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 316 Intermediate Analysis MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 480 History of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (4) make mathematical connections by: MATH 121 Calculus I MATH 122 Calculus II MATH 223 Calculus III MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics

27 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles MATH 316 Intermediate Analysis MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 480 History of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (a) demonstrating the MATH 121 Calculus I interconnectedness of the concepts and MATH 122 Calculus II procedures of mathematics; MATH 223 Calculus III MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 316 Intermediate Analysis MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 480 History of Mathematics MATH 484 Technology in Secondary School

28 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (b) making connections between MATH 121 Calculus I mathematics and other disciplines; MATH 122 Calculus II MATH 223 Calculus III MATH 247 Linear Algebra I MATH 316 Intermediate Analysis MATH 332 College Geometry MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 480 History of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (c) making connections between MATH 121 Calculus I mathematics and daily living; and MATH 122 Calculus II MATH 223 Calculus III MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 316 Intermediate Analysis MATH 332 College Geometry MATH 354 Concepts of Probability and Statistics

29 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles MATH 375 Introduction to Discrete Mathematics MATH 480 History of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (d) making connections between MATH 121 Calculus I equivalent representations of the same MATH 122 Calculus II concept. MATH 223 Calculus III MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 316 Intermediate Analysis MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 480 History of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics H. A teacher of mathematics must: MATH 121 Calculus I MATH 121 Calculus I MATH 480 History of MATH 122 Calculus II MATH 122 Calculus II Mathematics MATH 223 Calculus III MATH 223 Calculus III MATH 484 Technology in

30 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles MATH 247 Linear Algebra I MATH 247 Linear Algebra I Secondary School MATH 290 Foundations of MATH 290 Foundations of Mathematics Mathematics Mathematics MATH 485 Teaching Secondary MATH 316 Intermediate MATH 316 Intermediate School Mathematics Analysis Analysis MATH 495 Selected Topics MATH 332 College Geometry MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 345 Abstract Algebra I MATH 354 Concepts of MATH 354 Concepts of Probability and Probability and Statistics Statistics MATH 375 Introduction to MATH 375 Introduction to Discrete Mathematics Discrete Mathematics MATH 480 History of MATH 480 History of Mathematics Mathematics MATH 484 Technology in MATH 484 Technology in Secondary School Secondary School Mathematics Mathematics MATH 485 Teaching Secondary MATH 485 Teaching Secondary School Mathematics School Mathematics MATH 495 Selected Topics MATH 495 Selected Topics (1) understand the historical bases of MATH 121 Calculus I mathematics, including the contributions MATH 122 Calculus II made by individuals and cultures, and the MATH 223 Calculus III problems societies faced that gave rise to MATH 247 Linear Algebra I mathematical systems; MATH 316 Intermediate Analysis MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 480 History of Mathematics MATH 485 Teaching Secondary

31 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles School Mathematics MATH 495 Selected Topics (2) recognize that there are multiple MATH 121 Calculus I mathematical world views and how the MATH 122 Calculus II teacher's own view is similar to or different MATH 223 Calculus III from that of the students; MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 480 History of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (3) understand the overall framework of MATH 121 Calculus I mathematics including the: MATH 122 Calculus II MATH 223 Calculus III MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 316 Intermediate Analysis MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 354 Concepts of Probability and Statistics

32 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles MATH 375 Introduction to Discrete Mathematics MATH 480 History of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (a) processes and consequences of MATH 121 Calculus I expanding mathematical systems; MATH 122 Calculus II MATH 223 Calculus III MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 316 Intermediate Analysis MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 480 History of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (b) examination of the effects of broad MATH 121 Calculus I ideas, including operations or properties, as MATH 122 Calculus II these ideas are applied to various systems; MATH 223 Calculus III MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 316 Intermediate Analysis

33 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 354 Concepts of Probability and Statistics MATH 480 History of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (c) examination of the same object MATH 121 Calculus I from different perspectives; and MATH 122 Calculus II MATH 223 Calculus III MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 480 History of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (d) investigation of the logical MATH 121 Calculus I reasoning that takes place within a system; MATH 122 Calculus II

34 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles and MATH 223 Calculus III MATH 247 Linear Algebra I MATH 290 Foundations of Mathematics MATH 316 Intermediate Analysis MATH 332 College Geometry MATH 345 Abstract Algebra I MATH 354 Concepts of Probability and Statistics MATH 375 Introduction to Discrete Mathematics MATH 480 History of Mathematics MATH 484 Technology in Secondary School Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (4) understand the role of technology, manipulatives, and models in mathematics. I. A teacher of mathematics must MATH 484 Technology in MATH 484 Technology in MATH 484 Technology in demonstrate an understanding of the Secondary School Secondary School Secondary School teaching of mathematics that integrates Mathematics Mathematics Mathematics understanding of mathematics with the MATH 485 Teaching Secondary MATH 485 Teaching Secondary MATH 485 Teaching Secondary understanding of pedagogy, students, School Mathematics School Mathematics School Mathematics learning, classroom management, and MATH 495 Selected Topics MATH 495 Selected Topics MATH 495 Selected Topics professional development. The teacher of mathematics to preadolescent and adolescent students shall: (1) understand and apply educational MATH 484 Technology in principles relevant to the physical, social, Secondary School emotional, moral, and cognitive Mathematics development of preadolescents and MATH 485 Teaching Secondary

35 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles adolescents; School Mathematics MATH 495 Selected Topics (2) understand and apply the research MATH 484 Technology in base for and the best practices of middle Secondary School level and high school education; Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (3) develop curriculum goals and MATH 484 Technology in purposes based on the central concepts of Secondary School mathematics and know how to apply Mathematics instructional strategies and materials for MATH 485 Teaching Secondary achieving student understanding of this School Mathematics discipline; MATH 495 Selected Topics (4) understand the role and alignment of MATH 484 Technology in district, school, and department mission Secondary School and goals in program planning; Mathematics MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (5) understand the need for and how to MATH 484 Technology in connect students' schooling experiences Secondary School with everyday life, the workplace, and Mathematics further educational opportunities; MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (6) know how to involve representatives MATH 484 Technology in of business, industry, and community Secondary School organizations as active partners in creating Mathematics educational opportunities; MATH 485 Teaching Secondary School Mathematics MATH 495 Selected Topics (7) understand the role and purpose of MATH 484 Technology in cocurricular and extracurricular activities Secondary School in the teaching and learning process; Mathematics MATH 485 Teaching Secondary

36 Licensure Rule 8710.4600 Standards Knowledge and Understanding Practice in Applying the Assessment (demonstration of of the Standard Standard Attainment of the Standard) Course Numbers and Titles Course Numbers and Titles Course Numbers and Titles School Mathematics MATH 495 Selected Topics (8) understand the impact of reading MATH 495 Selected Topics ability on student achievement in mathematics, recognize the varying reading comprehension and fluency levels represented by students, and possess the strategies to assist students to read mathematical content materials more effectively; and (9) apply the standards of effective MATH 484 Technology in practice in teaching students through a Secondary School variety of early and ongoing clinical Mathematics experiences with middle level and high MATH 485 Teaching Secondary school students within a range of School Mathematics educational programming models. MATH 495 Selected Topics

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