Virginia Law

The program in Algebra I shall ensure that the candidate holds an active license with a teaching endorsement or endorsements issued by the Virginia Board of Education and has demonstrated the following competencies:

1. Understanding of the mathematics relevant to the content identified in the Mathematics Standards of Learning and how the standards provide the foundation for teaching middle level mathematics through Algebra I, including:

a. The structure of real numbers and subsets, basic operations, and properties;

b. Elementary number theory, ratio, proportion, and percent;

c. Algebra, trigonometry, and analytic geometry: operations with monomials and polynomials; rational expressions; linear, quadratic, and higher degree equations and inequalities; linear systems of equations and inequalities; nonlinear systems of equations; radicals and exponents; complex numbers; arithmetic and geometric sequences and series; algebraic, trigonometric, logarithmic, exponential, absolute value, and step functions; domain and range of functions; composite and inverse functions; one-to-one mapping; transformations between graphical, tabular, and symbolic forms of functions; direct and inverse variation; line and curve of best fit; conics; and recognition and application of trigonometric identities;

d. Calculus: applications of limits, differentiation, and integration;

e. Linear algebra: matrices, vectors, and linear transformations;

f. Geometry: geometric figures, their properties, relationships, and application of the Pythagorean Theorem; using deductive axiomatic methods of proof and inductive reasoning; perimeter, area, and surface area of two-dimensional and three-dimensional figures; coordinate and transformational geometry; constructions and applications of algebra in geometry;

g. Probability and statistics: experimental and theoretical probability; prediction; graphical representations, including box-and-whisker plots; and measures of center, range, standard deviation, z-scores, and simple and normal distributions; and

h. Discrete mathematics: symbolic logic, sets, permutations and combinations, functions that are defined recursively, and linear programming.

2. Understanding of varied pedagogical approaches to teaching algebraic concepts and their connected procedures.

3. Understanding of the connections among algebraic concepts, procedures, models, and practical applications.

4. Understanding of the sequential and interrelated nature of mathematics and the mathematical structures inherent in algebra.

5. Understanding of and the ability to use the five processes - becoming mathematical problem-solvers, reasoning mathematically, communicating mathematically, making mathematical connections, and using mathematical models and representations - at different levels of complexity.

6. Understanding how to utilize appropriate technologies for teaching and learning algebra, including graphing utilities, dynamic software, spreadsheets, and virtual manipulatives.

7. Understanding of and the ability to use strategies for managing, assessing, and monitoring student learning, including diagnosing student errors.

8. Understanding of and the ability to use strategies to teach algebra to diverse learners.

9. Understanding of and proficiency in grammar, usage, and mechanics and their integration in writing.

10. Understanding of and proficiency in pedagogy to incorporate writing as an instructional and assessment tool for candidates to generate, gather, plan, organize, and present ideas in writing to communicate for a variety of purposes.