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VIRGINIA DEPARTMENT OF EDUCATION
PROGRAM STATUS MATRIX
2007 MATHEMATICS -- ALGEBRA I (add-on endorsement)
8VAC 20-542-380
INSTITUTION:
Endorsement Competencies
Courses and Experiences
The program in Algebra I shall ensure that the candidate 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. The
use of technology shall be used in enhancing the student’s ability to develop
concepts, compute, solve problems, and apply mathematics in practical
applications with the mathematics content, including:
a. The structure of real numbers and subsets, basic operations, and
properties;
MATHEMATICS 671 College Algebra for Middle School Teachers
MATHEMATICS 672 Discrete Mathematics for Middle School
Teachers
MATHEMATICS 673 Trigonometry and Algebra for Middle School
Teachers.
b. Elementary number theory, ratio, proportion, and percent;
MATHEMATICS 671 College Algebra for Middle School Teachers
MATHEMATICS 672 Discrete Mathematics for Middle School
Teachers
MATHEMATICS 673 Trigonometry and Algebra for Middle School
Teachers.
c. Algebra, trigonometry, and analytic geometry: operations with
monomials and polynomials; algebraic fractions; linear, quadratic, and
MATHEMATICS 671 College Algebra for Middle School Teachers
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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 form of functions; direct and inverse
variation; line and curve of best fit; conics; and recognition and
application of trigonometric identities;
MATHEMATICS 672 Discrete Mathematics for Middle School
Teachers
MATHEMATICS 673 Trigonometry and Algebra for Middle School
Teachers.
MATHEMATICS 675 Linear Algebra for Middle School Teachers
MATHEMATICS 678 Calculus for Middle School Teachers
d. Calculus: applications of limits and standard integration and
differentiation;
MATHEMATICS 678 Calculus for Middle School Teachers
e. Linear algebra: matrices, vectors, and linear transformations;
MATHEMATICS 675 Linear Algebra for Middle School Teachers
f. Measurement systems, including U.S. customary and metric;
MATHEMATICS 677 Euclidean Geometry for Middle School
Teachers
g. 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- and three-dimensional figures; coordinate and
transformational geometry; and constructions;
MATHEMATICS 677 Euclidean Geometry for Middle School
Teachers
h. Probability and statistics: experimental and theoretical probability;
prediction; graphical representations, including box-and-whisker plots;
and measures of central tendency, range, standard deviation, and
simple distributions;
MATHEMATICS 679 Probability and Statistics for Middle School
Teachers
i. Discrete mathematics: symbolic logic, sets, permutations, and
combinations, functions that are defined recursively, and linear
programming; and
MATHEMATICS 672 Discrete Mathematics for Middle School
Teachers
MATHEMATICS 679 Probability and Statistics for Middle School
Teachers
j. Computer science: terminology, simple programming, and software
applications.
MATHEMATICS 674 Mathematical Programming for Middle School
Teachers
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2. Understanding of and proficiency in grammar, usage, and mechanics
and
their integration in writing.
EDUCATION 502 Research Design
* Description of what the institution offers to enable students to develop the knowledge and skills identified in the competency. When citing courses, provide course number, title,
and catalog description. Catalog descriptions and syllabi may be attached.
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MATHEMATICS 671. College Algebra for Middle School Teachers. Algebra is a tool for working with data and modeling physical situations. This
course is designed to provide additional mathematical background and expertise in Algebra I topics for teachers pursuing the algebra add on endorsement for
their teaching license. The primary topics to be covered will be algebraic expressions, exponents and exponential functions, direct & indirect variation,
proportions, linear functions, graphing, systems of equations and inequalities, polynomials, factoring, quadratic functions and roots. Best practice teaching
techniques will be modeled. 3 credits.
MATHEMATICS 672. Discrete Mathematics for Middle School Teachers. Mathematical problem solving is studied in the context of various mathematics
topics, which have applications in Algebra I and middle school mathematics. These topics may include cryptography, graph theory, linear programming,
logic, patterning, set theory, and financial models. 3 credits.
MATHEMATICS 673. Trigonometry and Algebra for Middle School Teachers. Teachers will explore logarithmic functions and introductory
trigonometry. Conceptual understanding and procedural fluency will be developed in problem settings based on real data. An emphasis is placed on
proportional reasoning and modeling. The course will use graphing calculators along with motion detectors and temperature probes. 3 credits.
MATHEMATICS 674. Mathematical Programming for Middle School Teachers. An introduction to basic computer programming with an emphasis on
mathematics applications applicable to the middle school curriculum. Topics include programming logic, iterations, functions, recursion, and algorithms.
Students will learn in a problem solving environment through student investigations using technology accessible to middle school and Algebra I students. 3
credits.
MATHEMATICS 675. Linear Algebra for Middle School Teachers. Solving systems of linear equations is an integral part of Algebra I. Student will study
various methods of solving these systems along with mathematical theory developed from those methods. The primary topics to be covered will be vector
spaces, dual spaces, linear transformations, and their relationships to matrix algebra. Best practice teaching techniques will be modeled. 3 credits.
MATHEMATICS 677. Euclidean Geometry for Middle School Teachers. The course will focus on the content and processes that support the
measurement and geometry strands of the Virginia 6-8 SOL, and Geometry SOL. Instruction will cover the geometry and measurement content topics that
are encountered from the particular and concrete thinking of school arithmetic to the abstract thinking associated with geometry. Major concepts include
problems solving and proportional reasoning involving area, perimeter, volume and surface area; geometric properties; characteristics of geometric figures
including lines, angles, triangles, circles and polygons; relationships between 2-dimensional and 3-dimensional figures. You will be encouraged to
recognize the thought processes involved in using geometry and what it means to employ geometric thinking, both as a teacher and a student. 3 credits.
MATHEMATICS 678. Calculus for Middle School Teachers. This course focuses on calculus concepts and applications that illustrate the connection between
calculus and the middle school curriculum. These concepts include sequences, series, limits, rates of change, derivates, and an introduction to integration. Best
practice teaching techniques will be modeled. 3 credits.
MATHEMATICS 679. Probability and Statistics for Middle School Teachers. Teachers will explore introductory descriptive statistics, probability, and
statistical inference. Conceptual understanding and procedural fluency will be developed in problem settings based on real data which investigate the use of
visual methods for summarizing quantitative information, basic experimental design, sampling methods, and interpretation of statistical analyzes. The course
will use calculators and statistical software, provide real world applications, and examine how statistical thinking develops in students. 3 credits.
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EDUCATION 502. Research Design. An examination of methodology in educational research with emphasis on the historical, descriptive, developmental
and experimental methods. Designed application and use by teachers, supervisors, administrators, counselors, and librarians. Required within the first nine
hours of the programs in which this course is a requirement. 3 credits