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Class Descriptions

Linear Algebra for Teachers - VCU Math 591 (Special Topics Course); transfers for RU Math 623.
Students use matrices and determinants to solve systems of linear equations.  Applications of matrices and matrix inverses are used in solving real world problems, and graphing calculators are used extensively in solving large scale problems using matrix techniques.

Course Topics Related Standards Career Readiness Expectations
Linear Equations and Matrices A.4(e), MA.14, AII.7(g), AII.7,(h) 16(i), 16 (j)
Applications of Linear Equations MA.14, A.4(e), AII.7(g), AII.7,(h) 16(i), 16 (j)
Determinants MA.2, AII.7(g) 16(i), 16 (j)
Vectors in AFDA.2 15
Real Vector Spaces A.4(e), MA.2 16(i)
Eigenvectors and Eigenvalues MA.4 16(j)
Linear Transformations and Matrices AFDA.2, AII.7(g), MA.2, AII.7, (h) 3(d), 15

Algebraic Structures, Functions, and Sequences for Teachers (VCU Math 591; transfers for RU Math 630.
This course will explore a variety of algebra-related topics including modular arithmetic; characteristics of polynomial, exponential, logarithmic, and trigonometric functions; and algebraic structures including semigroups, groups, rings, integral domains, and fields.

Course Topics Related Standards
Modular Arithmetic and Systems of Numbers: Divisibility, Euclid’s Algorithm, Linear Congruence, Integers mod m A.7, A.8, AII.7, AFDA.1
Function characteristics: Polynomials, Exponential functions, Logarithmic functions, Trigonometric functions AII.6, AII.7, AII.8, AII.9, A.7, AFDA.1, AFDA.3, AFDA.4
Sequences and Series: Algebraic, Geometric, Fibonacci AII.2, MA.5, MA.6
Algebraic Structures: Binary Operations, Semigroups & Groups, Subgroups, Cyclic Subgroups & Permutation Groups, Isomorphisms & Homomorphisms, Rings, Integral Domains, Fields A.2, A.3, A.4, A11.1, AII.5

Foundations of the Number System; transfers for RU Math 600.
This course provides a mathematical foundation for the number systems used in secondary and post-secondary mathematics courses, with an emphasis on rigorous logical and set-theoretical foundations of the natural numbers, integers, rational numbers, and real numbers. The course also covers the common algebraic extensions of the number system and familiarizes students with the historical development of the number system.

Course Topics Related Standards
Set Theory A.4(b), A.5 (a)(c)(d), A.7 (b)(c), AII.2, AII.4(a)
Relations and Functions A.7(a)(b)(e), A.8, AII.7(a)(g)(h), AFDA.1(c)
Real Number System A.1, A.2(a), A.5(b)(c)(d), AII.1(a)(b), AII.2
Complex Number System A.5(b), AII.3
Group, Ring and Field Theory A.2(b)(c), A.3, A.4(a)(b)(c), AII.1(a)(b)(c)(d), AII.5

Equity and Diversity in Mathematics Education; transfer for RU Math/EDUC 620.
This course emphasizes the NCTM’s (2000) Equity Principle of providing high expectations and strong support for all students and familiarizes students with cultural, social, and political issues in the teaching and learning of mathematics. Students explore equity and diversity topics and approaches in mathematics education, including strategies for teaching mathematics to diverse learners. This includes diversity with respect to social class, gender, race/ethnicity, students with disabilities, and ELL. Mathematics pedagogy and assessment strategies will be included and participating teachers will generate applied mathematical unit plans related to Mathematics Performance Expectations for the Capstone Course, with attention to meeting the needs of diverse learners.

Euclidan and Non-Euclidean Geometry; transfers for RU Math 635.
This course addresses a range of Euclidean and Non-Euclidean geometries, as summarized in the table below:

Course Topics Related Standards
Euclidean and Non-Euclidean geometries, systems of postulates in a comparison of Euclidean and Non-Euclidean geometries. Axiomatic systems and their role in problem-solving in mathematics development of Geometry as an axiomatic system G1; G6; G7;
Role of geometry in understanding the world and of how this understanding can be developed in their own classrooms G2; G5; G8; G9; G10
Conceptions of geometry beyond plane figures and their properties G13; G14
Development of geometric topics addressed in high school and discussion of current SOLs and Career Readiness Expectations G1; G2; G3; G4; G5; G6; G7; G8; G9; G10; G11; G12
Other topics may include: structures of transformational, fractal, projective geometry with a brief history of the development of axiomatic systems of geometry, trigonometry. G3; G4; G11; G12

Applied Statistics for Teachers (VCU Stat 591; transfers for RU STAT 644.
This course explores ways to collect, organize, display, and analyze data and make reasoned decisions based on it.  Students use statistical methods based on data, develop and evaluate inferences and predictions about data, and apply probability and distribution theory concepts.  The course helps prepare teachers to teach statistical concepts and AP statistics and to critically examine and comprehend data analysis in education literature.  Graphing calculators and computer software are incorporated.

Course Topics Related Standards
Probability laws and counting techniques AII.12, PS.11, PS.12
Probability distributions for discrete and continuous random variables PS.13, PS.14
Sampling techniques and experimental designs AII.11, PS.8, PS.10, AFDA.3, AFDA.7, AFDA.8
Analysis of categorical data, review of descriptive statistics A.9, A.10, PS.1, PS.2, SP.3, PS.4, PS.7
Statistical inference, evaluating experimental and descriptive research studies, two-sample t-tests for independent and dependent samples, correlation analysis A.11, PS.5, PS.16, PS.17, PS.18, PS.19, PS.20

Educational Technology (EDET 620).
This course emphasizes educational technologies appropriate for use in Algebra I, Algebra II, AFDA, Geometry, and the Mathematics Capstone Course. The course strengthens teachers' understandings of algebra, data analysis, and geometry by integrating instructional technologies in these areas. Content is aligned with Virginia SOLs and national standards for technology and for Algebra I, Algebra II, AFDA, and NCTM Communication Standard for grades 9-12. The course emphasizes research, practice, and policy involving current technologies in education and uses mathematics software such as Fathom, GeoGebra, and Mathematica. Students learn mathematics applications of word processors, databases, spreadsheets, fundamentals of Internet tools, and rudimentary hypermedia tools to create multimedia projects. They discuss what it means to be a responsible and effective technology user in classrooms and how to appropriately assess student learning using technology. Students analyze and synthesize their learning through presentations, group work, reflection papers, computer projects and discussions.

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