ARM 10.58.518. MATHEMATICS

(1) The program requires that successful candidates: (a) demonstrate knowledge and understanding of and apply the process of mathematical problem solving; (b) reason, construct, and evaluate mathematical arguments and develop an appreciation for mathematical rigor and inquiry; (c) communicate mathematical thinking orally and in writing to peers, faculty, and others; (d) recognize, use, and make connections between and among mathematical ideas and in contexts outside mathematics to build mathematical understanding; (e) use varied representations of mathematical ideas to support and deepen students' mathematical understanding; (f) appropriately use current and emerging technologies as essential tools for teaching and learning mathematics; and (g) support a positive disposition toward mathematical processes and mathematical learning; (2) demonstrate knowledge of how students learn mathematics and of the pedagogical knowledge specific to mathematics teaching and learning; (3) demonstrate content knowledge in: (a) numbers and operations by demonstrating computational proficiency, including a conceptual understanding of numbers, ways of representing number relations among number and number systems, and meanings of operations; (b) different perspectives on algebra including ways of representing mathematical relationships and algebraic structures; (c) geometries by using spatial visualization and geometric modeling to explore and analyze geometric shapes, structures, and their properties; (d) calculus by demonstrating a conceptual understanding of limit, continuity, differentiation, and integration and a thorough background in the techniques and application of the calculus; (e) discrete mathematics by applying the fundamental ideas of discrete mathematics in the formulation and solution of problems; (f) data analysis, statistics, and probability by demonstrating an understanding of concepts and practices related to data analysis, statistics, and probability; and (g) measurement by applying and using measurement concepts and tools.