(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.