The Learner and Learning -
Teacher candidates design and implement developmentally appropriate learning experiences and inclusive learning environments that enable each learner to meet high standards, are based on how students grow and develop, and recognize that patterns of learning and development vary individually within and across cognitive, linguistic, social, emotional, and physical areas. (InTASC 1, 2, 3)

• Create developmentally appropriate instruction that takes into account individual learners’ strengths, interests, and needs and that enables each learner to advance and accelerate their learning.
• Design instruction to address each student’s diverse learning strengths and needs and create opportunities for students to demonstrate their learning in different ways.
• Bring multiple perspectives to the discussion of content, including attention to learners' personal, family, and community experiences and cultural norms.
• Collaborate with learners, families/guardians, and colleagues to build a safe, positive learning climate of openness, mutual respect, support, and inquiry.
• Manage the learning environment to actively and equitably engage learners by organizing, allocating, and coordinating the resources of time, space, technology, and learners’ attention.

Application of Content -
Candidates apply the central concepts, tools of inquiry, and structures of the disciplines he/she teaches to engage students in critical thinking, creativity and collaborative problem-solving, making the content accessible and meaningful to assure mastery. (InTASC 4, 5)

• Apply content knowledge by engaging learners in diverse perspectives that question and challenge assumptions and approaches in order to master content and foster metacognition, innovation, and problem solving.
• Evaluate and modify instructional resources and curriculum materials for their comprehensiveness, accuracy for representing particular concepts in the discipline, and appropriateness for their learners.
• Create opportunities for students to learn, practice, and master academic language in their content.
• Facilitate learners’ collaborative use of current technology, tools, and resources to maximize content learning in varied contexts and support learner’s growth in international and global perspectives.
• Develop and implement supports for learner literacy development across content areas.

Instructional Practice -
Candidates plan and implement instruction using a variety of instructional strategies and multiple methods of assessments that support every student in meeting rigorous learning goals by drawing upon knowledge of content areas, cross-disciplinary skills, and pedagogy, as well as knowledge of learners and the community context. (InTASC 6, 7, 8)

• Select and adapt formative and summative assessments that minimizes sources of bias to support, verify, and document learning.
• Plan for instruction based on formative and summative assessment data, prior learner knowledge, and learner interest.
• Analyze assessment data to effectively provide feedback and inform future instructional practices.
• Select and create learning experiences and assessments that are appropriate for curriculum goals and content standards, aligned to learning objectives, and are relevant to learners.
• Select appropriate strategies, develop appropriate sequencing, and provide multiple ways to demonstrate knowledge and skill.
• Plan collaboratively with colleagues and other professionals who have specialized expertise to design and jointly deliver appropriate and effective learning experiences to meet unique learning needs.
• Guide learners in using a range of technology tools to access, interpret, evaluate, and apply information in content area learning and application.

Professional Responsibility -
Candidates engage in ongoing professional learning and use evidence to continually evaluate and improve their practice, as well as seek appropriate leadership roles and opportunities to take responsibility for student learning, to collaborate with learners, families, colleagues, other school professionals, and community members to ensure learner growth, and to advance the profession. (InTASC 9, 10)

• Engage in ongoing learning opportunities to develop knowledge and skills in order to provide all learners with engaging curriculum and learning experiences within the context of local and state standards.
• Reflect on personal biases and access resources to deepen understanding of cultural, ethnic, gender, and learning differences to promote ethical practice, build stronger relationships and create more relevant learning experiences.
• Work collaboratively with peers and school colleagues to build ongoing connections with digital and community resources to enhance student learning and well-being.
• Engage in leadership roles to advocate for meeting the needs of learners, strengthening the learning environment, and enacting system change.
• Uphold the expectations of the profession including codes of ethics, professional standards of practice, learner dispositions, and relevant law and policy.

Calculus -
Graduates of Grand Canyon University’s Bachelor of Science in Mathematics for Secondary Education program will use differential and integral calculus to solve problems in a variety of contexts. Students can connect visual, analytical, and data-driven descriptions of situations and use appropriate techniques to analyze and solve problems.

• Students can calculate limits, derivatives, definite integrals and indefinite integrals and determine points of continuity and discontinuity. (NCTMC A.5.1)
• Students can apply the Fundamental Theorem of Calculus to evaluate definite integrals. (NCTMC A.5.)
• Students can determine convergence of sequences and series and build power series for common functions. (NCTMC A.5.3)
• Students apply calculus concepts to functions of parametric, polar and vector functions of a single variable. (NCTMC A.5.2)
• Students graph and analyze multivariate functions. (NCTMC A.5.4)
• Students use calculus concepts to solve applied problems from a variety of fields. (NCTMC A.5.6)

Probability and Statistics -
Graduates of Grand Canyon University Bachelor of Science in Mathematics for Secondary Education program will apply ideas of probability to discrete and continuous processes involving random events. Students will understand distributions, estimation, sufficiency, and hypothesis testing.

• Students will examine the sources of statistical variability and the role randomness in statistical inference. (NCTMC A.4.1)
• Students will be able to select the appropriate probability distribution for a variety of data sets and estimate the parameters. (NCTMC A. 4. 2, A.4.3)
• Students will be able to develop and perform the most appropriate test of hypothesis using a variety of experimental designs. (NCTMC A.4.2, A. 4. 5.)
• Students will be able to construct a sufficient statistical representation of a variety of data sets. (NCTMC A.4.3)
• Students will be able to distinguish between empirical and theoretical probability and the impact on calculations of probability. (NCTMC A.4.4)

Number and Quantity -
Graduates of Grand Canyon University’s Bachelor of Science in Mathematics for Secondary Education program will develop an understanding of the structure of the Integers, Rational, Real and Complex number systems, and use appropriate technology and varied representational tools to answer questions about number and quantity.

• Use standard and non-standard algorithms of numbers. (NCTMC A.1.1)
• Apply the fundamental ideas of number theory – divisors, factorization, prime and composite numbers, GCF, LCM and modular arithmetic. (NCTMC A.1.2)
• Use reasoning to solve problems involving ration, rate, and proportion and be able to translate these to real-life problems with appropriate units. (NCTMC A1.3; NCTMS 2a, 2e)

Algebra -
Graduates of Grand Canyon University’s Bachelor of Science in Mathematics for Secondary Education program are fluent in pre-calculus algebra and linear algebra and can use multiple representations and appropriate technology to solve problems. They are familiar with the theory of algebra – groups, rings, and fields – and can apply those concepts to number systems.

• Use correct algebraic notation and symbols to manipulate expressions, solve equations and inequalities, and use their results to model, and justify processes. (NCTMC A.2.1; NCTMS 2b)
• Recognize polynomial, exponential, and logarithmic; absolute value; rational and trigonometric function classes; and understand the use of parameters to model situations with these function classes. (NCTMC A.2.2; NCTMS 2f)
• Use multiple representations of functions to describe, reason, interpret, and analyze relationships and build new functions. (NCTMC A.2.3)
• Model real life phenomena with linear, quadratic, polynomial, and exponential functions. (NCTMC A.2.4; NCTMS 2c)
• Solve problems involving groups, rings and fields, and apply those results to number systems and transformations of the plane. (NCTMC A.2.6, A.3.2)
• Use linear algebra - vector and matrix operations, and transformations - to model real life situations. ((NCTMC A.2.5, A.1.4)

Geometry and Trigonometry -
Graduates of Grand Canyon University’s Bachelor of Science in Mathematics for Secondary Education program use multiple representations to answer questions of geometry and trigonometry. Students are familiar with the axiomatic method and can prove theorems and provide counterexamples.

• Demonstrate understanding of two and three-dimensional objects as well as answer questions about, construct with compass and straightedge or technology, and explain the derivation of formulas related to these objects. (NCTMS 4e; A.3.6, A.3.7, A.8)
• Use the core concepts of Euclidean and non-Euclidean geometry and can use the axiomatic method to prove theorems in these systems. (NCTMC A.3.1, A.3.8; NCTMS 2b)
• Demonstrate understanding of similarity and scaling, including right triangle trigonometry, and can relate this knowledge to transformations of the plane. (NCTMC A.3.3, A.3.4, A.3.2)
• Apply trigonometry, including identities, to periodic phenomena. (NCTMC A.3.5)
• Use analytic geometry to solve problems and prove theorems about geometric objects. (NCTMC A.3.9; NCTMS 2b)
• Express Geometric Properties of conic sections with equations. (NCTMC A.3.9; NCTMS 2b)

Discrete Mathematics and Number Theory -
Graduates of Grand Canyon University’s Bachelor of Science in Mathematics for Secondary Education program use appropriate technology and multiple representations to answer questions of discrete mathematics.

• Use sets, relations, and functions to answer questions. (NCTMC A.6.1)
• Solve counting problems. (NCTMC A.6.2)
• Use graphs to answer real-life questions and basic topology questions. (NCTMC A.6.1)
• Use recursion and finite differences to answer questions. (NCTMC A.6.2)
• Use propositional and predicate logic to prove facts and provide counterexamples. (NCTMC A.6.3)
• Apply discrete mathematics to a variety of real-life situations including modeling and linear programming. (NCTMC A.6.4)

Historical and Cultural -
Graduates of Grand Canyon University’s Bachelor of Science in Mathematics for Secondary Education program develop an understanding of the history of the various branches of mathematics including the impact of significant figures in the individual fields and cultural diversity on findings. Students will also examine the interrelated nature of all branches of mathematics.

• Examine the concepts of numbers, quantity, and number systems both in the present and past. (NCTMC A.1.5)
• Examine the significant findings in the field of algebra and the cultures and individuals surrounding the findings. (NCTMC A.2.7)
• Examine the historical significance of the fields of geometry and trigonometry including the culture and individuals surrounding significant findings. (NCTMC A.3.10)
• Examine how and why statistics and probability came into being as a mathematical field of study including how diverse cultures and influential individuals shaped the field. (NCTMC A.4.6)
• Examine the historical progression of calculus including the impact of diverse cultures and the individuals influential in shaping the field. (NCTMC A.5.6)
• Examine the history of discrete mathematics including the contributions of significant individuals and diverse cultures. (NCTMC A.6.5)