Secondary Education - Mathematics, Bachelor of Science in Education
Department of Mathematics and Statistics
College of Engineering, Forestry, and Natural Sciences
This degree prepares future middle and high school educators to teach their students both the utility and potential of mathematics in our information-driven society. The plan includes content-rich coursework as well as significant preparation in teaching through the highly acclaimed NAUTeach science and mathematics teacher certification programs, using best practices and applied theory.
This program is nationally recognized by the National Council of Teachers of Mathematics.
This program is accredited by the National Council for Accreditation of Teacher Education (NCATE).
To receive a bachelor's degree at Northern Arizona University, you must complete at least 120 units of credit that minimally includes a major, the liberal studies requirements, and university requirements as listed below.
- All of Northern Arizona University's diversity, liberal studies, junior-level writing, and capstone requirements.
- All requirements for your specific academic plan(s).
- At least 30 units of upper-division courses, which may include transfer work.
- At least 30 units of coursework taken through Northern Arizona University, of which at least 18 must be upper-division courses (300-level or above). This requirement is not met by credit-by-exam, retro-credits, transfer coursework, etc.
- A cumulative grade point average of at least 2.0 on all work attempted at Northern Arizona University.
The full policy can be viewed here.
In addition to University Requirements:
- At least 78 units of major requirements which includes at least 31 units of Mathematics and Science Teaching requirements
- Up to 9 units of major prefix courses may be used to satisfy Liberal Studies requirements; these same courses may also be used to satisfy major requirements.
- For this major the liberal studies prefixes are MAT and STA
- Please note that the usual 35 units for liberal studies are reduced to 32 units for mathematics majors, who are exempted from the 3-unit mathematics foundation requirement
- Elective courses, if needed, to reach an overall total of at least 120 units.
Candidates in this program are required to demonstrate content knowledge, pedagogical knowledge and skills, professional knowledge, and professional dispositions to be eligible to enter student teaching or internship placements.
Content, pedagogical, and professional knowledge or skills, professional dispositions are demonstrated through candidate performance on key assessments embedded in the following course(s):
Students may be able to use some courses to meet more than one requirement. Contact your advisor for details.
|Minimum Units for Completion||120|
|Highest Mathematics Required||MAT 442|
|Additional Admission Requirements||Required|
|Student Teaching/Supervised Teaching||Required|
|University Honors Program||Optional|
|Progression Plan Link||Not Available|
Student Learning Outcomes
Secondary Education in Mathematics
Outcomes align with Standards from the Council for the Accreditation of Educator Preparation, the National Mathematics Teachers Association, and the Interstate New Teacher Assessment and Support Consortium
- Design instruction that develops all students’ abilities to meet academic standards
- Reflect on teaching practices including the creation of a classroom environment based on respect and rapport that fosters a positive climate for learning, equity, and excellence.
- Create and maintain a learning climate that supports the development of all students’ abilities to meet academic standards.
- Implement and manage instruction that develops all students’ abilities to meet academic standards.
- Assess learning and communicate results to all students, parents and other appropriate professionals with respect to all students’ abilities to meet academic standards.
- Collaborate with colleagues, parents the community and other appropriate agencies to design, implement, and support learning that supports all students’ abilities to meet academic standards.
- Review and evaluate personal performance in order to improve teaching practices through reflection.
- Develop and nurture current professional knowledge of the teaching/learning process.
- Provide evidence of student learning through the design and implementation of instruction that makes use of effective communication techniques, is based on student prior knowledge, actively engages students in the learning process, and provides timely high-quality feedback.
- Reflect on the roles and responsibilities and adhere to legal and ethical requirements of the profession.
- In collaboration with other professionals, participate in the design, implementation, and assessment of individual education programs.
- Provide evidence of meeting the Arizona Professional Teaching Standards by taking the AEPA Secondary Professional Knowledge exam.
- Number and Quantity: To be prepared to develop student mathematical proficiency, all secondary mathematics teachers should know the following topics related to number and quantity with their content understanding and mathematical practices supported by appropriate technology and varied representational tools, including concrete models:
- Structure, properties, relationships, operations, and representations including standard and non-standard algorithms, of numbers and number systems including integer, rational, irrational, real, and complex numbers
- Fundamental ideas of number theory (divisors, factors and factorization, primes, composite numbers, greatest common factor, least common multiple, and modular arithmetic)
- Quantitative reasoning and relationships that include ratio, rate, and proportion and the use of units in problem situations
- Vector and matrix operations, modeling, and applications
- Historical development and perspectives of number, number systems, and quantity including contributions of significant figures and diverse cultures
- Algebra: To be prepared to develop student mathematical proficiency, all secondary mathematics teachers should know the following topics related to algebra with their content understanding and mathematical practices supported by appropriate technology and varied representational tools, including concrete models:
- Algebraic notation, symbols, expressions, equations, inequalities, and proportional relationships, and their use in describing, interpreting, modeling, generalizing, and justifying relationships and operations
- Function classes including polynomial, exponential and logarithmic, absolute value, rational, and trigonometric, including those with discrete domains (e.g., sequences), and how the choices of parameters determine particular cases and model specific situations
- Geometry and Trigonometry: To be prepared to develop student mathematical proficiency, all secondary mathematics teachers should know the following topics related to geometry and trigonometry with their content understanding and mathematical practices supported by appropriate technology and varied representational tools, including concrete models:
- Core concepts and principles of Euclidean geometry in two and three dimensions and two-dimensional non-Euclidean geometries
- Transformations including dilations, translations, rotations, reflections, glide reflections; compositions of transformations; and the expression of symmetry in terms of transformations
- Congruence, similarity and scaling, and their development and expression in terms of transformations
- Right triangles and trigonometry
- Application of periodic phenomena and trigonometric identities
- Identification, classification into categories, visualization, and representation of two- and three-dimensional objects (triangles, quadrilaterals, regular polygons, prisms, pyramids, cones, cylinders, and spheres)
- Formula rationale and derivation (perimeter, area, surface area, and volume) of two- and three-dimensional objects (triangles, quadrilaterals, regular polygons, rectangular prisms, pyramids, cones, cylinders, and spheres), with attention to units, unit comparison, and the iteration, additivity, and invariance related to measurements
- Geometric constructions, axiomatic reasoning, and proof
- Analytic and coordinate geometry including algebraic proofs (e.g., the Pythagorean Theorem and its converse) and equations of lines and planes, and expressing geometric properties of conic sections with equations
- Historical development and perspectives of geometry and trigonometry including contributions of significant figures and diverse cultures
- Statistics and Probability: To be prepared to develop student mathematical proficiency, all secondary mathematics teachers should know the following topics related to statistics and probability with their content understanding and mathematical practices supported by appropriate technology and varied representational tools, including concrete models:
- Statistical variability and its sources and the role of randomness in statistical inference
- Creation and implementation of surveys and investigations using sampling methods and statistical designs, statistical inference (estimation of population parameters and hypotheses testing), justification of conclusions, and generalization of results
- Univariate and bivariate data distributions for categorical data and for discrete and continuous random variables, including representations, construction and interpretation of graphical displays (e.g., box plots, histograms, cumulative frequency plots, scatter plots), summary measures, and comparisons of distributions
- Empirical and theoretical probability (discrete, continuous, and conditional) for both simple and compound events
- Random (chance) phenomena, simulations, and probability distributions and their application as models of real phenomena and to decision making
- Historical development and perspectives of statistics and probability including contributions of significant figures and diverse cultures
- Calculus: To be prepared to develop student mathematical proficiency, all secondary mathematics teachers should know the following topics related to calculus with their content understanding and mathematical practices supported by appropriate technology and varied representational tools, including concrete models:
- Limits, continuity, rates of change, the Fundamental Theorem of Calculus, and the meanings and techniques of differentiation and integration
- Parametric, polar, and vector functions
- Sequences and series
- Multivariate functions
- Applications of function, geometry, and trigonometry concepts to solve problems involving calculus
- Historical development and perspectives of calculus including contributions of significant figures and diverse cultures
- Discrete Mathematics: To be prepared to develop student mathematical proficiency, all secondary mathematics teachers should know the following topics related to discrete mathematics with their content understanding and mathematical practices supported by appropriate technology and varied representational tools, including concrete models:
- Discrete structures including sets, relations, functions, graphs, trees, and networks
- Enumeration including permutations, combinations, iteration, recursion, and finite differences
- Propositional and predicate logic
- Applications of discrete structures such as modeling and solving linear programming problems and designing data structures
- Historical development and perspectives of discrete mathematics including contributions of significant figures and diverse cultures
Additional Admission Requirements
Admission requirements over and above admisssion to NAU are required.
To be eligible for admission to the teacher education program, candidates must meet the following requirements and apply for the program online.
30 units of coursework which includes:
- TSM 101, TSM 102 and TSM 301W with grades of "C" or better
- Program Mathematics Foundations requirement with a grade of "C" or better
- The English foundations requirement (ENG 105 or equivalent) with a minimum GPA of 3.0. (If your English GPA is below 3.0, you may take an approved writing course to achieve the 3.0 GPA.)
- Completion of or enrollment in TSM 350
- A minimum GPA of 2.5 in all content major coursework (must have taken at least 12 units) AND one of the following grade point average requirements:
- A cumulative 2.5 GPA in Liberal Studies courses
- A cumulative 2.5 GPA in all courses
- You must be declared in this major
- Submission of a copy of your State-approved Identity-Verified Print (IVP) fingerprint clearance card, obtainable through the Arizona Department of Public Safety (602-223-2279)
Take the following 78 units. You must complete the next 47 units with a Grade of "C" or better:
- MAT 136, MAT 137, MAT 185, MAT 226, MAT 318, MAT 365, MAT 401, MAT 402, MAT 442, (STA 270 or STA 275) (32 units)
- CS 122, CS 122L (If you complete a minor or major in computer science, you may add 3 units to your general electives instead of taking this course.) (3 units)
- MAT 320W (3 units)
- MAT 411 or MAT 431 (3 units)
- Select additional units from MAT 220, MAT 238, MAT 239 and/or MAT and STA courses numbered 300 or above (6 units)
Mathematics and Science Teaching Courses (31 units)
- TSM 301W with a grade of "C" or better (3 units)
- BME 200 and BME 437 with grades of “C” or better (6 units)
- TSM 495C (12 units)
- TSM 496C with a grade of "C" or better (1 unit)
- TSM 350, TSM 404, TSM 450 (9 units)
In all of our teacher education programs, you are required to apply for, and complete a student teaching or internship experience. Applications are due one year prior to the student teaching semester. In addition, a minimum number of units of practicum is required, which involves supervised field experience with a practicing teacher.
Before being accepted to student teaching, the following criteria must be met:
- Admission to the teacher education program
- NAU GPA must be at least 2.5, with a GPA of 2.5 in all teacher preparation courses, with no grade lower than a "C"
- Complete all plan requirements.
- Take the appropriate AEPA or NES Subject Knowledge test.
- All major coursework, with the exception of TSM 101, must be completed within six years prior to student teaching.
- All candidates must demonstrate social and emotional maturity consistent with professional standards of classroom instruction as well as adequate physical health for teaching.
Arizona Teacher Certification
In order to obtain an Arizona teaching certificate you must pass both the appropriate Arizona Educator Proficiency Assessment or National Evaluation Series subject matter test and the National Evaluation Series Secondary Assessment Professional Knowledge.
Additional coursework is required if, after you have met the previously described requirements, you have not yet completed a total of 120 units of credit.
You may take these remaining courses from any of the academic areas, using these courses to pursue your specific interests and goals. You may also use prerequisites or transfer credits as electives if they weren't used to meet major, minor, or liberal studies requirements.
We encourage you to consult with your advisor to select the courses that will be most advantageous to you.
- Please note that you may take as an elective POS 220 (or POS 110 and POS 241), which satisfies the state and federal constitution requirement for Arizona certification, or you may meet the requirement by demonstrating proficiency on a special exam.
Be aware that some courses may have prerequisites that you must also successfully complete. For prerequisite information, click on the course or see your advisor.
This degree plan is supported through the NAUTeach program.