Ed 612.18 Secondary Mathematics For Grades 7-12. The following requirements shall apply:

- In compliance with RSA 193-C:3,IV,(f), the teacher preparation program in secondary mathematics for grades 7-12 shall demonstrate competence in the NH “K-12 Mathematics Curriculum Framework,” including techniques for enhancing student learning in these areas and the use of assessment results to improve instruction.
- The mathematics program for grades 7-12 shall provide the teaching candidate with the skills, competencies and knowledge gained through a combination of academic and supervised practical experience in the following areas:
- In the area of pedagogy, the candidate shall have the ability to plan and conduct mathematics instruction which:
- Takes into consideration gender, socioeconomic status, culture, and ethnicity;
- Takes into consideration the following:
- Learning styles;
- Concrete and abstract thought processes;
- Deductive and inductive reasoning; and
- Auditory, visual, tactile, and kinesthetic modalities;

- Builds upon the varied prior experiences and knowledge which all students bring to the classroom; and
- Meets the needs of students with differing talents, interests, and development;

- In the area of instructional strategies, the candidate shall have the ability to plan and conduct units and lessons which:
- Enable students to construct new concepts through active participation in mathematical investigations;
- Proceed from concrete representations to symbolic representations in ways that make sense for each learner;
- Provide multiple representations of concepts being learned, alternate explanations, and intuitive as well as formal arguments;
- Provide opportunities for students to demonstrate their understanding of mathematical concepts in writing, and orally with both other learners and the teacher, and through various means of creative expression;
- Model and nurture within the context of mathematics important habits of mind including curiosity, perseverance, risk taking, making conjectures, and logical reasoning;
- Emphasize connections between mathematics and student’s interests and experiences, within mathematics, and between mathematics and other disciplines;
- Include interest building mathematical games, puzzles, and logic problems;
- Assess student achievement using methods that include but that are not limited to portfolios, math journals, technology, rubrics, paper and pencil tasks, presentations, projects, and teacher observations; and
- Use technology appropriately and effectively in the learning and teaching of mathematics, including, but not limited to:
- Scientific and graphing calculators;
- Computer-based laboratory (CBL);
- The internet; and
- Computer software including the 4 areas of:
- Symbolic manipulators;
- Dynamic geometry programs;
- Spreadsheets; and
- Statistical packages;

- In the area of knowledge of professional practices, the candidate shall have the ability to:
- Demonstrate the capacity to learn mathematics independently;
- Demonstrate the capacity to construct proofs and logical arguments using an axiomatic approach to verify hypotheses in mathematics;
- Demonstrate the capacity to communicate about mathematics and mathematics education in both written and oral ways that includes informal and professional formats;
- Articulate how the use of formal language and notation increases in importance as mathematical concepts are developed in the K-12 mathematics curriculum;
- Demonstrate the capacity to solve non-standard, real-world problems;
- Provide current examples of mathematical practices and notation within various cultures;
- Trace the historical development of mathematics topics including contributions by major world cultures;
- Provide examples of how mathematics is practiced in various fields, such as engineering, nursing, carpentry, and the arts;
- Demonstrate knowledge of state, regional, national and international professional associations and journals, and how to access resources on the Internet;
- Demonstrate knowledge of the history of mathematics education;
- Demonstrate knowledge of current state, national, and international findings and recommendations regarding the teaching and learning of mathematics; and
- Articulate the power of mathematics as an academic discipline, a tool for quantitative reasoning, and a gateway to many career choices;

- In the subject area of number and numeration, the candidate shall have the ability to:
- Demonstrate an understanding of the axiomatic development of the real and complex number systems;
- Demonstrate a capacity to use models to explore and explain relationships among fractions, decimals, percents, ratios, and proportions;
- Use estimation strategies and mental computation techniques to judge the reasonableness of answers and to approximate solutions;
- Use physical materials and models to explore and explain operations and properties of real numbers and their subsets; and
- Demonstrate a capacity to apply the concepts of proportional reasoning;

- In the subject area of geometry and measurement, the candidate shall have the ability to:
- Employ common geometric ideas such as the Pythagorean theorem, similar triangles, and trigonometry to solve problems involving direct and indirect measurement;
- Use the following to explore geometric constructions and relationships:
- A variety of tools such as compass and straightedge;
- Physical models; and
- Dynamic geometric software;

- Demonstrate knowledge of the axiomatic development of Euclidean geometry, non-Euclidean geometry, and transformational geometry;
- Solve problems and construct proofs in 2-dimensional geometry and 3-dimensional geometry that involve parallelism, perpendicularity, congruence, similarity, and symmetry; and
- Demonstrate relational understanding of important geometric concepts associated with visualization, description, measurement, and classification of geometric figures;

- In the subject area of algebra, the candidate shall have the ability to:
- Use functions and algorithms from analytic geometry and trigonometry to solve problems and to demonstrate connections between various representations such as the connection between functional relationships expressed symbolically, in a table, and graphically;
- Articulate the meaning of functions both formally and informally including, but not limited to:
- Exponential, polynomial, periodic, step, absolute value, root, and trigonometric; and
- Relations such as equivalence; and

- Understand and apply the major concepts of linear and abstract algebra and connect these concepts to secondary mathematics;

- In the subject area of probability and statistics, the candidate shall have the ability to:
- Demonstrate an understanding of basic concepts of probability and statistics, including discrete and continuous probability distributions, descriptive and inferential statistics, and exploratory data analysis;
- Design an experiment, collect appropriate data, analyze the data, and construct a valid statistical argument comparing the experimental and theoretical probabilities; and
- Explore the connections between statistics and probability by:
- Making use of various concepts that include hypothesis testing, correlation, regression, and analysis of variance; and
- Applying these concepts to everyday situations, such as games and lotteries;

- In the subject area of calculus, the candidate shall have the ability to:
- Demonstrate an understanding of both single and multi-variable calculus relating to limits, differentiation, integration, and infinite series; and
- Apply models of change and rates of change to problems within mathematics such as area, volume, and curve length and other disciplines such as physics, biology, and economics;

- In the subject area of discrete mathematics, the candidate shall have the ability to:
- Demonstrate a knowledge of:
- Counting techniques;
- Sets;
- Logic and reasoning;
- Patterning including iteration and recursion;
- Algorithms and induction;
- Networks;
- Graph theory;
- Social decision-making;
- Efficiency; and
- Binomial series; and

- Demonstrate the capacity to use combinations and permutations to solve probability problems.

- Demonstrate a knowledge of:

- In the area of pedagogy, the candidate shall have the ability to plan and conduct mathematics instruction which:

Source. #2055, eff 6-16-82; ss by #2714, eff 5-16-84, EXPIRED 5-16-90

New. #4851, eff 6-25-90; EXPIRED 6-25-96

New. #6366, eff 10-30-96; ss by #7273, eff 7-1-00; (See Revision Note at part heading for Ed 612) (renumbered from Ed 612.11)