High School Certification Standards

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

  1. 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.
  2. 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:
    1. In the area of pedagogy, the candidate shall have the ability to plan and conduct mathematics instruction which:
      1. Takes into consideration gender, socioeconomic status, culture, and ethnicity;
      2. Takes into consideration the following:
        1. Learning styles;
        2. Concrete and abstract thought processes;
        3. Deductive and inductive reasoning; and
        4. Auditory, visual, tactile, and kinesthetic modalities;
      3. Builds upon the varied prior experiences and knowledge which all students bring to the classroom; and
      4. Meets the needs of students with differing talents, interests, and development;
    2. In the area of instructional strategies, the candidate shall have the ability to plan and conduct units and lessons which:
      1. Enable students to construct new concepts through active participation in mathematical investigations;
      2. Proceed from concrete representations to symbolic representations in ways that make sense for each learner;
      3. Provide multiple representations of concepts being learned, alternate explanations, and intuitive as well as formal arguments;
      4. 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;
      5. Model and nurture within the context of mathematics important habits of mind including curiosity, perseverance, risk taking, making conjectures, and logical reasoning;
      6. Emphasize connections between mathematics and student’s interests and experiences, within mathematics, and between mathematics and other disciplines;
      7. Include interest building mathematical games, puzzles, and logic problems;
      8. 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
      9. Use technology appropriately and effectively in the learning and teaching of mathematics, including, but not limited to:
        1. Scientific and graphing calculators;
        2. Computer-based laboratory (CBL);
        3. The internet; and
        4. Computer software including the 4 areas of:
          1. Symbolic manipulators;
          2. Dynamic geometry programs;
          3. Spreadsheets; and
          4. Statistical packages;
    3. In the area of knowledge of professional practices, the candidate shall have the ability to:
      1. Demonstrate the capacity to learn mathematics independently;
      2. Demonstrate the capacity to construct proofs and logical arguments using an axiomatic approach to verify hypotheses in mathematics;
      3. Demonstrate the capacity to communicate about mathematics and mathematics education in both written and oral ways that includes informal and professional formats;
      4. Articulate how the use of formal language and notation increases in importance as mathematical concepts are developed in the K-12 mathematics curriculum;
      5. Demonstrate the capacity to solve non-standard, real-world problems;
      6. Provide current examples of mathematical practices and notation within various cultures;
      7. Trace the historical development of mathematics topics including contributions by major world cultures;
      8. Provide examples of how mathematics is practiced in various fields, such as engineering, nursing, carpentry, and the arts;
      9. Demonstrate knowledge of state, regional, national and international professional associations and journals, and how to access resources on the Internet;
      10. Demonstrate knowledge of the history of mathematics education;
      11. Demonstrate knowledge of current state, national, and international findings and recommendations regarding the teaching and learning of mathematics; and
      12. Articulate the power of mathematics as an academic discipline, a tool for quantitative reasoning, and a gateway to many career choices;
    4. In the subject area of number and numeration, the candidate shall have the ability to:
      1. Demonstrate an understanding of the axiomatic development of the real and complex number systems;
      2. Demonstrate a capacity to use models to explore and explain relationships among fractions, decimals, percents, ratios, and proportions;
      3. Use estimation strategies and mental computation techniques to judge the reasonableness of answers and to approximate solutions;
      4. Use physical materials and models to explore and explain operations and properties of real numbers and their subsets; and
      5. Demonstrate a capacity to apply the concepts of proportional reasoning;
    5. In the subject area of geometry and measurement, the candidate shall have the ability to:
      1. Employ common geometric ideas such as the Pythagorean theorem, similar triangles, and trigonometry to solve problems involving direct and indirect measurement;
      2. Use the following to explore geometric constructions and relationships:
        1. A variety of tools such as compass and straightedge;
        2. Physical models; and
        3. Dynamic geometric software;
      3. Demonstrate knowledge of the axiomatic development of Euclidean geometry, non-Euclidean geometry, and transformational geometry;
      4. Solve problems and construct proofs in 2-dimensional geometry and 3-dimensional geometry that involve parallelism, perpendicularity, congruence, similarity, and symmetry; and
      5. Demonstrate relational understanding of important geometric concepts associated with visualization, description, measurement, and classification of geometric figures;
    6. In the subject area of algebra, the candidate shall have the ability to:
      1. 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;
      2. Articulate the meaning of functions both formally and informally including, but not limited to:
        1. Exponential, polynomial, periodic, step, absolute value, root, and trigonometric; and
        2. Relations such as equivalence; and
      3. Understand and apply the major concepts of linear and abstract algebra and connect these concepts to secondary mathematics;
    7. In the subject area of probability and statistics, the candidate shall have the ability to:
      1. Demonstrate an understanding of basic concepts of probability and statistics, including discrete and continuous probability distributions, descriptive and inferential statistics, and exploratory data analysis;
      2. Design an experiment, collect appropriate data, analyze the data, and construct a valid statistical argument comparing the experimental and theoretical probabilities; and
      3. Explore the connections between statistics and probability by:
        1. Making use of various concepts that include hypothesis testing, correlation, regression, and analysis of variance; and
        2. Applying these concepts to everyday situations, such as games and lotteries;
    8. In the subject area of calculus, the candidate shall have the ability to:
      1. Demonstrate an understanding of both single and multi-variable calculus relating to limits, differentiation, integration, and infinite series; and
      2. 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;
    9. In the subject area of discrete mathematics, the candidate shall have the ability to:
      1. Demonstrate a knowledge of:
        1. Counting techniques;
        2. Sets;
        3. Logic and reasoning;
        4. Patterning including iteration and recursion;
        5. Algorithms and induction;
        6. Networks;
        7. Graph theory;
        8. Social decision-making;
        9. Efficiency; and
        10. Binomial series; and
      2. Demonstrate the capacity to use combinations and permutations to solve probability problems.

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)