High School Certification Standards

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

          (a)  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.

(b)  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:

a.  Takes into consideration gender, socioeconomic status, culture, and ethnicity;

b.  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;

c.  Builds upon the varied prior experiences and knowledge which all students bring to the classroom; and

d.  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:

a.  Enable students to construct new concepts through active participation in mathematical investigations;

b.  Proceed from concrete representations to symbolic representations in ways that make sense for each learner;

c.  Provide multiple representations of concepts being learned, alternate explanations, and intuitive as well as formal arguments;

d.  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;

e.  Model and nurture within the context of mathematics important habits of mind including curiosity, perseverance, risk taking, making conjectures, and logical reasoning;

f.  Emphasize connections between mathematics and student's interests and experiences, within mathematics, and between mathematics and other disciplines;

g.  Include interest building mathematical games, puzzles, and logic problems;

h.  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

i.  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:

(i)  Symbolic manipulators;

(ii)  Dynamic geometry programs;

(iii)  Spreadsheets; and

(iv)  Statistical packages;

(3)  In the area of knowledge of professional practices, the candidate shall have the ability to:

a.  Demonstrate the capacity to learn mathematics independently;

b.  Demonstrate the capacity to construct proofs and logical arguments using an axiomatic approach to verify hypotheses in mathematics;

c.  Demonstrate the capacity to communicate about mathematics and mathematics education in both written and oral ways that includes informal and professional formats;

d.  Articulate how the use of formal language and notation increases in importance as mathematical concepts are developed in the K-12 mathematics curriculum;

e.  Demonstrate the capacity to solve non-standard, real-world problems;

f.  Provide current examples of mathematical practices and notation within various cultures;

g.  Trace the historical development of mathematics topics including contributions by major world cultures;

h.  Provide examples of how mathematics is practiced in various fields, such as engineering, nursing, carpentry, and the arts;

i.  Demonstrate knowledge of state, regional, national and international professional associations and journals, and how to access resources on the Internet;

j.  Demonstrate knowledge of the history of mathematics education;

k.  Demonstrate knowledge of current state, national, and international findings and recommendations regarding the teaching and learning of mathematics; and

l.  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:

a.  Demonstrate an understanding of the axiomatic development of the real and complex number systems;

b.  Demonstrate a capacity to use models to explore and explain relationships among fractions, decimals, percents, ratios, and proportions;

c.  Use estimation strategies and mental computation techniques to judge the reasonableness of answers and to approximate solutions;

d.  Use physical materials and models to explore and explain operations and properties of real numbers and their subsets; and

e.  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:

a.  Employ common geometric ideas such as the Pythagorean theorem, similar triangles, and trigonometry to solve problems involving direct and indirect measurement;

b.  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;

c.  Demonstrate knowledge of the axiomatic development of Euclidean geometry, non-Euclidean geometry, and transformational geometry;

d.  Solve problems and construct proofs in 2-dimensional geometry and 3-dimensional geometry that involve parallelism, perpendicularity, congruence, similarity, and symmetry; and

e.  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:

a.  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;

b.  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

c.  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:

a.  Demonstrate an understanding of basic concepts of probability and statistics, including discrete and continuous probability distributions, descriptive and inferential statistics, and exploratory data analysis;

b.  Design an experiment, collect appropriate data, analyze the data, and construct a valid statistical argument comparing the experimental and theoretical probabilities; and

c.  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:

a.  Demonstrate an understanding of both single and multi-variable calculus relating to limits, differentiation, integration, and infinite series; and

b.  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:

a.  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

b.  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)