Ed 612.17 Mathematics for Grades 5-8.

- The teacher preparation program in mathematics for grades 5-8 shall be consistent with RSA 193-C:3, III and IV(f), including techniques for enhancing student learning in these areas and the use of assessment results to improve instruction.
- The mathematics program for grades 5-8 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) units;
- 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 a capacity to use models to explore and explain relationships among fractions, decimals, percents, ratios, and proportions;
- Apply, explain, and justify concepts in number, number theory, and number systems;
- 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;
- Demonstrate knowledge of the concepts of limits and infinity;
- Identify and illustrate properties of number systems from natural to complex and describe the relationships among them; 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;
- Connect the ideas of algebra and geometry through the use of coordinate geometry, graphing, vectors, and motion geometry;
- Use a variety of tools, physical models, and dynamic geometric software to explore geometric relationships;
- Demonstrate knowledge of the role of a parallel postulate in the development of a non-Euclidean geometry, such as spherical geometry;
- Solve simple problems of 2-dimensional geometry and 3-dimensional geometry that involve parallelism, perpendicularity, congruence, similarity, and symmetry;
- Demonstrate relational understanding of important geometric concepts associated with visualization, description, and classification of geometric figures;
- Construct proofs and write logical arguments; and
- Solve problems involving linear, area, volume, mass, and temperature measures within the metric system and the English system of measurement;

- In the subject area of algebra, the candidate shall have the ability to:
- Use algebraic reasoning, notation, and common algorithms to solve problems and communicate those ideas using proper terminology;
- Demonstrate an understanding of:
- Common sequences including, but not limited to, arithmetic, geometric, and Fibonacci, defined as the sequence of numbers, 1,2,3,5,8,13,…, in which each successive number is equal to the sum of the two preceding numbers; and
- Functional relationships including, but not limited to, exponential, polynomial, periodic, step, absolute value, root;

- Articulate the meaning of functions and their inverse relationships, both formally and informally, with the use of concrete materials and graphing utilities;
- Represent functions and solve problems verbally and by using symbols, tables, graphs, and demonstrate the capacity to move from one representation to another;
- Demonstrate an understanding of the underlying algebraic structures of the real number system; and
- Represent information and solve problems using matrices;

- In the subject area of probability and statistics, the candidate shall have the ability to:
- Collect data from real world experiences or surveys;
- Organize and display the data using various methods including, but not limited to:
- Charts;
- Graphs;
- Tables;
- Venn diagrams;
- Box-and-whisker plots;
- Stem-and-leaf plots; and
- Scatter plots;

- Use both descriptive and inferential statistics to analyze data, make predictions, test hypotheses, and make decisions;
- Judge the validity of a statistical argument;
- Find and interpret measures of:
- Central tendency including mean, median, and mode;
- Measures of dispersion including, but not limited to, standard deviation, range, and interquartile range; and
- Curves of best fit;

- Determine and compare experimental, theoretical, and conditional probabilities;
- Compute the mathematical expectation of simple games and lotteries; and
- Use combinations and permutations to solve probability problems;

- In the subject area of calculus, the candidate shall have the ability to:
- Use graphs, diagrams, charts, physical models, and graphing technology to explore the notions of change, limit, differentiation, and integration, and to interpret the relationships among them;
- Relate infinite sequences and series to topics such as non-terminating decimals and area; and
- Apply models of change and rates of change to problems within mathematics including but not limited to area, volume, and curve length and other disciplines such as physics, biology, and economics; and

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

- 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; ss by #4851, eff 6-25-90; ss by #5155, eff 5-13-91; ss by #6366, eff 10-30-96, EXPIRED: 10-30-04

New. #8229, eff 12-17-04; (See Revision Note at part heading for Ed 612) (renumbered from Ed 612.10)