Administrative Rules of Montana › Department 10 - EDUCATION › Chapter 10.58 - PROFESSIONAL EDUCATOR PREPARATION PROGRAM STANDARDS › Subchapter 10.58.5 - Teaching Areas: Specific Standards › Rule 10.58.518 - MATHEMATICS

Current through Register Vol. 13, July 5, 2024
(1) The program
				requires that successful candidates:
(a)
				demonstrate knowledge and understanding of and apply the process of
				mathematical problem solving;
(b)
				reason mathematically in constructing, evaluating, and communicating
				mathematical arguments;
(c) promote
				mathematical rigor and inquiry;
(d)
				recognize, formulate, and apply connections between mathematical ideas and
				representations in a wide variety of contexts;
(e) demonstrate understanding of the
				mathematical modeling process by interpreting, analyzing, and explaining
				mathematical results and models in terms of their reasonableness and
				usefulness;
(f) recognize, use, and
				make connections between and among mathematical ideas and in contexts outside
				mathematics to build mathematical understanding including the ability to:
(i) attend to precision in mathematical
				language, notation, approximations, and measurements by consistently and
				appropriately applying mathematical definitions and procedures; and
(ii) choose appropriate symbolic
				representations and labels such as specifying units of measure, calculating
				accurately and efficiently, and expressing numerical answers with a degree of
				precision appropriate for the context and the data used in
				calculation;
(g)
				appropriately use current and emerging technologies as essential tools for
				teaching and learning mathematics;
(h) look for and recognize repeated reasoning
				patterns and the mathematical structures behind those patterns to organize and
				generalize mathematical methods and results in mathematical problem solving and
				inquiry;
(i) demonstrate how
				students learn mathematics and the pedagogical knowledge specific to
				mathematics teaching and learning by demonstrating:
(i) how learners develop mathematical
				proficiency through the interdependent processes of integrating conceptual
				understanding, procedural fluency, strategic competence, adaptive reasoning,
				and productive disposition;
(ii) an
				understanding of individual differences and diverse cultures and communities to
				ensure inclusive learning environments in mathematics and ensure high standards
				of mathematical work for all students;
(iii) an understanding of learning
				environments that promote mathematical learning, including individual and
				collaborative learning, positive social interaction about mathematics, active
				engagement in mathematics learning, and promote self-motivation among
				mathematical learners;
(iv) an
				understanding of multiple methods of assessment of mathematical learner growth,
				progress, and decision making;
(v)
				an understanding of a variety of instructional strategies that encourage
				learners to develop deep understanding of mathematics; and
(vi) an understanding of grades 5-12
				mathematics curriculum as specified by the State of Montana Content Standards
				and of the assessment process as specified by the Montana statewide
				assessment;
(j)
				demonstrate content knowledge in:
(i) numbers
				and operations including knowledge and understanding of number systems,
				arithmetic algorithms, fundamental ideas of number theory, proportion and rate,
				quantitative reasoning, modeling, and applications;
(ii) different perspectives on algebra
				including knowledge and understanding of algebraic structures, basic function
				classes, functional representations, algebraic models and applications, formal
				structures and linear algebra;
(iii) geometry and trigonometry including
				knowledge and understanding of Euclidean and non-Euclidean geometries,
				geometric transformations, axiomatic reasoning and proof, formulas and
				calculations related to classical geometric objects, and properties of
				trigonometric functions;
(iv)
				calculus including knowledge and understanding of limit, continuity,
				differentiation, integration involving single and multiple-variable functions,
				sequences and series, and a thorough background in the techniques and
				application of the calculus;
(v)
				discrete mathematics including knowledge and understanding of basic discrete
				structures, counting techniques, iteration, recursion, formal logic, and
				applications in the formulation and solution of problems;
(vi) data analysis, statistics, and
				probability including knowledge and understanding of descriptive statistics
				using numbers and graphs, survey design, sources of bias and variability,
				empirical and theoretical probability, simulation, and inferential statistics
				related to univariate and bivariate data distributions; and
(vii) historical development and perspectives
				of various branches of mathematics including contributions of significant
				historical figures and diverse cultures, including American Indians and tribes
				in Montana.