New Mexico Administrative Code
Title 6 - PRIMARY AND SECONDARY EDUCATION
Chapter 64 - SCHOOL PERSONNEL - COMPETENCIES FOR LICENSURE
Part 4 - COMPETENCIES FOR ENTRY-LEVEL MATHEMATICS TEACHERS
Section 6.64.4.9 - COMPETENCIES FOR ENTRY-LEVEL MATHEMATICS TEACHERS
Universal Citation: 6 NM Admin Code 6.64.4.9
Current through Register Vol. 35, No. 18, September 24, 2024
A. Teachers will understand and use mathematics in problem-solving.
(1) Teachers
for grades K-8 will be able to:
(a) use
problem-solving approaches to investigate and understand mathematical
content;
(b) formulate and solve
problems from both mathematical and everyday situations;
(c) identify, select and use appropriate
problem-solving strategies; as well as develop and apply their own
strategies;
(d) verify and
interpret solutions to problems;
(e) use mathematical language and symbolism
to model problem situations.
(2) Teachers for grades 5-9 will be able to
meet the standards set for K-8 teachers.
(3) Teachers for grades 7-12 will be able to:
(a) use a problem solving approach to
investigate and understand mathematical concepts;
(b) formulate and solve problems from both
mathematical and everyday experiences;
(c) develop their own processes and
techniques for solving problems.
B. Teachers will understand and use mathematics in communication.
(1) Teachers for
grades K-8 will be able to:
(a) identify and
define mathematical concepts in a variety of situations;
(b) communicate mathematical ideas both
verbally and in writing;
(c) use
drawings, discussion, reading, and listening to learn and communicate
mathematical ideas;
(d) use a
variety of electronic media and manipulatives to explore and communicate
mathematical concepts and problem solutions.
(2) Teachers for grades 5-9 will be able to
meet the standards set for K-8 teachers.
(3) Teachers for grades 7-12 will be able to:
(a) develop skills in both written and oral
communication of mathematical concepts;
(b) learn to communicate effectively at
various levels of formality and with people who have differing levels of
mathematical understanding.
C. Teachers will understand and use mathematics in reasoning.
(1) Teachers for
grades K-8 will be able to:
(a) describe
logical conclusions;
(b) use
information sources, models and known facts to explain mathematical
thinking;
(c) make and evaluate
mathematical conjectures and validate their own mathematical
thinking;
(d) recognize and
construct logical arguments for mathematical statements, concepts, and
principles;
(e) apply a variety of
reasoning processes to include deductive and inductive reasoning.
(2) Teachers for grades 5-9 will
be able to meet the standards set for K-8 teachers.
(3) Teachers for grades 7-12 will be able to:
(a) recognize patterns, make and refine
conjectures and definitions, and construct both formal and heuristic
proofs;
(b) judge the validity of
mathematical arguments;
(c)
formulate counterexamples.
D. Teachers will understand and use mathematical connections.
(1) Teachers for
grades K-8 will be able to:
(a) show an
understanding of the interrelationships within mathematics;
(b) connect mathematics to other disciplines
and everyday situations.
(2) Teachers for grades 5-9 will be able to
meet the standards set for K-8 teachers.
(3) Teachers for grades 7-12 will be able to:
(a) develop an understanding of the
interrelationships within mathematics and an appreciation of its
unity;
(b) understand and
appreciate the power of mathematical language and symbolism in the development
of mathematical concepts;
(c)
explore the connections between mathematics and other disciplines;
(d) apply mathematics learned in one context
to other contexts.
E. Teachers will understand and use numbers, and their relationships, systems and theory.
(1) Teachers for grades K-8 will be able to:
(a) construct number meanings through
everyday experiences and the use of physical materials;
(b) understand prenumeration
concepts.
(c) describe and compare
ancient and modern numeration systems by relating counting, grouping, and place
value concepts;
(d) develop number
sense;
(e) identify different sets
of numbers in the real number system;
(f) understand representations of numbers,
including mixed numbers, fractions, decimals, and scientific
notation;
(g) demonstrate ability
to use models to explore and explain relationships among fractions, decimals,
percents, ratios, and proportions;
(h) use the relations of equality and
inequality.
(2) Teachers
for grades 5-9 will be able to meet the standards set for K-8
teachers.
(3) Teachers for grades
7-12 will be able to: Explore and discuss the properties, relations, and
extensions of the real and complex numbers.
F. Teachers will understand and use computation and estimation.
(1) Teachers for
grades K-8 will be able to:
(a) model,
explain, and develop proficiency with the basic number facts and algorithms,
including addition, subtraction, multiplication and division;
(b) recognize alternative algorithms for the
four basic operations;
(c) select
and use computation techniques appropriate to specific problems and determine
the reasonableness of solutions;
(d) use estimation strategies;
(e) recognize when estimates are
appropriate.
(2)
Teachers for grades 5-9 will be able to meet the standards set for K-8
teachers.
(3) Teachers for grades
7-12 will be able to:
(a) understand and
apply numerical computational and estimation techniques and extend them to
symbolic expressions;
(b) use
estimation to assess the reasonableness of solutions.
G. Teachers will have a foundation in geometric concepts.
(1) Teachers for grades
K-8 will be able to:
(a) describe, model, draw
and classify geometric figures;
(b)
investigate, predict, and describe the results of combining, subdividing and
changing shapes;
(c) develop
spatial sense and relationships;
(d) relate geometric and measurement
ideas;
(e) use geometric concepts
and relationships to describe and model mathematical ideas and relationships to
the world;
(f) solve simple
problems in two- and three-dimensional geometry involving parallelism,
perpendicularity, congruence, similarity, translation, reflection, rotation,
symmetry, and incidence.
(2) Teachers for grades 5-9 will be able to
meet the standards set for K-8 teachers.
(3) Teachers for grades 7-12 will be able to:
(a) understand the role of axiomatic systems
in geometry;
(b) develop both
synthetic and algebraic geometric concepts using coordinates and
vectors;
(c) use geometry as a
source of mathematical models for a variety of applications;
(d) employ geometric reasoning as a problem
solving strategy;
(e) model
features of the real world using different geometries.
H. Teachers will understand and use measurement.
(1) Teachers for grades K-8
will be able to:
(a) determine what needs to
be measured, select an appropriate unit of measurement, and then select an
appropriate tool with which to measure;
(b) use standard and nonstandard units for
measurement to an appropriate degree of accuracy;
(c) use estimation, informal procedures, and
formulas to solve problems involving linear measures, area, volume, mass, and
temperature by using both traditional and metric systems.
(2) Teachers for grades 5-9 will be able to
meet the standards set for K-8 teachers.
(3) Teachers for grades 7-12 will be able to:
(a) identify and use the appropriate units,
tools of measurement, and degree of accuracy required in particular problems,
making calculations of relative error as necessary;
(b) apply measurement as a tool in other
disciplines.
I. Teachers will understand and use statistics and probability.
(1) Teachers for
grades K-8 will be able to:
(a) collect data
from real world experiences or surveys, organize and display data using various
charts/graphs manually and by using appropriate technology, analyze and
interpret the data, and write convincing arguments based on the data;
(b) solve elementary statistical problems
relating to measures of central tendency, measures of dispersion, regression
equations, and non-linear regression;
(c) critically examine and analyze data for
reliability and validity;
(d)
demonstrate an understanding of randomness by conducting sampling
experiments;
(e) find experimental
and theoretical discrete probabilities using sample spaces, tree diagrams, and
other representations;
(f) plan and
conduct simulations to determine experimental probabilities;
(g) compute the mathematical expectation of
simple games and lotteries;
(h)
solve simple problems involving probability, inference, and the testing of
hypotheses;
(i) use simple
combinations and permutations to solve counting problems.
(2) Teachers for grades 5-9 will be able to
meet the standards set for K-8 teachers.
(3) Teachers for grades 7-12 will be able to:
(a) understand measures of central tendency,
variability, and correlation;
(b)
collect, display, analyze, and interpret sample data in a variety of
situations;
(c) investigate the
role of estimation and probability in statistical analysis;
(d) use experimental and theoretical
probabilities to formulate and solve problems;
(e) develop strategies for reasoning and
making decisions based on uncertainty;
(f) explore the probabilistic nature of
statistical analyses including hypothesis testing, correlation, analysis of
variance, and nonparametric methods.
J. Teachers will understand and use patterns and functions.
(1) Teachers for grades K-8
will be able to:
(a) recognize, describe,
extend, and create a wide variety of patterns;
(b) represent relationships with
manipulatives, tables, graphs, verbal and written statements, and
formulas;
(c) describe what a
function means both intuitively and using formal mathematical
language;
(d) demonstrate a basic
understanding of classes of functions and their properties; e.g. linear,
exponential, polynomial, and periodic.
(2) Teachers for grades 5-9 will be able to
meet the standards set for K-8 teachers.
(3) Teachers for grades 7-12 will be able to:
(a) use multiple representations of
functions, including symbolic expressions, verbal descriptions, tables, and
graphs, and relate one representation to another;
(b) use the language of functions to describe
and model change;
(c) use the
concept of function in the study of mathematics and other
disciplines.
K. Teachers will understand and apply algebraic concepts.
(1) Teachers for grades
K-8 will be able to:
(a) explore and use
variables and open sentences to express mathematical relationships;
(b) solve real world problems involving
linear and quadratic equations and inequalities by using traditional techniques
and graphing methods that use technology.
(2) Teachers for grades 5-9 will be able to
meet the standards set for K-8 teachers.
(3) Teachers for grades 7-12 will be able to:
(a) understand and apply the major concepts
of linear and abstract algebra;
(b)
use theoretical results to understand tangible situations.
L. Teachers will understand and apply concepts of calculus.
(1) Not required
of teachers for grades K-8.
(2)
Teachers for grade 5-9 will be able to:
(a)
recognize particular types of change such as linear, quadratic and
exponential;
(b) use graphs,
diagrams, charts, physical models, and graphing technology to explore the
notions of limit, differentiation, and integration, and interpret the
relationships among them;
(c)
construct infinite sequences and series, relating them to non-terminating
decimals and the approximation of functions;
(d) solve real world problems involving
average and instantaneous rates of change, area, volume, and curve length, and
relate those to differentiation and integration.
(3) Teachers for grades 7-12 will be able to:
(a) investigate the phenomenon of change as a
limiting process;
(b) explore
intuitively and in depth the concepts of limit, continuity, differentiation,
and integration;
(c) demonstrate an
understanding of the underlying theory of analysis;
(d) use properties and techniques of calculus
to model phenomena in diverse settings.
M. Teachers will understand and apply discrete processes.
(1) not required of
teachers for grades K-8;
(2) not
required of teachers for grades 5-9;
(3) teachers for grades 7-12 will be able to:
understand concepts and applications of discrete mathematics, such as graph
theory, recurrence relations, linear programming, difference equations, and
combinatorics.
N. Teachers will understand the use of technology.
(1) Teachers for grades K-8 will be able to:
(a) use calculators and computers to
represent mathematical ideas and construct different representations of
mathematical concepts;
(b) use
calculators and computers to develop and use alternate strategies for solving
problems;
(c) use networking and
information technologies to solve problems and broaden the scope of
inquiry.
(2) Teachers
for grades 5-9 will be able to meet the standards set for K-8
teachers.
(3) Teachers for grades
7-12 will be able to:
(a) engender a broad
array of mathematical modes of thinking through the use of powerful computing
tools (including function graphers, curve fitters, symbolic manipulators,
dynamic geometric software, and programming languages);
(b) use calculators, spreadsheets, and
statistical packages to solve problems;
(c) use technology to explore probabilities
through simulations;
(d) use
graphing calculators and computer algebra systems in the study and application
of the calculus.
O. Teachers will develop perspectives on mathematics as a human endeavor.
(1) Teachers
for grades K-8 will be able to:
(a)
understand the dynamic nature of mathematics and its increasingly significant
role in social, cultural, and economic development;
(b) develop an appreciation for the
contributions made by various cultures to the growth and development of
mathematical ideas;
(c) investigate
the contributions made by individuals, both female and male, and from a variety
of cultures, in the development of ancient, modern, and current mathematical
topics;
(d) gain an understanding
of the historical development of major school mathematics concepts.
(2) Teachers for grades 5-9 will
be able to meet the standards set for K-8 teachers.
(3) Teachers for grades 7-12 will be able to:
(a) explore the dynamic nature of mathematics
and its increasingly significant role in social, cultural, and economic
development;
(b) gain an
understanding of the historical development of major school mathematics
concepts;
(c) understand the
historical development of non-Euclidean geometries and the questions relating
to the parallel postulate involved in this development;
(d) develop an appreciation of the
contributions made by the various cultures to the growth and development of
mathematical ideas;
(e) investigate
the contributions made by individuals, both female and male, and from a variety
of cultures, in the development of ancient, modern, and current mathematical
topics.
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