MOSTEP Specialty Area: Secondary Mathematics
Secondary Mathematics Competencies Matrix --- by Course
MTH MTH MTH MTH MTH MTH MTH MTH MTH MTH MTH MTH MTH MTH MTH MTH PHY PHY CSC
Courses 261
280
302
315
345
460
497
503
532
533
Y
Y
Y
Y
Y
Y
Y
Y
536
540
567
575
409
410
123
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
203 121
Competencies for the
Beginning Secondary
Mathematics Teacher in
Missouri
1 Mathematical
Processes and Tools
1.1 Use problem
solving to investigate
and understand
mathematical content.
Y
Y
Y
Y
Y
1.2 Communicate
mathematical ideas in
writing and orally, using
mathematical language
and symbols.
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
1.3 Develop and
evaluate mathematical
conjectures and
arguments to explain
and validate
Y
Y
mathematical reasoning.
1.4 Use mathematical
modeling to simulate
events and occurrences.
Y
Y
Y
1.5 Analyze and
articulate connections
within mathematics.
Y
Y
Y
1.6 Analyze and
articulate connections of
mathematics to other
disciplines through
applications
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
1.7 Understand
historical development of
mathematics, including
the contributions of
under-represented
groups and diverse
cultures.
Y
1.8 Use manipulatives
to model and explain
mathematical concepts.
Y
1.9 Articulate the
dynamic nature of
mathematics and its
significant role in social,
cultural, and economic
development.
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
1.10 Using calculators
and computers as tools
to generate multiple
representations of
mathematical concepts.
Y
Y
Y
Y
Y
Y
1.12 Demonstrate
facility with technological
tools to support
geometric
construction/investigatio
n, graphing, matrix
exploration, and data
investigation; and
Y
Y
Y
Y
Y
Y
1.13 Understand and
articulate the role of
technology in supporting
the development of
mathematical
understanding.
Y
Y
Y
Y
Y
Y
2 Number Operation
2.2 Understand
properties of real and
complex numbers,
including equivalent
representations of
numbers
Y
Y
Y
Y
2.4 Analyze the effect of
and relationships among
operations on real and
complex numbers
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
2.5 Use estimation in
working with quantities,
measurement,
computation, and
problem-solving
Y
Y
Y
2.6 Develop, use, model,
and explain
computational
algorithms
Y
Y
Y
2.7 Understand and
apply numerical
computation techniques
(mental, paper/pencil,
calculator) and extend
them to algebraic
expressions.
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
3 Geometry and
Measurement
3.1 Understand and
apply various systems
and tools of
measurement
Y
3.2 Understand and
apply Euclidean
geometric concepts,
properties, and
relationships to describe
and model mathematical
ideas in real-world
constructs
Y
Y
Y
Y
Y
3.3 Identify, describe,
measure, compare,
classify, and represent
two- and threedimensional geometric
figures
Y
Y
Y
3.4 Understand and
apply trigonometric
concepts, properties,
and relationships
Y
Y
Y
3.6 Understand and
apply concepts of motion
in two- and threedimensional space
through transformations
Y
Y
Y
Y
Y
3.7 Perform geometric
constructions using
straight-edge and
compass and prove that
the constructions yield
the desired result.
Y
Y
Y
Y
Y
4 Data Analysis,
Probability, and Statistics
4.1 Collect, organize,
and display data in
meaningful form(s)
4.2 Use experimental
and theoretical
probabilities as
appropriate to formulate
Y
Y
Y
Y
Y
and solve problems
involving uncertainty
4.4 Use descriptive
statistics (e.g. measures
of central tendency and
dispersion) and
inferential statistics (e.g.
hypothesis testing) to
analyze data and to
make predictions and
decisions.
Y
Y
5 Patterns, Functions, and
Relationships
5.1 Identify and describe
patterns and relations
Y
Y
Y
5.2 Represent patterns
and functions as
symbolic expressions,
verbal descriptions, and
tables and graphs; and
move from one
representation to
another
Y
Y
Y
5.3 Discover and
analyze functional
relations which arise
from diverse problem
situations
Y
Y
Y
Y
Y
Y
5.4 Use algebraic
concepts and notation to
Y
Y
Y
Y
Y
Y
Y
Y
describe relationships
and solve problems
5.5 Use basic
trigonometric relations
including the graphic
representation and realworld application
Y
Y
Y
5.6 Use trigonometric
equations and
inequalities to solve
problems
Y
Y
Y
6 Mathematical Systems
6.1 Construct logical
proofs to validate or
refute mathematical
conjectures
Y
Y
Y
Y
Y
Y
Y
Y
6.2 Understand the
nature and purpose of
axiomatic systems
Y
Y
Y
Y
Y
Y
Y
Y
6.3 Understand and
apply the major
concepts of linear and
abstract algebra
Y
Y
Y
Y
Y
Y
7 Discrete Mathematics
7.1 Use a variety of
counting techniques and
principles, such as
permutations and
Y
combinations
7.2 Identify, model, and
analyze situations
represented by discrete
and continuous data
Y
Y
Y
Y
Y
Y
Y
7.3 Represent problem
situations using discrete
structures such as sets,
finite graphs, matrices,
sequences, and
recurrence relations
Y
Y
Y
Y
Y
Y
Y
7.4 Understand and use
algorithmic and
recursive techniques in
solving problems
Y
Y
Y
7.5 Represent and solve
problems using linear
programming and
difference equations
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
8 Concepts of Calculus
8.2 Understand and
apply the concepts of
limit, continuity,
differentiation,
integration, and other
continuous processes
8.3 Use properties and
techniques of calculus to
model two- and three-
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
dimensional phenomena
8.4 Understand and
apply infinite sequences,
infinite series, and power
series
Y
MTH MTH MTH MTH MTH MTH MTH MTH MTH MTH MTH MTH MTH MTH MTH MTH PHY PHY CSC
Courses 261 280 302 315 345 460 497 503 532 533 536 540 567 575 409 410 123 203 121