Mathematics (5-12) Endorsement Standards
Note: the
following draft represents possible changes in the secondary (5-12) Mathematics
endorsement competencies being considered by an OSPI-established work group in
response to a recommendation from the Professional Educator Standards Board.
The proposed
changes are closely modeled after secondary teacher standards established by
the National Council for the Teaching of Mathematics. Each section consists of
the competency, followed by a number of indicators that clarify the intent.
1.0 Common
Core
Mathematical
Problem Solving: Candidates know, understand, and apply
the process of mathematical problem solving. |
1.1 Apply and
adapt a variety of appropriate strategies to solve problems. |
1.2 Solve
problems that arise in mathematics and those involving mathematics in other
contexts. |
1.3 Build new
mathematical knowledge through problem solving. |
1.4 Monitor and
reflect on the process of mathematical problem solving. |
2.0
Common Core Reasoning and Proof : Candidates
reason, construct, and evaluate mathematical arguments and develop an
appreciation for mathematical rigor and inquiry. |
2.1 Recognize
reasoning and proof as fundamental aspects of mathematics. |
2.2 Make and
investigate mathematical conjectures. |
2.3 Develop and
evaluate mathematical arguments and proofs. |
2.4 Select and
use various types of reasoning and methods of proof. |
3.0
Common Core Mathematical Communication: Candidates communicate
their mathematical thinking orally and in writing to peers, faculty, and
others. |
3.1 Communicate
their mathematical thinking coherently and clearly to peers, faculty, and
others. othersothers. |
3.2 Use the
language of mathematics to express ideas precisely. |
3.3 Organize
mathematical thinking through communication. |
3.4 Analyze and
evaluate the mathematical thinking and strategies of others. |
4.0
Common Core Mathematical Connections: Candidates
recognize, use, and make connections between and among mathematical ideas and
in contexts outside mathematics to build mathematical understanding. |
4.1 Recognize
and use connections among mathematical ideas. |
4.2 Recognize
and apply mathematics in contexts outside of mathematics. |
4.3 Demonstrate
how mathematical ideas interconnect and build on one another to produce a
coherent whole. |
5.0
Common Core Mathematical
Representation: Candidates use varied representations of
mathematical ideas to support and deepen students’ mathematical
understanding. |
5.1 Use
representations to model and interpret physical, social, and mathematical
phenomena. |
5.2 Create and
use representations to organize, record, and communicate mathematical ideas. |
5.3 Select,
apply, and translate among mathematical representations to solve problems. |
6.0
Common Core Technology: Candidates
embrace technology as an essential tool for teaching and learning
mathematics. |
6.1 Use
knowledge of mathematics to select and use appropriate technological tools,
such as but not limited to, spreadsheets, dynamic graphing tools, computer
algebra systems, dynamic statistical packages, graphing calculators,
data-collection devices, and presentation software |
7.0
Common Core Mathematics
Pedagogy: Candidates possess a deep understanding of how students
learn mathematics and of the pedagogical knowledge specific to mathematics
teaching and learning. |
7.1 Select, use,
and determine suitability of the wide variety of available mathematics
curricula and teaching materials for all students including those with
special needs such as the gifted, challenged and speakers of other languages. |
7.2 Select and
use appropriate concrete materials for learning mathematics. |
7.3 Use multiple
strategies, including listening to and understanding the ways students think
about mathematics, to assess students’ mathematical knowledge. |
7.4 Plan
lessons, units and courses that address Washington Essential Academic
Learning Requirements (EALRs) and Grade-Level Expectations (GLEs). |
7.5 Participate
in professional mathematics organizations and use their print and on-line
resources. |
7.6 Demonstrate
knowledge of research results in the teaching and learning of mathematics. |
7.7 Use
knowledge of different types of instructional strategies in planning
mathematics lessons. |
7.8 Demonstrate
the ability to lead classes in mathematical problem solving and in developing
in-depth conceptual understanding, and to help students develop and test
generalizations. |
7.9 Develop
lessons that use technology’s potential for building understanding of
mathematical concepts and developing important mathematical ideas. |
7.10 Demonstrate
a positive impact on student learning of mathematics. |
7.11 Engage in
culturally responsive teaching of mathematics. |
8.0
Common Core Number and Operation: Candidates demonstrate
computational proficiency, including a conceptual understanding of numbers,
ways of representing number, relationships among number and number systems,
and meanings of operations. |
8.1 Analyze and
explain the mathematics that underlies the procedures used for operations
involving integers, rational, real, and complex numbers. |
8.2 Use
properties involving number and operations, mental computation, and
computational estimation. |
8.3 Provide
equivalent representations of fractions, decimals, and percents. |
8.4 Create,
solve, and apply proportions. |
8.5 Apply the
fundamental ideas of number theory. |
8.6 Make sense
of large and small numbers and use scientific notation. |
8.7 Compare and
contrast properties of numbers and number systems. |
8.8 Represent,
use, and apply complex numbers. |
8.9 Recognize
matrices and vectors as systems that have some of the properties of the real
number system. |
8.10 Demonstrate
knowledge of the historical development of number and number systems
including contributions from diverse cultures. |
9.0
Common Core Different Perspectives on Algebra Candidates
emphasize relationships among quantities including functions, ways of
representing mathematical relationships, and the analysis of change. |
9.1 Analyze
patterns, relations, and functions of one and two variables. |
9.2 Apply
fundamental ideas of linear algebra. |
9.3 Apply the
major concepts of abstract algebra to justify algebraic operations and
formally analyze algebraic structures. |
9.4 Use
mathematical models to represent and understand quantitative relationships. |
9.5 Use
technological tools to explore algebraic ideas and representations of
information and in solving problems. |
9.6 Demonstrate
knowledge of the historical development of algebra including contributions
from diverse cultures. |
10.0
Common Core Geometries:
Candidates use spatial visualization and geometric modeling
to explore and analyze geometric shapes, structures, and their properties. |
10.1 Demonstrate
knowledge of core concepts and principles of Euclidean and non-Euclidean
geometries in two and three dimensions from both formal and informal
perspectives. |
10.2 Exhibit
knowledge of the role of axiomatic systems and proofs in geometry. |
10.3 Analyze
characteristics and relationships of geometric shapes and structures. |
10.4 Build and
manipulate representations of two- and three- dimensional objects and
visualize objects from different perspectives. |
10.5 Specify
locations and describe spatial relationships using coordinate geometry,
vectors, and other representational systems. |
10.6 Apply
transformations and use symmetry, similarity, and congruence to analyze
mathematical situations. |
10.7 Use
concrete models, drawings, and dynamic geometric software to explore
geometric ideas and their applications in real-world contexts. |
10.8 Demonstrate
knowledge of the historical development of Euclidean and non-Euclidean
geometries including contributions from diverse cultures. |
11.0
Common Core
Calculus: Candidates demonstrate a conceptual
understanding of limit, continuity, differentiation, and integration and a
thorough background in the techniques and application of the calculus. |
11.1 Demonstrate
a conceptual understanding of and procedural facility with basic calculus
concepts. |
11.2 Apply
concepts of function, geometry, and trigonometry in solving problems
involving calculus. |
11.3 Use the
concepts of calculus and mathematical modeling to represent and solve
problems taken from real-world contexts. |
11.4 Use
technological tools to explore and represent fundamental concepts of
calculus. |
11.5 Demonstrate
knowledge of the historical development of calculus including contributions
from diverse cultures. |
2
12.0 Common Core Discrete
Mathematics: Candidates
apply the fundamental ideas of discrete mathematics in the formulation and
solution of problems. |
12.1 Demonstrate
knowledge of basic elements of discrete mathematics such as graph theory,
recurrence relations, finite difference approaches, linear programming, and
combinatorics. |
12.2 Apply the
fundamental ideas of discrete mathematics in the formulation and solution of
problems arising from real-world situations. |
12.3 Use
technological tools to solve problems involving the use of discrete
structures and the application of algorithms. |
12.4 Demonstrate
knowledge of the historical development of discrete mathematics including
contributions from diverse cultures. |
13.0
Common Core Data Analysis, Statistics, and
Probability: Candidates
demonstrate an understanding of concepts and practices related to data
analysis, statistics, and probability. |
13.1 Design
investigations, collect data, and use a variety of ways to display data and
interpret data representations that may include bivariate data, conditional
probability and geometric probability. |
13.2 Use
appropriate methods such as random sampling or random assignment of
treatments to estimate population characteristics, test conjectured
relationships among variables, and analyze data. |
13.3 Use
appropriate statistical methods and technological tools to describe shape and
analyze spread and center. |
13.4 Use
statistical inference to draw conclusions from data. |
13.5 Identify
misuses of statistics and invalid conclusions from probability. |
13.6 Draw
conclusions involving uncertainty by using hands-on and computer-based
simulation for estimating probabilities and gathering data to make inferences
and conclusions. |
13.7 Determine
and interpret confidence intervals. |
13.8 Demonstrate
knowledge of the historical development of statistics and probability
including contributions from diverse cultures. |
14.0 Common Core Measurement: Candidates apply and use measurement
concepts and tools. |
14.1 Recognize
the common representations and uses of measurement and choose tools and units
for measuring. |
14.2 Apply
appropriate techniques, tools, and formulas to determine measurements and
their application in a variety of contexts. |
14.3 Completes
error analysis through determining the reliability of the numbers obtained
from measures. |
14.4 Demonstrate
knowledge of the historical development of measurement and measurement
systems including contributions from diverse cultures. |
3