MIDDLE LEVEL –
MATH/SCIENCE ENDORSEMENT COMPETENCIES (59)
Note: the
following draft represents possible changes in the Middle Level Math Science
endorsement competencies being considered by an OSPIestablished work group in
response to a recommendation from the Professional Educator Standards Board. The
competencies listed below are only the mathrelated portions of the
endorsement; no changes in the other sections are under discussion at this
time.
The proposed
changes are closely modeled after middle level 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. The
competencies below would replace the following language in the current
standards: “Teach the following Mathematics concepts to middle level students:
(a) understanding and application of concepts and procedures of mathematics;
(b) how to use mathematics to define and solve problems; (c) ability to use
mathematical reasoning; (d) to communicate knowledge and understanding in both
everyday and mathematical language; and (e) relate how mathematical ideas
connect within mathematics, to other subject areas and to reallife
situations.“
8.0
Common Core Mathematical understanding 
8.1 Mathematical problem
solving: Candidates know, understand,
and apply the process of mathematical problem solving. 
8.1.1 Apply and adapt a variety
of appropriate strategies to solve problems. 
8.1.2 Solve problems that arise
in mathematics and those involving mathematics in other contexts. 
8.1.3 Build new mathematical
knowledge through problem solving. 
8.1.4 Monitor and reflect on the
process of mathematical problem solving. 

8.2 Reasoning and Proof :Candidates
reason, construct, and evaluate mathematical arguments and develop an
appreciation for mathematical rigor and inquiry. 
8.2.1 Recognize reasoning and
proof as fundamental aspects of mathematics. 
8.2.2 Make and investigate
mathematical conjectures. 
8.2.3 Develop and evaluate mathematical
arguments and proofs. 
8.2.4 Select and use various
types of reasoning and methods of proof. 

8.3 Mathematical
Communication: Candidates communicate
their mathematical thinking orally and in writing to peers, faculty, and
others. 
8.3.1 Communicate their
mathematical thinking coherently and clearly to peers, faculty, and others. 
8.3.2 Use the language of
mathematics to express ideas precisely. 
8.3.3 Organize mathematical
thinking through communication. 
8.3.4 Analyze and evaluate the
mathematical thinking and strategies of others. 

8.4 Mathematical Connections:
Candidates recognize, use, and make
connections between and among mathematical ideas and in contexts outside
mathematics to build mathematical understanding. 
8.4.1 Recognize and use connections
among mathematical ideas. 
8.4.2 Recognize
and apply mathematics in contexts outside of mathematics

8.4.3 Demonstrate how
mathematical ideas interconnect and build on one another to produce a
coherent whole. 

8.5 Mathematical Representation: Candidates use varied representations of mathematical
ideas to support and deepen students’ mathematical understanding. 
8.5.1 Use representations to
model and interpret physical, social, and mathematical phenomena. 
8.5.2 Create and use
representations to organize, record, and communicate mathematical ideas. 
8.5.3 Select, apply, and
translate among mathematical representations to solve problems. 

8.6 Technology: Candidates
embrace technology as an essential tool for teaching and learning
mathematics. 
8.6.1 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, datacollection
devices, and presentation software. 

8.7 Mathematics Pedagogy: Candidates possess a deep understanding of how students
learn mathematics and of the pedagogical knowledge specific to mathematics
teaching and learning. 
8.7.1 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. 
8.7.2 Select and use appropriate
concrete materials for learning mathematics. 
8.7.3 Use multiple strategies,
including listening to and understanding the ways students think about
mathematics, to assess students’ mathematical knowledge. 
8.7.4 Plan lessons, units and courses that address Washington
Essential Academic Learning Requirements (EALRs) and GradeLevel Expectations
(GLEs). 
8.7.5 Participate in
professional mathematics organizations and use their print and online
resources. 
8.7.6 Demonstrate knowledge of
research results in the teaching and learning of mathematics. 
8.7.7 Use knowledge of different
types of instructional strategies in planning mathematics lessons. 
8.7.8 Demonstrate the ability to
lead classes in mathematical problem solving and in developing indepth
conceptual understanding, and to help students develop and test
generalizations. 
8.7.9 Develop lessons that use
technology’s potential for building understanding of mathematical concepts
and developing important mathematical ideas. 
8.7.10 Demonstrate a positive impact on student learning of
mathematics. 
8.7.11 Engage in
culturally responsive teaching of mathematics. 

8.8 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. 
8.8.1 Develop the mathematics
that underlies the procedures used for operations involving whole numbers,
integers, and rational numbers. 
8.8.2 Use properties involving
number and operations, mental computation, and computational estimation. 
8.8.3 Provide equivalent
representations of fractions, decimals, and percents. 
8.8.4 Create, solve, and apply
proportions. 
8.8.5 Apply the fundamental
ideas of number theory. 
8.8.6 Make sense of large and
small numbers and use scientific notation. 
8.8.7 Analyze and explain the
distinctions among whole numbers, integers, rational numbers, and real
numbers and whether or not the field axioms hold. 
8.8.8 Demonstrate knowledge of
the historical development of number and number systems including
contributions from diverse cultures. 

8.9 Different Perspectives on Algebra: Candidates emphasize relationships among quantities
including functions, ways of representing mathematical relationships, and the
analysis of change. 
8.9.1 Explore, analyze, and
represent patterns, relations, and functions. 
8.9.2 Represent and analyze
mathematical structures. 
8.9.3 Investigate equality,
equations, and proportional relationships. 
8.9.4 Use mathematical models to
represent quantitative relationships. 
8.9.5 Analyze change in various
contexts. 
8.9.6
Demonstrate knowledge of the historical development of algebra including
contributions from diverse cultures. 

8.10 Geometries: Candidates use spatial visualization and geometric
modeling to explore and analyze geometric shapes, structures, and their
properties. 
8.10.1 Demonstrate knowledge of
core concepts and principles of Euclidean geometry in two and three
dimensions. 
8.10.2 Exhibit knowledge of
informal proof. 
8.10.3 Build and manipulate
representations of two and threedimensional objects and perceive an object
from different perspectives. 
8.10.4 Specify locations and
describe spatial relationships using coordinate geometry. 
8.10.5 Analyze properties and
relationships of geometric shapes and structures. 
8.10.6 Apply transformation and
use congruence, similarity, and line or rotational symmetry. 
8.10.7
Demonstrate knowledge of the historical development of Euclidean and
nonEuclidean geometries including contributions from diverse cultures. 

8.11 Data Analysis,
Statistics, and Probability: Candidates
demonstrate an understanding of concepts and practices related to data
analysis, statistics, and probability. 
8.11.1 Design investigations,
collect data through random sampling or random assignment to treatments, and
use a variety of ways to display the data and interpret data representations. 
8.11.2 Draw conclusions
involving uncertainty by using handson and computerbased simulation for
estimating probabilities and gathering data to make inferences and decisions. 
8.11.3 Identify misuses of
statistics and invalid conclusions from probability. 
8.11.4 Use appropriate
statistical methods and technological tools to analyze data and describe
shape, spread, and center. 
8.11.5 Investigate, interpret,
and construct representations for conditional probability, geometric
probability, and for bivariate data. 
8.11.6 Demonstrate knowledge of
the historical development of probability and statistics including
contributions from diverse cultures. 

8.12 Measurement: Candidates apply and use measurement concepts and tools . 
8.12.1 Recognize measurement
attributes and their effect on the choice of appropriate tools and units. 
8.12.2 Apply techniques, tools,
and formulas to determine measurements. 
8.12.3 Employ estimation as a
way of understanding measurement units and processes. 
8.12.4 Complete error analysis
through determining the reliability of the numbers obtained from measurement. 
8.12.5 Demonstrate knowledge of
the historical development of measurement and measurement systems including
contributions from diverse cultures. 
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