Note: the following draft represents possible changes in the Middle Level Math Science endorsement competencies being considered by an OSPI-established work group in response to a recommendation from the Professional Educator Standards Board. The competencies listed below are only the math-related 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 real-life 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, data-collection 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 Grade-Level Expectations (GLEs).

8.7.5 Participate in professional mathematics organizations and use their print and on-line 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 in-depth 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 three-dimensional 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 non-Euclidean 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 hands-on and computer-based 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.