2.3 Mathematics

2.3.1 Number and Operation
Candidates demonstrate computational proficiency, including a conceptual understanding of numbers, ways of representing number, relationships among number and number systems, and the meanings of operations.

2.3.1.1 Develop the meaning of addition, subtraction, multiplication, and division and provide multiple models for whole number operations and their applications.

2.3.1.2 Recognize the meaning and use of place value in representing whole numbers and finite decimals, comparing and ordering numbers, and understanding the relative magnitude of numbers.

2.3.1.3 Demonstrate proficiency in multi-digit computation using algorithms, mental mathematics, and computational estimation.

2.3.1.4 Analyze integers and rational numbers, their relative size, and how operations with whole numbers extend to integers and rational numbers.

2.3.1.5 Demonstrate knowledge of the historical development of number and number systems including contributions from diverse cultures.

2.3.2 Different Perspectives on Algebra
Candidates emphasize relationships among quantities including functions, ways of representing mathematical relationships, and the analysis of change. **see indicators from NCTM Standard 10 listed below:

2.3.2.1 Explore and analyze patterns, relations, and functions.

2.3.2.2 Recognize and analyze mathematical structures.

2.3.2.3 Investigate equality and equations.

2.3.2.4 Use mathematical models to represent quantitative relationships.

2.3.2.5 Analyze change in various contexts.

2.3.2.6 Demonstrate knowledge of the historical development of algebra including contributions from diverse cultures.

2.3.3 Geometries
Candidates use spatial visualization and geometric modeling to explore and analyze geometric shapes, structures, and their properties.

2.3.3.1 Use visualization, the properties of two- and three-dimensional shapes, and geometric modeling.

2.3.3.2 Build and manipulate representations of two- and three-dimensional objects using concrete models, drawings, and dynamic geometry software.

2.3.3.3 Specify locations and describe spatial relationships using coordinate geometry.

2.3.3.4 Apply transformations and use symmetry, congruence, and similarity.

2.3.3.5 Demonstrate knowledge of the historical development of Euclidean and non-Euclidean geometries including contributions from diverse cultures.

2.3.4 Data Analysis, Statistics, and Probability: Candidates demonstrate an understanding of concepts and practices related to data analysis, statistics, and probability.

2.3.4.1 Design investigations that can be addressed by creating data sets and collecting, organizing, and displaying relevant data.

2.3.4.2 Use appropriate statistical methods and technological tools to analyze data and describe shape, spread, and center.

2.3.4.3 Apply the basic concepts of probability.

2.3.4.4 Demonstrate knowledge of the historical development of probability and statistics including contributions from diverse cultures.

2.3.5 Measurement: Candidates apply and use measurement concepts and tools.

2.3.5.1 Select and use appropriate measurement units, techniques, and tools.

2.3.5.2 Recognize and apply measurable attributes of objects and the units, systems, and processes of measurement.

2.3.5.3 Employ estimation as a way of understanding measurement units and processes.

2.3.5.4 Demonstrate knowledge of the historical development of measurement and measurement systems including contributions from diverse cultures.

2.3.6 Mathematics Pedagogy: Candidates possess a deep understanding of how students learn mathematics and of the pedagogical knowledge specific to mathematics teaching and learning.

2.3.6.1 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.

2.3.6.2 Select and use appropriate concrete materials for learning mathematics.

2.3.6.3 Use multiple strategies, including listening to and understanding the ways students think about mathematics, to assess students’ mathematical knowledge.

2.3.6.4 Plan lessons, units and courses that address Washington Essential Academic Learning Requirements (EALRs) and Grade-Level Expectations (GLEs).

2.3.6.5 Demonstrate knowledge of research results in the teaching and learning of mathematics, and use print and online resources of professional mathematics organizations.

2.3.6.6 Use knowledge of different types of instructional strategies in planning mathematics lessons.

2.3.6.7 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.

2.3.6.8 Develop lessons that use technology’s potential for building understanding of mathematical concepts and developing important mathematical ideas.

2.3.6.9 Demonstrate a positive impact on student learning of mathematics.

2.3.6.10 Engage in culturally responsive teaching of mathematics.

2.3.7 Mathematical Problem Solving: Candidates know, understand, and apply the process of mathematical problem solving.

2.3.7.1 Apply and adapt a variety of appropriate strategies to solve problems.

2.3.7.2 Solve problems that arise in mathematics and those involving mathematics in other contexts.

2.3 7.3 Build new mathematical knowledge through problem solving.

2.3.7.4 Monitor and reflect on the process of mathematical problem solving.

2.3.8 Reasoning and Proof: Candidates reason, construct, and evaluate mathematical arguments and develop an appreciation for mathematical rigor and inquiry.

2.3.8.1 Recognize reasoning and proof as fundamental aspects of mathematics.

2.3.8.2 Make and investigate mathematical conjectures.

2.3.8.3 Develop and evaluate mathematical arguments and proofs.

2.3.8.4 Select and use various types of reasoning and methods of proof.

2.3.9 Mathematical Communication: Candidates communicate their mathematical thinking orally and in writing to peers, faculty, and others.

2.3.9.1 Communicate their mathematical thinking coherently and clearly to peers, faculty, and others.

2.3.9.2 Use the language of mathematics to express ideas precisely.

2.3.9.3 Organize mathematical thinking through communication.

2.3.9.4 Analyze and evaluate the mathematical thinking and strategies of others.

2.3.10 Mathematical Connections: Candidates recognize, use, and make connections between and among mathematical ideas and in contexts outside mathematics to build mathematical understanding.

2.3.10.1 Recognize and use connections among mathematical ideas.

2.3.10.2 Recognize and apply mathematics in contexts outside of mathematics.

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

2.3.11 Mathematical Representation: Candidates use varied representations of mathematical ideas to support and deepen students’ mathematical understanding.

2.3.11.1 Use representations to model and interpret physical, social, and mathematical phenomena.

2.3.11.2 Create and use representations to organize, record, and communicate mathematical ideas.

2.3.11.3 Select, apply, and translate among mathematical representations to solve problems.

2.3.12 Technology: Candidates embrace technology as an essential tool for teaching and learning mathematics.

2.3.12.1 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.