Board Approved – April 24, 2003

Definitions

For best printing results, click here (pdf).

Number Sense: Number Sense is the deep and fundamental understanding of, and proficiency with counting, numbers, and arithmetic, as well as an understanding of numbers systems and their structures. Development of number sense enables all students to understand numbers, ways of representing numbers, relationships among numbers, and number systems. Students understand the meanings of operations and how they relate to one another. They understand how to compute fluently and make reasonable estimates. Students should have experiences that help them learn to choose among mental computation, paper-and-pencil strategies, estimation and calculator use. (NCTM Principles and Standards for School Mathematics 2000)

Measurement: Measurement is the assignment of a numerical value to an attribute of an object or assigning a number to a characteristic of a situation. Development of measurement skills and understandings enables all students to understand measurable attributes of objects and the units systems, and processes of measurement. They understand how to appropriate techniques, tools, and formulas to determine measurements. Students should learn both customary and metric systems. (NCTM Principles and Standards for School Mathematics 2000)

Geometric Sense: Geometric ideas are useful in representing and solving problems. Development of geometric sense enables all students to analyze characteristics and properties of two- and three- dimensional geometric shapes and develop mathematical understandings about geometric relationships. They understand how to specify locations and describe spatial relationships using coordinate geometry and other representational systems. Students apply transformations and use symmetry to analyze mathematical situations. They understand how to use visualization, spatial reasoning, and geometric modeling to solve problems. (NCTM Principles and Standards for School Mathematics 2000)

Probability and Statistics: The study of probability and statistics involves learning how to collect, organize, display and analyze data in order to formulate questions, make inferences and develop conclusions. Development of probability and statistical understandings enables all students to formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them. Students understand how to use appropriate statistical methods to analyze data and develop and evaluate inferences and predictions that are based on data. Students develop an understanding of how to apply the basic concepts of probability. (NCTM Principles and Standards for School Mathematics 2000)

Algebraic Sense: Algebra emphasizes relationships among quantities, including functions, ways of representing mathematical relationships, and the analysis of change. Development of algebraic sense enables all students to understand patterns, relationships and functions. They are able to represent and analyze mathematical situations and structures using algebraic symbols. Students use mathematical models to represent and understand quantitative relationships and are able to analyze change in various contexts. (NCTM Principles and Standards for School Mathematics 2000)

Problem Solving: Problem solving means engaging in a task for which the solution method is not known in advance. Development of problem solving skills enables all students to build new mathematical knowledge by solving problems that arise in mathematics and in other contexts. Students apply and adapt a variety of appropriate strategies to solve problems and monitor and reflect on the process of mathematical problem solving. (NCTM Principles and Standards for School Mathematics 2000)

Reasoning: A mathematical proof is a formal way of expressing particular kinds of reasoning and justification. Development of mathematical reasoning enables all students to make and investigate mathematical conjectures, develop and evaluate mathematical arguments and proofs. Students are able to select and use various types of reasoning and methods of proof. (NCTM Principles and Standards for School Mathematics 2000)

Communication: Communication is a way of sharing ideas, clarifying understanding, building meaning and permanence for ideas by making them public. Development of communication skills enables all students to organize and consolidate their mathematical thinking through communication. They are able to communicate their mathematical thinking coherently and clearly to peers, teachers and others. They can analyze and evaluate the mathematical thinking and strategies of others and use the language of mathematical ideas precisely. (NCTM Principles and Standards for School Mathematics 2000)

Connections: When students can connect mathematical ideas, their understanding is deeper and more lasting. Development of connection skills enables all students to recognize and use connections among mathematical ideas. They are able to understand how mathematical ideas interconnect and build on one another to produce a coherent whole. They can recognize and apply mathematics in contexts outside of mathematics. (NCTM Principles and Standards for School Mathematics 2000)