2014 Mathematics SOL Institutes Grade Band: Geometry

Making Connections and Using Representations The purpose of the 2014 Mathematics SOL Institutes is to provide professional development focused on instruction that supports process goals for students in mathematics. Emphasis will be on fostering students’ ability to make mathematical connections and use effective and appropriate representations in mathematics.

Mathematical Representations Students will represent and describe mathematical ideas, generalizations, and relationships with a variety of methods. Students will understand that representations of mathematical ideas are an essential part of learning, doing, and communicating mathematics. Students should move easily among different representations ⎯ graphical, numerical, algebraic, verbal, and physical ⎯ and recognize that representation is both a process and a product. Now let’s look at what the DOE says about representations. Similarities?? Differences?? Virginia Department of Education. (2009). Introduction Mathematics Standards of Learning for Virginia Public Schools

Regardless of their form, representations can enhance students' communication, reasoning, and problem-solving abilities; help them make connections among ideas; and aid them in learning new concepts and procedures. The true power comes when students are able to understand the connections that exist between each one of these models for any given concept or skill.

extend a mathematical idea “Representations are useful in all areas of mathematics because they help us develop, share, and preserve our mathematical thoughts. They help to portray, clarify, or extend a mathematical idea by focusing on its essential features.” National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. (p. 206). Reston, VA. representations should be imbedded in student discussions and class presentations to support students in communicating their mathematical thinking.

Defining Connection What does it mean for students to make mathematical connections? Think/Pair/Share

Mathematical Connections Students will relate concepts and procedures from different topics in mathematics to one another and see mathematics as an integrated field of study. Through the application of content and process skills, students will make connections between different areas of mathematics and between mathematics and other disciplines, especially science. Science and mathematics teachers and curriculum writers are encouraged to develop mathematics and science curricula that reinforce each other. How is our list alike? How is our lists different? Virginia Department of Education. (2009). Introduction Mathematics Standards of Learning for Virginia Public Schools

“Connections are useful because they help students see mathematics as a unified body of knowledge rather than a set of complex and disjoint concepts, procedures and processes. Real world contexts provide opportunities for students to connect what they are learning to their own environment. Their mathematics may also be connected to other disciplines which provides opportunities to enrich their learning.” National Council of Teachers of Mathematics. 2000, p. 200. Principles and Standards for School Mathematics. Reston, VA Representations should be imbedded in student discussions and class presentations to support students in communicating their mathematical thinking.

Planning for the Use of Representations How do we plan for the purposeful use of representations and connections in the classroom? What questions do we need to consider? Brainstorm as many questions as you can, and share on your chart paper.