Draft Content Standards for High School Mathematics State Board of Education June 19, 2009 Colleen Mileham, Michelle Hooper, & Paul Hibbard Office of Educational Improvement and Innovation Oregon Department of Education

High School Math Standards Algebra Statistics Geometry Oregon’s HS math standards include three subject areas.

Advanced Mathematics Knowledge & Skills Provide students more learning options (advanced coursework) Assist teachers in designing differentiated instruction In addition to the standards, the content & assessment panel created advanced k&s statements to…

High School Standards Advanced Knowledge & Skills Contain: facts (definitions & formulas) procedures (algorithms) concepts (how math is connected as a whole) Both the standards and the advanced k&s contain important components for helping students understand math.

Facts and Procedures Facts, such as definitions and formulae, and procedures or algorithms, are one aspect of mathematics.

Facts and Procedures Example from Oregon Standards: H.1A.1 Compare, order, and locate real numbers on a number line Paul will provide detail here.

Conceptual Understanding To be a versatile problem solvers in mathematics, students must understand concepts, and see mathematics as a connected whole.

Conceptual Understanding Example from Oregon Standards: H.2A.6 Analyze how changing the parameters transforms the graph of f (x) = m x + b Paul will provide detail here.

Mathematical Process Expectations Instructional programs Pre-K through 12th grade should help all students to develop a conceptual depth of knowledge of the content standards Intentional instructional strategies & contexts are required to achieve this.

Mathematical Process Expectations The Actions of Doing Mathematics Problem Solving Reasoning & Proof Communication Connections Representation (Reflection) -National Council of Teachers of Mathematics (NCTM) NCTM developed these “process standards”

Mathematical Processes Representing Reflecting Reasoning and Proving Connecting Communicating Problem Solving Reasoning and Proving Reflecting Communicating Representing NCTM processes These processes form the primary gear of the metaphor. The interconnected processes of Representing, Reflecting, Reasoning and Proving, and Connecting make up disk of the gear. Communicating and Problem Solving are closely linked to each of the other 5 processes. It is essential that our students are capable of communicating their mathematics therefore it is essential that they are given opportunities to practice. Communicating is integral in each of the other processes. Problem Solving is the driver of all mathematics. The solution of rich mathematics questions requires the application of skills and understanding of concepts and incorporates some or all of the mathematical processes. Connecting Problem Solving

Mathematical Proficiency Representing Reflecting Reasoning and Proving Selecting Tools and Computational Strategies Connecting Communicating Problem Solving As the gears mesh, the three components come together to build our model. Interacting with the mathematics through the mathematical processes provides students the opportunity to connect facts and procedures to conceptual understanding. For example, the volume of all right prisms, including cylinders, is found by multiplying the area of the base by the height. Students extend this conceptual understanding of the volume of a right prism to develop the procedure for finding the volume of pyramids by interacting with some of the mathematical processes. The 3 gears are clearly connected and working together to enhance students overall understanding and ability to do mathematics. <<Click to next slide>>

Implementation & Communications Strategy Our next steps: Moving Math Education Forward summer workshops (Sisters, LaGrande, Ashland, Eugene, & McMinnville) Monthly webinars (beginning fall 2009) Standards “connections’ and other guidance documents (by winter 2009) Teachers will receive guidance & assistance through these implementation plans. Will utilize TOSAs, other math org. partners to help create these items.

Why these standards? Are they the right ones?