Jean Howard, OPI Mathematics Curriculum Specialist August 2011

INSTRUCTION What does it look and sound like in classroom where all students are engaged in learning mathematics?

is an elusive term with multiple meanings. To a pure mathematician, rigor is a mark of excellence. To a K-12 educator, “rigorous” often means “difficult,” as in “AP calculus is rigorous.” In the Montana Standards for Mathematical Practices...

◦ approach mathematics with a disposition to accept challenge and apply effort; ◦ engage in mathematical work that promotes deep knowledge of content, analytical reasoning, and use of appropriate tools; and ◦ emerge fluent in the language of mathematics, proficient with the tools of mathematics, and empowered as mathematical thinkers.

1. Make sense of complex problems and persevere in solving them. 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. (CCSS, 2010)

Process Standards The five standards address the processes of  Problem solving  Reasoning and proof  Connections  Communication  Representation

Adding It Up: Helping Children Learn Mathematics By Jeremy Kilpatrick, Jane Swafford, & Bob Findell (Editors). (2001). Washington, DC: National Academy Press p. 117

 Not “Problem Solving Fridays”  Not “enrichment” for advanced students  Is a process, not just one correct answer  Student’s proficiency in Content and Practice standards is part of every lesson

(McCallum, 2011)

McDonald’s Claim Wikipedia reports that 8% of all Americans eat at McDonalds every day. In the US, there are approximately 310 million Americans and 12,800 McDonalds. Do you believe the Wikipedia report to be true? Create a mathematical argument to justify your position. (Briars, Feb 2011)

Traditional U.S. Problem Which fraction is closer to 1: 4/5 or 5/4 ? Same Problem integrating content and practice standards 4/5 is closer to 1 than is 5/4. Using a number line, explain why this is so. (Daro, Feb 2011)

Math Class MakeoverMath Class Makeover (10 min) Curriculum MakeoverCurriculum Makeover (5 min)

Consider the description of the Practices within the document and discuss within grade and/or grade band groups the following questions:

 How will incorporating the Standards for Mathematical Practice impact teaching and learning, including:  Planning for instruction?  Rigor?  Student learning as they progress through the grades?  How will you begin to integrate these practices in your classroom?

 There are typically two to four Critical Areas for instruction in the introduction for each grade level or course.  They bring focus to the standards at each grade by grouping and summarizing the big ideas that educators can use to build their curriculum and to guide instruction.

Critical Areas Warm-up  How will it improve teaching and learning when each grade focuses on a few Critical Areas? Grade level PKK # of Critical Areas CourseAlg IGeoAlg IIMath I Math II Math III # of Critical Areas

 Describe Critical Areas ◦ Read your grade level introduction about Critical Areas. ◦ Record the Critical Areas on individual Foldable. ◦ Complete Poster to share with whole group: use words and/or pictures to describe the focus for your grade level  Complete Explore Focus Through Critical Areas record sheet.

 Search for standards within a grade level (or course) that connect to a particular Critical Area ◦ √ when a standard strongly matches your Critical Area and ◦ ? when you are not sure  Group members share a brief summary of their focus Critical Area.

 How do the Critical Areas help organize and bring focus to your grade level standards?  How should we as a school (or district) use what we have learned today about Critical Areas in planning for the implementation of the new standards?

 Standards for Mathematical Practice  Inside Mathematics  Linking Content and Practices (Arizona)  Office of Public Instruction _7#gpm1_7  Resource on Wiki ◦ Other states ◦ Blogs ◦ Assessment ◦ Projects ◦ Reports, Articles, Documents ◦ Presentations ◦ Miscellaneous

Jean Howard (406)