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MathematicsPractices
and Progressions
Jean Howard, OPI Mathematics Curriculum Specialist
August2011
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NWhat 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 . . .
Mathematical rigor
◦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.
Rigor is a process where students:
1. Make sense of complex problems and persevere in solving them.
2. Reason abstractly and quantitatively3. 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.
Standards for (Student) Mathematical Practice
(CCSS, 2010)
NCTM – Principles & Standards for School Mathematics
Process Standards
The five standards address the processes of
Problem solving Reasoning and proof Connections Communication Representation
Intertwined Strands of Proficiency
Adding It Up: Helping Children Learn MathematicsBy Jeremy Kilpatrick, Jane Swafford, & Bob Findell (Editors). (2001).Washington, DC: National Academy Press
p. 117
Integration of Practices for Rigor and Relevance
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
Grade Level Overview Page
(McCallum, 2011)
Grouping the Standards for Mathematical Practices
McDonald’s ClaimWikipedia 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)
Standards for Mathematical Practice in a Classroom
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)
Standards for Mathematical Practice in a Classroom
Math Class Makeover (10 min)
Curriculum Makeover (5 min)
Linking Content and Practices (AZ)
Standards for Mathematical Practice by Grade Level
Consider the description of the Practices within the document and discuss within grade and/or grade band groups the following questions:
Reflection
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?
BREA
K
FOCUS
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
Critical Areas Warm-up
How will it improve teaching and learning when each grade focuses on a few Critical Areas?
Grade level
PK
K 1 2 3 4 5 6 7 8
# of Critical Areas
2 2 4 4 4 3 3 4 4 3
Course
Alg I Geo Alg II Math I
Math II
Math III
# of Critical Areas
4 6 4 6 5 4
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.
Examine Critical Areas
Relate content standards to Critical Areas
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.
ReflectionHow 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 Instructionhttp://www.opi.mt.gov/Curriculum/Index.html?gpm=1_7#gpm1_7 Resource on Wikihttp://ccssmtteam.wikispaces.com/message/list/home
◦ Other states◦ Blogs◦ Assessment◦ Projects◦ Reports, Articles, Documents◦ Presentations◦ Miscellaneous
Tools You Can Use
