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The Standards for Mathematical Practice
2010 Alabama Course of Study: Mathematics
College- and Career-Ready Standards
Standards for Mathematical Practice
“The Standards for Mathematical Practice describe
varieties of expertise that mathematics educators at all
levels should seek to develop in their students. These practices rest on important “processes
and proficiencies” with longstanding importance in mathematics education.”
(CCSS, 2010)
Underlying Frameworks
National Council of Teachers of Mathematics
NCTM (2000M). Principles and Standards for School Mathematics.
Reston, VA: Author.
5 PROCESS Standards
•Problem Solving•Reasoning and Proof•Communication•Connections•Representations
Underlying Frameworks
Strands of Mathematical Proficiency
NRC (2001). Adding It Up. Washington, D.C.: National
Academies Press.
• Conceptual Understanding• Procedural Fluency • Strategic Competence• Adaptive Reasoning• Productive Disposition
National Research Council
Standard 1: Make sense of problems and persevere in
solving them.Standard 2: Reason abstractly and quantitatively.Standard 3: Construct viable arguments and critique
the reasoning of others.Standard 4: Model with mathematics.Standard 5: Use appropriate tools strategically.Standard 6: Attend to precision.Standard 7: Look for and make use of structure.Standard 8: Look for and express regularity in repeated
reasoning.
The Standards for Mathematical Practice
Mathematically proficient students:
1. What student behaviors are included in this standard?
2. What type of activities could help my students develop this behavior?
Adapted from Kathy Berry, Monroe County ISD, Michigan
QUESTIONS TO CONSIDER…
Analyze givens, constraints, relationships Make conjectures Plan solution pathways Make meaning of the solution Monitor and evaluate their progress Change course if necessary Ask themselves if what they are doing
makes sense
Standard 1: Make sense of problems and persevere in solving them.What do mathematically proficient students do?
Make sense of quantities and relationships Able to decontextualize
◦ Abstract a given situation◦ Represent it symbolically◦ Manipulate the representing symbols
Able to contextualize◦ Pause during manipulation process◦ Probe the referents for symbols involved
Standard 2: Reason abstractly and quantitatively. What do mathematically proficient students do?
Construct arguments Analyze situations Justify conclusions Communicate conclusions Reason inductively Distinguish correct logic from flawed logic Listen to/Read/Respond to other’s
arguments and ask useful questions to clarify/improve arguments
Standard 3: Construct viable arguments and critique the reasoning of others. What do mathematically proficient students do?
Apply mathematics to solve problems from everyday life situations
Apply what they know Simplify a complicated situation Identify important quantities Map math relationships using tools Analyze mathematical relationships to draw
conclusions Reflect on improving the model
Standard 4: Model with mathematics. What do mathematically proficient students do?
Consider and use available tools Make sound decisions about when different
tools might be helpful Identify relevant external mathematical
resources Use technological tools to explore and
deepen conceptual understandings
Standard 5: Use appropriate tools strategically. What do mathematically proficient students do?
Communicate precisely to others Use clear definitions in discussions State meaning of symbols consistently and
appropriately Specify units of measurements Calculate accurately & efficiently
Standard 6: Attend to precision. What do mathematically proficient students do?
Discern patterns and structures Use strategies to solve problems Step back for an overview and can shift
perspective
Standard 7: Look for and make use of structure. What do mathematically proficient students do?
Notice if calculations are repeated Look for general methods and shortcuts Maintain oversight of the processes Attend to details Continually evaluates the reasonableness of
their results
Standard 8: Look for and express regularity in repeated reasoning. What do mathematically proficient students do?
The Standards for [Student] Mathematical Practice
SMP1: Explain and make conjectures…SMP2: Make sense of…SMP3: Understand and use…SMP4: Apply and interpret…SMP5: Consider and detect…SMP6: Communicate precisely to others…SMP7: Discern and recognize…SMP8: Note and pay attention to…
www.insidemathematics.org
This task gives students the chance to:
• Find relationships between graphs, equations, tables, and rules.
• Explain reasoning for answers.
Algebra Task 3 Sorting Functions
Algebra Task 3 Sorting Functions
Algebra – 2008 Copyright © 2008 by Noyce Foundation. All rights reserved.The information provided in the following slides is for professional development only.
The mathematics of this task: Making connections between different
algebraic representations: graphs, equations, verbal rules, and tables
Understanding how the equation determines the shape of the graph
Developing a convincing argument using a variety of algebraic concepts
Being able to move from specific solutions to thinking about generalizations
Algebra – 2008 Copyright © 2008 by Noyce Foundation. All rights reserved.
Standard 1: Make sense of problems and persevere in
solving them.Standard 2: Reason abstractly and quantitatively.Standard 3: Construct viable arguments and critique
the reasoning of others.Standard 4: Model with mathematics.Standard 5: Use appropriate tools strategically.Standard 6: Attend to precision.Standard 7: Look for and make use of structure.Standard 8: Look for and express regularity in repeated
reasoning.
The Standards for Mathematical Practice
Mathematically proficient students:
The Standards for [Student] Mathematical Practice
“Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.”
Stein, Smith, Henningsen, & Silver, 2000
“The level and kind of thinking in which students engage
determines what they will learn.”Herbert, Carpenter, Fennema, Fuson, Wearne, Murray, Oliver, & Human, 1997
But, WHAT TEACHERS DO with the tasks matters too!
The Mathematical Tasks Framework
Tasks as they
appear in
curricular
materials
Tasks are set up by
teachers
Tasks are
enacted by
teachers and
students
Student Learnin
g
Stein, Grover, & Henningsen (1996)Smith & Stein (1998)
Stein, Smith, Henningsen, & Silver (2000)
Standards for [Student] Mathematical Practice
The Standards for Mathematical Practice place an emphasis on
student demonstrations of learning…
Equity begins with an understanding of how the selection of tasks, the assessment of tasks,
and the student learning environment create inequity in our
schools…
Leading with theMathematical Practice
StandardsYou can begin by implementing the 8 Standards for Mathematical Practice now
Think about the relationships among the practices and how you can move forward to implement BEST PRACTICES
Analyze instructional tasks so students engage in these practices repeatedly
Contact Information
ALSDE Office of Student LearningCurriculum and Instruction
Cindy Freeman, Mathematics Specialist Phone: 334.353.5321
E-mail: [email protected]