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 o.... ID: 712158
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The Standards for
Mathematical Practice
2010
Alabama Course of Study: Mathematics
College- and Career-Ready Standards
Slide2Standards 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)
Slide3Underlying 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
Slide4Underlying 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
Slide5Standard 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:
Slide6What does this standard look like in the classroom?
What will students need in order to do this?What will teachers need in order to do this?Adapted from Kathy Berry, Monroe County ISD, Michigan
Questions to consider…
Slide7Analyze givens, constraints, relationshipsMake conjectures Plan solution pathways
Make meaning of the solutionMonitor and evaluate their progressChange course if necessaryAsk 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?
Slide8Make sense of quantities and relationshipsAble to decontextualize
Abstract a given situationRepresent it symbolicallyManipulate the representing symbolsAble to contextualize
Pause during manipulation processProbe the referents for symbols involved
Standard 2
: Reason abstractly and quantitatively.
What do mathematically proficient students do?
Slide9Construct argumentsAnalyze situationsJustify conclusions
Communicate conclusionsReason inductivelyDistinguish correct logic from flawed logicListen 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
?
Slide10Apply mathematics to solve problems from everyday life situationsApply what they know
Simplify a complicated situationIdentify important quantitiesMap math relationships using toolsAnalyze mathematical relationships to draw conclusionsReflect on improving the model
Standard 4: Model with mathematics.
What do mathematically proficient students do?
Slide11Consider and use available toolsMake sound decisions about when different tools might be helpfulIdentify 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?
Slide12Communicate precisely to othersUse clear definitions in discussionsState meaning of symbols consistently and appropriately
Specify units of measurementsCalculate accurately & efficiently
Standard 6: Attend to precision.
What do mathematically proficient students do?
Slide13Discern patterns and structuresUse strategies to solve problemsStep back for an overview and can shift perspective
Standard 7
: Look for and make use of structure. What do mathematically proficient students do?
Slide14Notice if calculations are repeatedLook for general methods and shortcutsMaintain oversight of the processes
Attend to detailsContinually evaluates the reasonableness of their results
Standard 8: Look for and express regularity in repeated reasoning. What do mathematically proficient students do?
Slide15The 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…
Slide16CONNECTION and BALANCE
Slide17Slide18Slide19Draw Pattern 4 next to Pattern 3
.
See answer above.How many white buttons does Gita need for Pattern 5 and Pattern 6? Explain how you figured this out. 15 buttons and 18 buttons
How many buttons in all does
Gita
need to make Pattern 11? Explain how you figured this out.
34 buttons
Gita
thinks she needs 69 buttons in all to make Pattern 24. How do you know that she is NOT correct? How many buttons does she need to make Pattern 24?
73 buttons
Slide20Slide21Slide22Slide23Analyzing the Button Task
The Button Task was:
Scaffolded
Foreshadows linear relationships
Requires critical thinking skills
Did not suggest specific strategy
Slide24www.insidemathematics.org
Slide25The 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,
Henningtsen
& 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
Slide26But, 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 Learning
Stein, Grover, &
Henningsen
(1996)
Smith & Stein (1998)
Stein, Smith,
Henningsen
, & Silver (2000)
Slide27Standards 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 how the student learning environment create inequity in our schools…
Slide28Leading with theMathematical Practice Standards
You 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
Slide29?? Questions ??
Slide30ALSDE Office of Student Learning
Curriculum and Instruction SectionCindy Freeman, Mathematics Specialist Phone: 334.353.5321
E-mail: cfreeman@alsde.eduContact Information
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