best practices math nsu mst
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Best Practices PPT - MathTRANSCRIPT
NHS Mathematics
Tompkins - 2010
Mathematics ~ Best PracticesNorthwood High School
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NHS Mathematics
Tompkins - 2010
NCTM Standards
“The Standards for high school students are ambitious. The demands made on high school teachers in achieving the Standards will require extended and sustained professional development and a large degree of administrative support.” (NCTM, 2010)
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NHS Mathematics
Tompkins - 2010
Grades 9-12 Mathematics
Number and Number Relations
Understand numbers, ways of representing numbers, relationships among numbers, and number systems
Understand meanings of operations and how they relate to one another
Compute fluently and make reasonable estimates
Algebra
Understand patterns, relations, and functions
Represent and analyze mathematical situations and structures using algebraic symbols
Use mathematical models to represent and understand quantitative relationships
Analyze change in various contexts
Measurement
Understand measurable attributes of objects and the units, systems, and processes of measurement
Apply appropriate techniques, tools, and formulas to determine measurements
Geometry
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
Specify locations and describe spatial relationships using coordinate geometry and other representational systems
Apply transformations and use symmetry to analyze mathematical situations
Use visualization, spatial reasoning, and geometric modeling to solve problems
Data Analysis, Probability, and Discrete Math
Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them
Select and use appropriate statistical methods to analyze data
Develop and evaluate inferences and predictions that are based on data
Understand and apply basic concepts of probability
Problem Solving, Reasoning & Proof, Communication, Connections, and Representation
build new mathematical knowledge, apply and adapt strategies, and monitor and reflect on the process of problem solving
analyze and evaluate the mathematical thinking and strategies of others, communicate mathematical knowledge to others and use the language of mathematics to express mathematical ideas precisely.
understand how mathematical ideas interconnect and build on one another to produce a coherent whole
recognize and apply mathematics in contexts outside of mathematics
select, apply, and translate among mathematical representations to solve problems and create and use representations to organize, record, and communicate mathematical ideas
use representations to model and interpret physical, social, and mathematical phenomena.
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NCTM Standards - Summarized
Through Content & Process, Students will:
Learn to value all mathematicsBecome confident in the ability to do mathBecome mathematical problem solversLearn to reason mathematically
NHS Mathematics
Tompkins - 2010
The NCTM Standards Overview
Students should:“Experience the interplay of algebra,
geometry, statistics, probability, and discrete mathematics. They need to understand the fundamental mathematical concepts of function and relation, invariance, and transformation. They should be adept at visualizing, describing, and analyzing situations in mathematical terms. And they need to be able to justify and prove mathematically based ideas.” (NCTM, 2010)
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NHS Mathematics
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“Students of teachers who conduct hands-on learning activities outperform their peers by more than 70 percent of a grade level in math and 40 percent of a grade level in science.”
(National Council for Accreditation of Teacher Education, 2010)
Researched-Based Strategies
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Qualities of Best Practice Strategies
According to a Research Brief from The Principal’s Partnership, “Exceptional high school math programs seem to share some or all of the following characteristics:
Connected to standardsReflect high expectationsConnected to students’ lives & culturesMake learning interactiveConnect math to other disciplinesTeach math in contextUse mathematical modeling” (Principal’s
Partnership, 2010)
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(Brad Fountain, Discovery Education, 2009)
Best Practices Drive:
Interest
Curiosity
Flexibility
Thinking
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NHS Mathematics
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Best Practices Relate To Their World
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(Browne, D., 2007)
NHS Mathematics
Tompkins - 2010From Doing What Works at U.S. D.O.E. website: dww.ed.gov
Hands On Learning
…using manipulatives and activities to motivate students…
Researched-Based Strategies
using manipulatives and activities to
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NHS Mathematics
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Teacher Students
TeacherStudents
Teacher Students
What Do Best Practices Look Like?What Do Best Practices Sound Like?
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NHS Mathematics
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Best Practices ApproachesA constructivist approach which provides
students with opportunities for active mental engagement
Peer groups help each other master academic content
Challenging and rigorousCollaborative discoursePeer discovery promotes a synergistic
groupAn assessment approach and monitoring
style which help keep students on task
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NHS Mathematics
Tompkins - 2010
EXAMPLES
Student Centered - Real QuestionsExperiential – Active, Hands On
Challenging - Choices & Responsibility in Own LearningCognitive- HOTS & Self-Monitoring
Social -Interactive, ScaffoldingCollaborative - Cooperative Learning
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NHS Mathematics
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Student Centered LearningChallenging & Rigorous
Choices & responsibility in their own learningTeacher as Facilitator“Teachers are responsible for moving the mathematics along
while affording students opportunities to offer solutions, make claims, answer questions, and provide explanations to their peers.”
(National Academies Press, 2010)
Video Example Experiential-Active Hands On Exploration
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NHS Mathematics
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NHS Mathematics
Tompkins - 2010
CognitiveSelf-Discovery
Students are actively engaged and exploring concepts
Higher Order ThinkingTeacher is framing questions to engage thought processes
Video ExampleStudents are expressing ideas freely
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NHS Mathematics
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SocialPeer Interactions
Discussions are flowing among group members
CollaborationIdeas are being exchanged with each other
ExampleRespectful behavior among peers
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NHS Mathematics
Tompkins - 2010
Best Practices Strategies
Collaboration
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NHS Mathematics
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Questions & Activities are designed to guide lesson directionStructured math stations
The students are expected to actively in developing knowledgeMobility to move about the room & take
ownership of the learning
The goal is to merge conceptual understanding and reasoningCooperative groups & Individual learning
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Exemplary Lesson
NHS Mathematics
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Connections to other subject areasStudents relate to other lessons or interests
Using real-world, familiar materialsBoard GamesLunch MenusRecipes
Are you surprised that this is in a 2nd Grade Classroom?
Exemplary lessons can be adapted to all learners.
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Exemplary Lesson
NHS Mathematics
Tompkins - 2010
“Mathematics classrooms are more likely to be places in which mathematical proficiency develops when they are communities of learners and not collections of isolated individuals.”
The National Academies Press
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NHS Mathematics
Tompkins - 2010
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Use Technology Tools to Involve All Stakeholders
Develop a Plan with Principals to Implement Best Practices
Use Websites to Inform (Pictures, Blogs, Wikis) Create Partnerships with Community
Businesses (Guest Speakers) Involve Parents in Lessons (PBL, Digital Diaries) Partner with Experts in the Field (NASA,
Siemens) Share Ideas and Information with other
Educators
NHS Mathematics
Tompkins - 2010
Be Creative in Involving Parents in the Lesson or Project Assignment
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NHS Mathematics
Tompkins - 2010
(Foundations for Success: The Final Report of the National Mathematics Advisory Panel, 2010)
“Teachers and other educational leaders should consistently help students and parents to understand that an increased emphasis on the importance of effort is related to improved mathematics performance.”
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NHS Mathematics
Tompkins - 2010
References: http://standards.nctm.org/document/chapter7/index.ht
http://dww.ed.gov/see/?T_ID=20&P_ID=50&c1=814&c2=832&c3=715#cluster-3
http://www.ncate.org/public/conc1.asp?ch=48
http://search.nap.edu/nap-cgi/skimchap.cgi?recid=9822&chap=313-368
http://www.principalspartnership.com/mathbrief.pdf
www.sfapowerteaching.org
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NHS Mathematics
Tompkins - 2010
References: http://www.nap.edu/openbook.php?record_id=9822&page=329
http://74.125.47.132/search?q=cache:Lff5c0y3jI8J:www.principalspartnership.com/mathbrief.pdf+research+based+exemplary+math+teaching&cd=8&hl=en&ct=clnk&gl=us&client=firefox-a
http://epaa.asu.edu/epaa/v10n12/
Browne, D. (2007). Hagar the Horrible. The Shreveport Times, 2007, December 16.
Fountain, Brad (2009). Presentation from Discovery Education Virtual Conference held on April 2, 2009.
Zemelman, D., Daniels, H., & Hyde, A. (2005). Best practice: Today’s standards for teaching & learning in America’s schools (3rd Ed.). Portsmouth, NH: Heinemann.
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