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Best Practices PPT - Math

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- 1. I.<br />Mathematics ~ Best PracticesNorthwood High School<br />
- 2. I.I<br />NCTM Standards<br /> “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)<br />
- 3. Grades 9-12 Mathematics <br />Number and Number Relations<br />Understand numbers, ways of representing numbers, relationships among numbers, and number systems<br />Understand meanings of operations and how they relate to one another<br />Compute fluently and make reasonable estimates <br />Algebra<br />Understand patterns, relations, and functions <br />Represent and analyze mathematical situations and structures using algebraic symbols<br />Use mathematical models to represent and understand quantitative relationships <br />Analyze change in various contexts <br />Measurement<br />Understand measurable attributes of objects and the units, systems, and processes of measurement <br />Apply appropriate techniques, tools, and formulas to determine measurements <br />Geometry<br />Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships <br />Specify locations and describe spatial relationships using coordinate geometry and other representational systems <br />Apply transformations and use symmetry to analyze mathematical situations <br />Use visualization, spatial reasoning, and geometric modeling to solve problems <br />Data Analysis, Probability, and Discrete Math<br />Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them <br />Select and use appropriate statistical methods to analyze data <br />Develop and evaluate inferences and predictions that are based on data<br />Understand and apply basic concepts of probability <br />Problem Solving, Reasoning & Proof, Communication, Connections, and Representation<br />build new mathematical knowledge, apply and adapt strategies, and monitor and reflect on the process of problem solving <br />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. <br />understand how mathematical ideas interconnect and build on one another to produce a coherent whole <br />recognize and apply mathematics in contexts outside of mathematics<br />select, apply, and translate among mathematical representations to solve problems and create and use representations to organize, record, and communicate mathematical ideas <br />use representations to model and interpret physical, social, and mathematical phenomena. <br />I.II<br />NCTM Standards - Summarized<br />Through Content & Process, Students will:<br />Learn to value all mathematicsBecome confident in the ability to do mathBecome mathematical problem solversLearn to reason mathematically<br />
- 4. I.III<br />The NCTM Standards Overview<br />Students should:<br />“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)<br />
- 5. “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.”<br /> (National Council for Accreditation of Teacher Education, 2010)<br />Researched-Based Strategies<br />I.IV<br />
- 6. Qualities of Best Practice Strategies<br />II.I<br />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:<br />Connected to standards<br />Reflect high expectations<br />Connected to students’ lives & cultures<br />Make learning interactive<br />Connect math to other disciplines<br />Teach math in context<br />Use mathematical modeling”<br /> (Principal’s Partnership, 2010)<br />
- 7. II.II<br />Best Practices Drive:InterestCuriosity FlexibilityThinking<br /> (Brad Fountain, Discovery Education, 2009)<br />
- 8. Best Practices Relate To Their World<br />II.III<br />(Browne, D., 2007)<br />
- 9. Researched-Based Strategies<br />II.IV<br />…using manipulatives and activities to motivate students…<br />Hands On Learning<br />using manipulatives and activities to<br />From Doing What Works at U.S. D.O.E. website: dww.ed.gov<br />
- 10. II.V<br />Teacher<br />Students<br />Students<br />What Do Best Practices Look Like?<br />What Do Best Practices SoundLike?<br />Teacher<br />Students<br />?<br />?<br />?<br />Teacher<br />
- 11. III.I<br />Best Practices Approaches<br />A constructivist approach which provides students with opportunities for active mental engagement<br />Peer groups help each other master academic content <br />Challenging and rigorous<br />Collaborative discourse<br />Peer discovery promotes a synergistic group<br />An assessment approach and monitoring style which help keep students on task<br />
- 12. III.II<br />EXAMPLESStudent Centered - Real QuestionsExperiential – Active, Hands OnChallenging - Choices & Responsibility in Own LearningCognitive- HOTS & Self-MonitoringSocial -Interactive, ScaffoldingCollaborative - Cooperative Learning<br />
- 13. III.III<br />Student Centered Learning<br />Challenging & Rigorous<br /> Choices & responsibility in their own learning<br />Teacher as Facilitator<br />“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)<br />Video Example<br />Experiential-Active Hands On Exploration<br />
- 14. III.IV<br />
- 15. III.V<br />Cognitive<br />Self-Discovery<br />Students are actively engaged and exploring concepts<br />Higher Order Thinking<br />Teacher is framing questions to engage thought processes<br />Video Example<br />Students are expressing ideas freely<br />
- 16. III.VI<br />
- 17. III.VII<br />Social<br />Peer Interactions<br />Discussions are flowing among group members<br />Collaboration<br />Ideas are being exchanged with each other<br />Example<br />Respectful behavior among peers<br />
- 18. Best Practices Strategies<br />III.VIII<br />Collaboration<br />
- 19. IV.I<br />Exemplary Lesson<br />Questions & Activities are designed to guide lesson direction<br />Structured math stations<br />The students are expected to actively in developing knowledge<br />Mobility to move about the room & take ownership of the learning<br />The goal is to merge conceptual understanding and reasoning<br />Cooperative groups & Individual learning<br />
- 20. IV.II<br />Exemplary Lesson <br />Connections to other subject areas<br />Students relate to other lessons or interests<br />Using real-world, familiar materials<br />Board Games<br />Lunch Menus<br />Recipes<br />Are you surprised that this is in a 2nd Grade Classroom?<br /> Exemplary lessons can be adapted to all learners.<br />
- 21. V.I<br />“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<br />
- 22. V.II<br />Use Technology Tools to Involve All Stakeholders<br />Develop a Plan with Principals to Implement Best Practices<br />Use Websites to Inform (Pictures, Blogs, Wikis)<br />Create Partnerships with Community Businesses (Guest Speakers)<br />Involve Parents in Lessons (PBL, Digital Diaries)<br />Partner with Experts in the Field (NASA, Siemens)<br />Share Ideas and Information with other Educators<br />
- 23. V.III<br />Be Creative in Involving Parents in the Lesson or Project Assignment<br />
- 24. V.IV<br />“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.”<br />(Foundations for Success: The Final Report of the National Mathematics Advisory Panel, 2010)<br />
- 25. VI.I<br />References:<br />http://standards.nctm.org/document/chapter7/index.ht<br />http://dww.ed.gov/see/?T_ID=20&P_ID=50&c1=814&c2=832&c3=715#cluster-3<br />http://www.ncate.org/public/conc1.asp?ch=48<br />http://search.nap.edu/nap-cgi/skimchap.cgi?recid=9822&chap=313-368<br />http://www.principalspartnership.com/mathbrief.pdf<br />www.sfapowerteaching.org<br />
- 26. VI.II<br />References:<br />http://www.nap.edu/openbook.php?record_id=9822&page=329<br />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<br />http://epaa.asu.edu/epaa/v10n12/<br />Browne, D. (2007). Hagar the Horrible. The Shreveport Times, 2007, December 16.<br />Fountain, Brad (2009). Presentation from Discovery Education Virtual Conference held on April 2, 2009.<br />Zemelman, D., Daniels, H., & Hyde, A. (2005). Best practice: Today’s standards for teaching & learning in America’s schools (3rd Ed.). Portsmouth, NH: Heinemann.<br />

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