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Making Math Success Happen

Making Math Success Happen. The Best of Learning and Leading With Technology on Mathematics Ivan W. Baugh Anne Raymond ISTE Publications. Making Math Success Happen closely examines the use of technology in the teaching of mathematics – BEYOND USING A GRAPHING CALCULATOR.

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Making Math Success Happen

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  1. Making Math Success Happen The Best of Learning and Leading With Technology on Mathematics Ivan W. Baugh Anne Raymond ISTE Publications

  2. Making Math Success Happen closely examines the use of technology in the teaching of mathematics – BEYOND USING A GRAPHING CALCULATOR.

  3. The text is organized around the NCTM Standards: • Process Standards • Communication: Do mathematicians communicate? • Connections: Does mathematics relate to other curriculum content? • Problem Solving: Why is everything in mathematics a problem? • Reasoning and Proof: Are the results really evident? • Representation: Are pictures worth a thousand words?

  4. And the NCTM Technology Principle: “Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances student’s learning. • As essential tools for teaching and learning, calculators and computers: • provide visual images of mathematical ideas • facilitate organizing • compute efficiently and accurately • Further, when such tools are available students can focus more on mathematical process, such as decision making, reasoning and problem solving.

  5. And the ISTE Technology Standards for students which are centered around the six categories: • Basic operations and concepts • Social, ethical, and human isues • Technology productivity tools • Technology communications tools • Technology research tools • Technology problem-solving and decision-making tools

  6. And the ISTE Technology Standards for teachers which are centered around the six categories: • Technology operations and concepts • Planning and designing learning environments and experiences • Teaching, learning, and the curriculum • Assessment and evaluation • Productivity and professional practice • Social, ethical, legal, and human issues

  7. It is particularly important to ponder these issues when planning lessons that integrate technology into the mathematics pedagogy because appropriate technology should be a TOOL that encourages discourse and establishes an engaging learning environment.

  8. When students engage in mathematical problem solving, particularly when using technology as a tool for solving problems, they become mathematically empowered and gain a confidence that students may never achieve in a traditional mathematics classroom.

  9. This will require a significant philosophical change for many mathematics educators. They must stop teaching as they were taught and start teaching in a manner that enables students to master the concepts.

  10. Text Layout: • Conversation: Ann and Ivan introduce each NCTM standard • Theory into Practice: Ideas for incorporating the standard • Insight: Reflections on the standard • Articles: Field tested activities/lessons

  11. Chapter 1: Communication • Pictures express more than a thousand words • NETS Communication Standard 4 – Technology Communication tools: • Students use telecommunications to collaborate, publish, and interact with peers, experts, and other audiences • Students use a variety of media and formats to communicate information and ideas effectively to multiple audiences

  12. Assigned Readings • NCTM Conference – Anyone interested?

  13. NCTM Position Paper – Technology in the Learning and Teaching of Mathematics • Technology is an essential tool for teaching and learning mathematics effectively: it extends the mathematics that can be taught and enhances student’s learning • Teachers must be prepared to serve as knowledgeable decision makers in determining when and how their students can use these tools most effectively • Examples: • Square roots • Logs • Factoring

  14. NCTM Position Paper – Calculators in the Education of Youth • NCTM recommends the integration of calculators into the school mathematics program AT ALL GRADE LEVELS • Skill in estimation, both numerical and graphical, and the ability to determine if a solution is reasonable are essential elements for the effective use of calculators

  15. In-Class ActivityBottles and Beyond • Skills • Measurement • Graphing • Drawing • Software • MS Draw • MS Excel

  16. Summary • Insert your lesson plan • Expansions: • Hot tub graphs • Popcorn graphs • As the caterpillar crawls • Match the graph – Student generated data • Assignment – from the handout

  17. Additional Activities • The Spreadsheet – Absolutely Elementary • Offers ideas for enhancing spreadsheet presentations • Journaling with a Database • Offers ideas for writing journals • Teaching Students to Communicate Mathematically • Offers organizational techniques for mathematics communications • ANY OF THESE MAY BE USED AS A GUIDE FOR YOUR END OF SEMESTER PROJECT

  18. Chapter 2 - Connections • Mathematicians turned artist: • Lewis Carroll – Alice in Wonderland • Art Garfunkel – Simon and Garfunkel • Artists turned mathematicians: • M.C. Escher – geometric drawings • Benjamin Bennaker – architech of Washington D.C.

  19. NCTM Standard - Connections Instructional program from pre-kindergarten through grade 12 should enable all students to: • Recognize and use connections among mathematical idesa • Understand how mathematical ideas interconnect and build on one another • Recognize and apply mathematics in contexts outside of mathematics (commonly overlooked!)

  20. NETS Standard – Technology Research Tools • Students use technology to locate, evaluate and collect information from a variety of sources (web searching techniques to be discussed later) • Students use technology tools to process data and report results • Students evaluate and select new information resources and technological innovations based on the appropriateness to specific tasks

  21. NOWHERE does the math content become secondary – rather through making connections while learning skills, students associate the skills with daily life and better internalize them for future use

  22. Assigned ReadingISTE Standards • www.iste.org • http://cnets.iste.org.index2ns.html

  23. Activity – State Representatives • Skills: • Collect data from the WWW • http://www.census.gov/prod/2001pubs/c2kbr01-2.pdf • Formulas in Excel • Analyze results in writing • Software • WWW • MS Excel • MS Word

  24. Summary • Insert your lesson plan • Expansions: • Search for any other allocation methods • Which method(s) work best for your home state? • Increase/decrease the population of your home state and examine the effect on the allocation to the remaining states.

  25. ActivityLeonard’s Proportions • Skills: • Measurement • Data entry • Formulas – proportions • Software: • MS Excel • Student Data Sheet

  26. Summary • Insert your lesson plan • Expansions: • Search for additional data on the golden section (AKA The golden ration or the golden number) • Search for a biography of Leonardo Da Vinci (a good resource for the History of Math course) • Applications of the golden ration in Geometry (to be explored later using different software)

  27. Chapter 3 – Problem Solving Calls for reform repeatedly include the need to improve the teaching and learning of mathematics by engaging students in more problem-solving tasks

  28. George Polya • Understand the problem • Examine the information, Identify the question • Devise a Plan • Make a list, Draw a picture, Guess and check • Carry out the plan • Modify as needed • Look back • Make sure the answer is reasonable

  29. NCTM Standard • Build new mathematical knowledge through problem solving • Solve problems that arise in mathematics and other contexts • Apply and adapt a variety of appropriate strategies to solve problems • Monitor and reflect on the process of mathematical problem solving

  30. NET-S Standard • Students use technology resources for solving problems and making informed decisions • Students employ technology in the development of strategies for solving problems in the real world

  31. Two important issues • Via technology, “problem solving can focus on more real-life issues and on the process of problem solving…rather than the complicated mathematical computations. • Rather than teaching students about problem solving, educators need to think about teaching students via problem solving. (Masingila, Lester, and aymond, 2001)

  32. Guess and Check Method • Page 79 of the text – Problems on ticket sales and temperature conversion • Using the spread sheet – page 79 of text • Using a sequence and list on TI 83 • Using y-variables on TI 83

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