Making Math Success Happen

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Making Math Success Happen

• The Best of Learning and Leading
• With Technology on Mathematics
• Ivan W. Baugh
• Anne Raymond
• ISTE Publications

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

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And the NCTM Technology Principle Technology
is essential in teaching and learning
mathematics it influences the mathematics that
is taught and enhances students 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.

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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

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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

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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.
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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.
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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.
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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

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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

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Assigned Readings

• NCTM Conference Anyone interested?

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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
  students 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

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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

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In-Class ActivityBottles and Beyond

• Skills
• Measurement
• Graphing
• Drawing
• Software
• MS Draw
• MS Excel

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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

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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

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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.

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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!)

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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

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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
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Assigned ReadingISTE Standards

• www.iste.org
• http//cnets.iste.org.index2ns.html

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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

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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.

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ActivityLeonards Proportions

• Skills
• Measurement
• Data entry
• Formulas proportions
• Software
• MS Excel
• Student Data Sheet

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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)

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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

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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

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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

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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

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Two important issues

• Via technology, problem solving can focus on
  more real-life issues and on the process of
  problem solvingrather 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)

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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