Technology and the Teaching of Mathematics

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Technology and the Teaching of Mathematics

• Margaret Rogan
• CEP 805
• December 2003

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Active Learners Are

• Engaging in various types of learning activities
  and interacting with other learners.
• Working hard and are independently motivated.
• Developing, building, or constructing knowledge
  and understanding.
• Involved in making sense of the world in which
  they finds themselves.
• People who learn by making sense of what they
  encounter.

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NCTM Principles

• Equity- There should be high expectations and
  support for all students.
• Curriculum- The curriculum must be coherent and
  well-focused, and consistent across the grades.
• Teaching- Effective teaching requires that the
  teacher understands what students know and what
  they need to learn.

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NCTM Principles

• Learning- Students must learn mathematics with
  understanding, actively building new knowledge.
• Assessment- Assessments should support the
  learning of important mathematics and furnish
  useful information to both teachers and students.
  
• Technology- Technology is essential in teaching
  and learning mathematics it influences the
  mathematics that is taught and enhances students'
  learning.

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NCTM Areas

• Geometry
• Number and Operations
• Data Analysis and Probability
• Algebra
• Problem solving
• Reasoning and proof
• Communication

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4 Affordances

• the ways in which technology offers or support
  certain things
• Providing access to information
• Automating, simplifying and transforming tasks
• Representing knowledge and thinking
• Communicating and collaborating with peers and
  experts

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Geometry Standards

• 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

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Geometry Technology

• What we already do
• Geoboard Activities
• E-lab activities from Harcourt Brace
• Mighty Math CD- Calculating Crew
• Mighty Math CD- Number Heroes
• Shape nets from the EMC

• What can we do now
• NCTM e-example Exploring Properties of
  Rectangles
• Create tables in Word to show number of faces,
  corners, and edges of geometric figures
• Geometers Sketchpad
• http//homepage.mac.com/efithian/geometry.html

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Number and Operation Standards

• 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

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Number and Operation Technology

• What we already do
• E-lab activities from Harcourt Brace
• Mighty Math CD- Calculating Crew
• Mighty Math CD- Number Heroes
• CD game- Math Blaster
• Calculators

• What can we do now
• NCTM e-example Communicating about Mathematics
  Using Games
• Expand CD game library to include Operation
  Neptune, Carmen San Diego Math Detective, Clue
  Finders Math

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Data Analysis and Probability Standards

• 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

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Data Analysis and Probability Technology

• What we already do
• Mighty Math CD- Calculating Crew
• Mighty Math CD- Number Heroes

• What can we do now
• NCTM e-examples
• Accessing and Investigating Data
• Collecting, Representing, and Interpreting Data
• Use Excel to organize data and construct various
  types of graphs

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Algebra Standards

• 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

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Algebra Technology

• What we already do
• Mighty Math CD- Calculating Crew
• Mighty Math CD- Number Heroes

• What can we do now
• NCTM e-example Understanding Distance, Speed,
  and Time Relationships
• Use Excel to create tables to find multiples,
  find the LCM of two numbers, or coordinates of an
  equation.
• SimCalc activities

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Problem Solving Standards

• build new mathematical knowledge through problem
  solving
• solve problems that arise in mathematics and in
  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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Problem Solving Technology

• What we already do
• Math Olympiad program as an after school club.

• What can we do now
• CD game Logical Journey of the Zoombinis.
• Jasper Project- use real world information to
  solve problems

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Reasoning and Proof Standards

• recognize reasoning and proof as fundamental
  aspects of mathematics
• make and investigate mathematical conjectures
• develop and evaluate mathematical arguments and
  proofs
• select and use various types of reasoning and
  methods of proof

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Reasoning and Proof Technology

• What we already do
• Ask students to justify the process that they
  follow.
• Ask probing questions about why they solve
  problems a certain way.

• What can we do now
• Use the Jasper program to help students learn to
  justify the choices that they make.

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Communication Standards

• organize and consolidate their mathematical
  thinking through communication
• communicate their mathematical thinking
  coherently and clearly to peers, teachers, and
  others
• analyze and evaluate the mathematical thinking
  and strategies of others
• use the language of mathematics to express
  mathematical ideas precisely

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Communication Technology

• What we already do
• Communicate with parents about learning by way of
  classroom web pages.

• What can we do now
• NCTM e-examples Communicating about Mathematics
  Using Games and Collecting, Representing, and
  Interpreting Data
• Allow students to communicate with other students
  about similar problems or with experts in the
  field.

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Technology We Have

• Hardware
• 40 iBook computers
• Wireless web connections
• Color Printer
• Black and White Printer

• Software
• KidPix
• Microsoft Office Suite- Excel, Word, Powerpoint
• Mighty Math- Calculating Crew
• Mighty Math- Number Heroes
• Math Blaster

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Technology to Invest in

• Network Assistant
• Logical Journey of the Zoombinis
• Jasper- advanced problem-solving
• SimCalc-
• Geometer Sketchpad

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References

• The National Council of Teachers of Mathematics,
  Inc.
• 1906 Association Drive, Reston, VA 20191-9988
• www.nctm.org