Exploring the Possibilities: Teaching and Learning Mathematics with Technology

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Exploring the Possibilities Teaching and
Learning Mathematics with Technology

• Carly Hall
• CEP 805
• Fall 2004

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NCTM Principles

• Equity High expectations and support for all
  students
• Curriculum Activities that are coherent,
  focused on important content, and articulated
  across grade levels
• Teaching - Requires understanding of student
  knowledge, what needs to be learned, and when to
  challenge and provide support

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NCTM Principles (continued)

• Learning Students learn and understand by
  actively building new knowledge through
  experience and prior knowledge.
• Assessment Supports learning and provides
  useful information
• Technology Essential in influencing and
  enhancing learning

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NCTM Strands Explored

• Number Operation
• Algebra
• Geometry
• Data Analysis Probability
• Problem Solving

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Affordances of Technology

• Providing Access to information
• Automating, simplifying, and transforming tasks
• Representing knowledge and thinking
• Communicating and collaborating with peers and
  experts

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Number Operations Standard Grade 3-5 and 6-8

• Understand numbers, ways of representing numbers,
  relationships among numbers, and number systems
• Understand meaning of operations and how they
  relate to one another
• Compute fluently and make reasonable estimate

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What This Looks like in a Grades 3-5 Classroom

• Students continue to develop number sense
  with an emphasis on multiplication and division.
  They work with larger number, fractions, and
  decimals using models and other strategies. They
  look at the relationship between multiplication
  and division and the types of problems that can
  be solved with these operations. Students compute
  whole numbers, develop algorithms, often using
  estimation, and selecting the appropriate
  computational tool.

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What This Looks Like in a Grades 6-8 Classroom

• Students build on prior number sense knowledge
  to broaden their understanding with more complex
  numbers and operations They divide fractions and
  decimals, use place value to extend their
  understanding of whole number addition and
  subtraction to decimals by examining and using
  properties of operations. Students examine
  whether an exact answer or an estimate is
  appropriate, determine the reasonableness of
  their answers, and choose methods in which to
  solve the problem.

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Examples of Technology

• Tools for Understanding Website
• Using spreadsheets to explore Number and
  Operation concepts
• - Lowest Common Multiple Activity
• - Prime, Composite, and Square Number Activity

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Algebra Standard for Grades 3-5 and 6-8

• 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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What This Looks Like in a Grade 3-5 Classroom

• Students begin to develop emerging algebraic
  ideas that serve as a precursor to grades 6-8.
  They build numerical and geometric patterns, look
  for and apply relationships between quantities,
  make generalizations, use graphs to describe
  patterns or make predictions, explore number
  properties, and use invented notation, symbols
  and variables to express a situation.

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What This Looks Like in a Grade 6-8 Classroom

• Students make more use of algebraic symbols,
  represent patterns related to linear functions,
  use tables, graphs words and expressions to
  examine and represent patterns of change, such as
  comparing and contrasting sets of data to two
  different representations of the same data. They
  also use formulas, and analyze change in
  graphical representations. All of this serves as
  a precursor to calculus. Student use of graphing
  calculators and computer software is also more
  prevalent in this grade span.

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Examples of Technology

• SimCalc
• Magic Squares Lesson
• Mangoes Problem Lesson
• - From NCTMs Illuminations website
  (http//illuminations.nctm.org)

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Geometry StandardGrades 3-5 and 6-8

• 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

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Geometry StandardGrades 3-5 and 6-8 (continued)

• Apply transformations and use symmetry to analyze
  mathematical situations
• Use visualization, spatial reasoning, and
  geometric modeling to solve problems

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What This Looks Like in a Grade 3-5 Classroom

• Students describe and classify geometric
  objects and sort, build, draw, trace, measure,
  and construct geometric relationships. They
  construct mathematical arguments and expand
  vocabulary. Students learn about location,
  direction and distance on the coordinate plane.
  They explore transformations and reason about
  spatial relationships.

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What This Looks Like in a Grade 6-8 Classroom

• Students build on their knowledge of two-and
  three-dimensional shapes, visualizing figures
  from their experience with interacting with these
  objects in their daily lives. They explore a
  variety of geometric shapes and examine their
  characteristics using different types of
  manipulatives or geometry software. Students
  investigate congruence and similarity, draw
  representations of figures on the coordinate
  plane, and interpret shapes through
  transformations, They visualize spatial
  relationships by analyzing views of solid figures
  and using models to represent relationships.

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Examples of Technology

• Geometers Sketchpad
• Symmetry and Pattern The Art of Oriental Carpets
  (http//mathforum.org/geometry/rugs/symmetry)
• Getting It Right- The Pythagorean Theorem
  (http//cnets.iste.org/students/pf/pf_get_it_right
  .html)

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Data Analysis Probability Standard Grades 3-5
and 6-8

• 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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What This Looks Like in a Grade 3-5 Classroom

• Students build on their experiences with data
  to seeing a set of data as a whole, describing
  its shape, and using statistical characteristics
  to compare sets of data. They should pose
  questions relevant to themselves and their
  environment, become familiar with representations
  of data and construct graphs. Students use data
  to make inferences and predictions. They learn
  that probability is is a measurement of the
  likelihood of events and explore experiences to
  determine outcomes.

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What This Looks Like in a Grade 6-8 Classroom

• Students formulate questions, design surveys,
  and compare data to build upon their knowledge of
  collecting, organizing, and representing data.
  They use and interpret measures of central
  tendency and explore more complex graphical
  representations such as histograms, stem-and-leaf
  plots, and scatterplots. Questions are answered
  based on data representations and comparisons
  made between data sets. Students also use the
  idea of chance and number theory to examine and
  describe events.

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Examples of Technology

• Tools for Understanding Website
• (Using spreadsheets to explore Data Analysis)
• - Soda Survey Activity

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Problem Solving Standard for Grades 3-5 and 6-8

• 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
• At each grade span, students should have
  experiences with problems that interest,
  challenge, and engage their thinking.

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Examples of Technology

• Jasper Software that allows students to solve
  problems given a real-life scenario while using
  various skills found in each content area of
  mathematics.
• (http//peabody.vanderbilt.edu/projects/funded/ja
  sper/)

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Summary

• Using the NCTM standards and the affordances
  of technology as the basis for planning
  instruction, teachers have a wide variety of
  technology resources to explore for engaging
  students in meaningful, relevant, and interactive
  learning. The possibilities are endless!