Data Handling and Graphical Representation

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Data Handling and Graphical Representation

• Hannah O'Donoghue

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Motivation

• Always been enthusiastic about the sciences

• Worked in schools and saw the enthusiasm when
  studying data handling capture it!

• Graphs are very real

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Project Goals

• To validate the importance of developing
  graphical literacy in schools
• Illustrate the full scope of graphs in all areas
  of education and study
• Show that learning these skills is not a waste
  of time

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Graphs and Data Handling

• Graph
• gräf n. a symbolic diagram a drawing depicting
  the relationship between two or more variables
• Data
• known facts used for inference or in reckoning

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History of Graphs

• Relatively new topic not before eighteenth
  century
• Clear development of ideas
• Study of area at Pythagorean School
• Greek geometers used the geometrical diagram to
  represent some physical quantities
• Maps

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Development of ideas cont

• Cont
• Fourteenth century Nicole Orseme began
  representing time and velocity by lengths and
  distance by area
• 1600s maps began to contain data
• Newton and Leibniz did extensive work on v-t
  graphs, developed useful tool
• William Playfair published first time series
  graph

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Importance of Developing Graphical Literacy

• Of recent years there has been a great reform in
  respect to graphs. But at its present stage it
  has either gone too far or not far enough. It is
  not enough merely to draw a graph. The idea
  behind the graph - like the man behind the gun -
  is essential in order to make it effective. At
  present there is some tendency merely to set the
  children to draw curves, and then to leave
  it.Alfred North Whitehead, 1932

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National Curriculum

• Level 1 Pupils sort objects and classify them,
  demonstrating the criterion they have used.

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More Levels

• Level 2 Pupils sort objects and classify them
  using more than one criterion. When they have
  gathered information, pupils record results in
  simple lists, tables and block graphs, in order
  to communicate their findings.
• Level 4 Pupils collect discrete data and record
  them using a frequency table. They understand and
  use the mode and range to describe sets of data.
  They group data, where appropriate, in equal
  class intervals, represent collected data in
  frequency diagrams and interpret such diagrams.
  They construct and interpret simple line graphs.

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More levels

• Level 5
• Pupils understand and use the mean of discrete
  data.
• They compare two simple distributions, using the
  range and one of the mode, median or mean.
• They interpret graphs and diagrams, including pie
  charts, and draw conclusions.
• They understand and use the probability scale
  from 0 to 1.
• Pupils find and justify probabilities, and
  approximations to these, by selecting and using
  methods based on equally likely outcomes and
  experimental evidence, as appropriate.
• They understand that different outcomes may
  result from repeating an experiment.
• Level 6
• Pupils collect and record continuous data,
  choosing appropriate equal class intervals over a
  sensible range to create frequency tables.
• They construct and interpret frequency diagrams.
• Pupils have a basic understanding of correlation.
  
• When dealing with a combination of two
  experiments, pupils identify all the outcomes.
• In solving problems, they use their knowledge
  that the total probability of all the mutually
  exclusive outcomes of an experiment is 1.

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Tools Developed at A-level

• Development of characteristics of graphs

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More Tools

• Calculus
• Determination of what gradient and area can
  represent and how we can calculate this
  properties on a curve
• Turning points, increasing and decreasing
  functions
• IT
• Use of spreadsheets, databases, data handling
  programmes
• Internet?

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How Will This Assist in Advanced Mathematics?

• Statistics
• Modelling data
• Looking for outliers
• Dynamical Systems
• Display equilibrium solutions to non linear
  dynamical systems
• Mathematical Biology
• Describe the behaviour of biological systems

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Real Life?