# Data Handling and Graphical Representation

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```					Data Handling and Graphical
Representation

Hannah O'Donoghue

Hannah O'Donoghue   1
Motivation
 Always been enthusiastic about the
sciences
 Worked in schools and saw the
enthusiasm when studying data
handling – capture it!
Graphs   are very ‘real’

Hannah O'Donoghue     2
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’

Hannah O'Donoghue          3
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

Hannah O'Donoghue           4
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
Hannah O'Donoghue          5
Development of ideas cont…
   Cont…
– Fourteenth century Nicole Orseme
began representing time and velocity by
lengths and distance by area
– 1600’s 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
Hannah O'Donoghue         6
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.
Hannah O'Donoghue                7
National Curriculum
   Level 1: Pupils sort objects and classify them, demonstrating
the criterion they have used.

Hannah O'Donoghue                        8
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.

Hannah O'Donoghue                               9
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.

Hannah O'Donoghue                                      10
Tools Developed at A-level
   Development of characteristics of
graphs
y=mx

0

y=mx+a              y=m(x-b)
a

0                  0     b
y=sin(x)   y=cos(x)

Hannah O'Donoghue                    11
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?

Hannah O'Donoghue              12
How Will This Assist in
   Statistics
– Modelling data
– Looking for outliers
   Dynamical Systems
– Display equilibrium solutions to non linear
dynamical systems
   Mathematical Biology
– Describe the behaviour of biological systems

Hannah O'Donoghue              13
Real – Life?

Hannah O'Donoghue   14

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 views: 26 posted: 4/10/2012 language: English pages: 14