Transcript NSW Curriculum and Learning Innovation Centre

NSW Curriculum and Learning Innovation Centre
Tinker with Tinker Plots
Elaine Watkins, Senior Curriculum Officer, Numeracy
Graphs in the curriculum
• Graphs play a significant role in the mathematics
curriculum, providing visual means of presenting
information.
• The visual representations provide numerical, pictorial,
and statistical information by combining symbols, points,
lines, numbers, shading and colour (Tufte, 1983) with the
aim of conveying information quickly and efficiently.
• Students should have the experience to create graphs
with and without technology, so that they can explain
what they have created and draw conclusions from the
representations.
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Comparison of Syllabus Outcomes
2002 Syllabus – Key ideas
Chance and Data
Collect data
about students &
their
environment
Organise actual
objects or
pictures
of the objects
into a data
display
Interpret data
displays made
from objects and
pictures
Stage 1
Gather & record data
using tally marks
Display the data using
concrete materials &
pictorial representations
Use objects or pictures as
symbols to represent
other objects, using oneto-one correspondence
Interpret information
presented in picture
graphs & column graphs
Recognise the element of
chance in familiar daily
events
Use familiar language to
describe the element of
chance
Early Stage 1
Statistics and probability
Early Stage 1
Draft Syllabus
Stage 1
Uses concrete materials
and/or pictorial
representations to support
conclusions
Supports conclusions by
explaining or demonstrating
how answers were obtained
(data1 & data 2)
Represents data & interprets
data displays made from
objects & pictures
Gathers & organises data,
representing data in column &
picture graphs, & interprets the
results
(data 1 & data 2)
Uses objects, diagrams &
technology to explore
mathematical problems
(data 2)
Describes mathematical
situations using everyday
language, actions, materials
and informal recordings
Describes mathematical
situations & methods using
everyday & some mathematical
language, actions, materials,
diagrams and symbols
(data 1 & data 2)
NSW Curriculum and Learning Innovation Centre
Comparison of Syllabus Outcomes
Draft Syllabus
Stage 2
Stage 3
Stage 2
Data 1 & 2
Stage 3
Data 1 & 2
Conduct surveys,
classify & organise data
using tables
Draw picture, column, line
& divided bar graphs using
scales of many-to-one
correspondence
Uses appropriate
terminology to
describe, & symbols
to represent,
mathematical ideas
Describes & represents
mathematical situations in
a variety of ways using
mathematical terminology
& some conventions
Construct vertical &
horizontal column
graphs& picture graphs
Read & interpret sector (pie)
graphs
Gives a valid reason for
supporting one possible
solution over another
Interpret data presented
in tables, column
graphs and picture
graphs
Read & interpret graphs
with scales of many-to-one
correspondence
Selects & uses
appropriate mental or
written strategies, or
technology to solve
problems
Checks the accuracy
of a statement &
explains the
reasoning used
Uses appropriate data
collection methods,
constructs & interprets
data displays & analyses
sets of data
Determine the mean
(average) for a small set of
data
Explore all possible
outcomes in a simple
chance situation
Conduct simple chance
experiments
Collect data & compare
likelihood of events in
different contexts
Assign numerical values to
the likelihood of simple
events occurring
Order the likelihood of
simple events on a number
from 0 to 1
Statistics & probability
Chance and data
2002 Syllabus – Key ideas
Selects appropriate
data collection
methods &
constructs, compares
& interprets data
displays
NSW Curriculum and Learning Innovation Centre
What is Tinker Plots?
• Tinker Plots is a data analysis program designed to enable students
in grades 4–8 to get excited about what they can learn from data.
• The students will analyse data by creating colourful visual
representations that will help the students make sense out of real
data and recognize patterns as they unfold.
• Students can use Tinker Plots to produce reports that include
graphs, along with text that explains their findings and even photos
they take or locate on the Internet.
• Students can manipulate data and learn what the relationships
mean.
NSW Curriculum and Learning Innovation Centre
How can Tinker plots be used?
Students can use Tinker plots to:
• construct dot plots for numerical data
• consider the data type to determine & draw the most appropriate display for
the data, including column graphs, dot plots and line graphs
• name & label the horizontal & vertical axes when constructing graphs
• tabulate collected data, including numerical data with & without the use of
digital technologies such as spreadsheets
• discuss & draw conclusions from different data displays
• interpret information presented in two-way tables
• create a two-way table to organise data involving two categorical variables
• interpret & compare different displays of the same data
• interpret data representations found in digital media and in factual texts.
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What is a stacked dot plot?
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A stacked dot plot is a way of representing numerical data.
They are ideal for making comparisons of data.
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Table group task using a stacked dot plot
• As a table group collect data to create a stacked dot plot.
• Write down your height (estimate if not known), and shoe
size.
• As a whole group, determine an appropriate scale for
creating a stacked dot plot.
• Use a paper streamer for the scale and the coloured
dots to create a stacked dot plot to represent the data
you collected.
• Label the stacked dot plot.
• What questions could you ask about your graph and
data?
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Features of a stacked dot plot
Features include:
• An automatic sorting of data - once the axis is chosen
the data points can be plotted in any order but are
actually sorted by the plotting process.
• A good choice of scale in a dot plot can make the shape
of the data clearer
• Easy identification of the range and highlighting of
extreme values (‘outliers’).
• Reveals any peaks and/or mode/s in the data.
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Looking at data in Tinker Plots
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Importing data from Excel spreadsheet
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Stacked dot plots - teaching implications
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Use real data, relevant to the students
Students need to determine an appropriate scale from the data collected.
Identify the lowest score and the highest score.
In a stacked dot plot, the dots must align vertically and horizontally.
Example of a poor stacked dot plot
Stacked dot plots only give a good pictorial representation of frequency when
the 'dots' are aligned.
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Stacked dot plots - teaching implications
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The graph and the axis need to be labelled.
Is the data accurate? Look at outliers.
Students should be able to describe what the stacked dot plot shows about
the data
Introduce statistical terminology to assist students to describe their data
(e.g. mode, median, range, mean, outlier)
When comparing two stacked dot plots, have the same range and scale on
the axis
NSW Curriculum and Learning Innovation Centre
Resource to support the statistics and probability strand
• This report focuses on the
application of graphs for
portraying data, and their
potential as instruments for
reasoning about quantitative
information.
• Available from
• http://www.curriculumsupport.e
ducation.nsw.gov.au/primary/m
athematics/resources/data/ind
ex.htm