Weather - its all around us and its always changing. This makes it a great resource for gathering and organizing data with graphs. Graphs help us organize information and data in an understandable way. In todays New Times we are surrounded by data, from sports statistics to politics to numbers presented in science textbooks. Graphs are the visual representations that focus on the relations between the objects of representation in terms of a part-whole structure. Koulaidis (p.1998) What are we trying to teach our students? 1. Collect and organize appropriate data 2. Represent the data graphically,
by selecting the appropriate graph 3. Read and interpret graphs 4. Evaluate and analyze information presented in graphs that are found in textbooks, newspapers, digital media, etc. Look for intent behind the graphic representation of the data. When students make graphs from data they collect, graph interpretation is easier and more interesting because it is based on actual experience with the numbers involved. The experience of interpreting their own graphs gives students the skills to interpret graphs made by others. Children begin by recording data, computing the range of data (the difference between two sets of data to give a sense of how spread out they are), and finding the central tendency (mean) to get an idea of a typical value. Day
Outside Temp (F) Inside Difference Temp (F) (Out minus In) (F) 1 80F 72F 8F sunny 2 71F 71F 0F
cloudy & rain 3 86F 73F 13F windy 4 89F 70F 19F sunny 5 79F
69F 10F cloudy 6 95F 80F 15F broken a/c Notes How do we help students decide which type of graph is best for the data? In the same way that educators use concept maps or graphic organizers, chapter outlines, webbing, and structured overviews to help students navigate text, so can graphs and charts be used as tools to organize and present data.
Circle map Double bubble Tree map Flow map Dealing with Data Line Graphs Pie Charts Bar Graphs Organizational Charts Column Graph Bar Graph 100 7
90 6 70 60 Series1 Series2 50 40 30 Temperature Temperature 80 5 Series2 Series1 4 3 20
2 10 1 0 1 2 3 4 5 6 7 0 20 40
Days 80 100 Days Line Graph Area Graph 100 100 90 90 80 80 70
70 60 Series1 Series2 50 40 30 Temperature Temperature 60 60 40 30 20 20 10
10 0 Series1 Series2 50 0 1 2 3 4 Days 5 6 7 1
2 3 4 Days 5 6 7 Vocabulary Needed for Decoding Graphs Key/legend (symbols) Axes (X, Y and Z) Gridlines Scale Data Labels Data Table 2 Dimension Variables and their relationships to each other Does the scale make a difference in how you react to the data? Do the graphs below show the same information?
Do the pictures suggest the same idea? Is one graph misleading? Temperatures Plummet 100 96 90 94 80 92 70 60 50 Series1 40 30 20 Temperature (F)
Temperature (F) Temperatures Stable 90 88 Series1 86 84 82 80 10 78 0 1 2 3 4
Days 5 6 7 1 2 3 4 5 Days Does the line graph tell you anything about the temperatures in between the times the readings were taken? 6 7
Where in the World is All the Water? Students were asked to guess what part of the total amount of water on Earth (unchanged since when the Earth was formed) is in the oceans, ice, groundwater, atmosphere (clouds) and lakes & rivers. QuickTime and a TIFF (LZW) decompressor are needed to see this picture. QuickTime and a TIFF (LZW) decompressor are needed to see this picture. The students then graphed their predictions against
the actual amounts, dramatically illustrating their misconceptions about Earths water sources. Pie Charts Distribution of Water in the World Where in the World is all the Water? 1000 900 mls of Water 800 700 600 1 Series1 Series2 500 400 2
3 4 300 5 200 100 0 1 2 3 4 5 Location of Water 1 = Oceans 3 = Groundwater 2 = Ice water 4 =Atmospheric water
5 = Lakes & River Back to temperature From simple to.. complex! Note: a example of nominalization used in the context of analyzing this type of data is rate of change of temperature Clues that something is fishy about a graph: 1. The axis should begin with zero so that the measurement scale is shown whole. 2. If one of the axes is not labeled, you do not really know what is being displayed. 3. The numbers are identified by their units. 4. The X to Y axis scaling is not fair, i.e. one axis has been stretched out.
Proportion of Page comprised of Images versus Words High Image High Image. Low Word Elementary School High Image. Moderate Word Middle School Moderate Image. High Word High School Low Image
Low Word High Word Juggling 2 variables at once What does this graph tell us? Do you believe the data? Who collected the data? Where and how were the temperatures taken? Predicting the Future Importance of titles and captions Human activities are changing the environment. Global temperatures have risen by 0.6 degrees Celsius in the last 200 years. Does scale make a difference in this graph?
This graph shows carbon dioxide emissions increasing the last 130 years. What kind of impact does the image have on the reader? Reader Beware! 1. Graphs have more impact than the raw data because they are visual. 2. Graphs represent interpretations of data. If the data has been specially selected, then the interpretation is only of the selected data. 3. Data can be plotted to create an impression of (or hide) a dramatic trend
when in fact the data does not support such an apparent change. 4. The creator of the graph can influence the impact of the information and therefore influence the viewer. What is the social cost of innumeracy and illiteracy? The inability to deal rationally with large numbers, or with the probabilities [and their graphic representations] associated with them, results in misinformed government policies, confused personal decisions, and an increased susceptibility to pseudo-sciences of all kinds. Paulos (1988) There are cases where there is no dishonesty involved, but where people are tricked into false results by a lack of understanding about what human beings can do to themselves in the way of being led astray by subjective efforts, wishful thinking or threshold interactions.
Cromer (1993) Why do we care about visual literacy? If our students do not understand and get meaning from visual information, they will be excluded, their point of view not considered, or they may even manipulated into believing something not in their best interest.
