# Interpreting graphs

Students often interpret graphs incorrectly because they do not consider the scale on each axis and may not think about the units involved. You could test this with some examples where the scale on the axes is different or the units are not what you might expect. Show familiar scientific graphs without a title, scale or axis labels and ask students what the graph could be showing. It is often helpful to students if you tell the story of the graph and relate this to the behaviour of the variables.

Show students unusual examples of graphs to represent scientific information including examples that may be distorted or misleading. Ask students what they think is the aim of the representation, is it informative or could it be misleading? Ask them what is good/bad about the representation.

The use of graphs to provide representations of data is very common in Science. The types of graphs may change between subjects and so this may also cause problems. For example, in Biology they may be used to represent population or variation data and so will be of one form whereas in other cases (across all three science subjects) they will be used to represent how a variable changes over time. This change from both the type of graphs and what they represent is known to be a challenge for many students and so thought and time is needed when support students graph drawing skills.

In 1999 the ASE published a book based on a research project designed to help students (and teachers ) in this area and if you can find a copy it is well worth tracking down. Getting to grips with graphs by Goldsworthy, Watson, and Wood-Robinson ( ISBN: 086 357 3029)

Some common difficulties students have with line graphs

• Many don't know what ‘Graph a-versus-b’ means. Often a goes on horizontal and so graph is reversed
• Many think that the slope is y/x and not Δy/Δx
• The ‘slope at a point’ is a difficult idea. Comparing between various slopes can be problematic
• The area under graph and slope have units
• 45° slope does not necessarily have a gradient =1
• The area under a curve can be difficult as a concept as well as a measurement exercise

The use of motion graphs in the Force and Motion topic in physics is one area where students sometimes have to do a great deal of work with graphs both drawing and interpreting them. This adds some extra challenges over and above the ones motioned above.

• It’s hard to connect a dynamic process with a static graph
• Connecting and switching between distance time and speed/velocity time is difficult
• The difference between speed and velocity can cause challenges (a velocity graph may have a positive or negative value for velocity but a speed graph will only have a positive value)
• Axis labelling is often incomplete or unclear [velocity (m/s)]
• In diagrams, we often draw and show changing position along a horizontal line and then plot it along a vertical one

## Links and Resources

### Interpreting Distance – Time Graphs A6

This resource requires get students to think a little bit more carefully about how they interpret graphical representations.

If you look at the starting points on page 1 it describes how students have often constructed distance–time graphs before but may still interpret them as if they are pictures of situations rather than abstract representations.

These resources are designed to reveal common misconceptions about distance–time graphs. The resources include clear guidance on how to run the lesson including key questions you can use to probe students understanding. Your Maths department may have used this resources before. If so you could build on that by using a similar lesson structure but a different context that involve the interpretation of graphs in a scientific context.

This resource uses a matching exercise which is one of the strategies described in the guidance material outlined in the introduction to these lists. Look at the guidance in the introduction if you would like to read more about these strategies.

publication year
2000 - 2009

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### Interpreting Distance-Time Graphs with a Computer A5

In this resource, students interpret linear and non-linear distance-time graphs using the computer programme Traffic. This program provides a simple yet powerful way of helping learners to visualise distance–time graphs from first principles. The program generates situations involving traffic moving up and down a straight section of road. It then allows the user to take ‘photographs’ of this situation at one-second intervals, places these side-by-side, and then gradually transforms this sequence of pictures into a distance–time graph. In this way, direct correspondences between speeds and gradients are obtained.

Learners are asked to describe situations, and draw and interpret distance–time graphs. Later, examples are offered that involve cars travelling at non-uniform speeds

publication year
2000 - 2009

2 files 1

### Guide to maths for scientists

publication year
2010 to date

1 file 0