# 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

### The Universe and More (graph game)

An interactive game-like approach to learning about the various motion graphs you need to cover in physics. It’s fun but the game is well thought through and it’s almost impossible to play and not learn physics at the same time.

### Graphing Stories

A great classroom resource to help students develop their graphing skills in an easy and accessible way. The site has a number of short video clips of various things that change over time (e.g. clock hand going round, child going down a slide, bouncing balls). There are downloadable templates but in the simplest sense you show the video and then the class sketch the graphs. It’s just as easy to do this with mini whiteboards. The template has the time axis marked and then the rest it up to you (or the class). Initially it may be worth helping students become familiar with the shapes without any numbers but the possibilities are endless.

### Physics and Birdsong

An interesting and alternative approach to the teaching of graphs and sound. This site provides a free download teaching pack (with full teachers notes and an annotated slideshow) that aims to support students graph drawing skills whilst also teaching them about sound, pitch, frequency, loudness and amplitude. Students listen to birds sounds and then have to sketch frequency/time or loudness/time graphs to help them get a ‘feel’ for how a variable that changes over time can be represented.

### Distance time graph

The way in which the shape of the graph relates to the behaviour of variables may not be obvious to some students. Discuss this using examples of scientific graphs. A classic example is a distance time graph

### velocity time graph

A less familiar example could be a velocity time graph

### Interpreting Distance – Time Graphs A6 *suitable for home teaching*

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.

### 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