STG22 Thinking with Graphs

Aims

1.Revise your understanding of constructivism

2.Become familiar with teaching strategies a) to help pupils construct graphs correctly,

b) to use graphs with understanding.

3.Develop a collaborative learning strategy

Constructivism

Write down the main features of constructivism.

Explain what these features mean for the classroom.

Why are graphs important?

• Summaries a lot of numbers• Helps you understand what went on in the

experiment e.g., get pupils to look at a series of numbers and ask them

what is happening. Then draw graph and see how much more can be understood.

• Helps find particular values/missing data/extrapolate, you are interested in, especially those that do not go through the origin.

• Visual way of looking at data is easier for most people

• Saves work

Planning

What do you need to plan into your lesson to help pupils learn?

What do you need to plan into your lesson to help

pupils learn? 1. Make it relevant so pupils can understand why the graph

will help them2. Check on misconceptions/what they find difficult to

understand about graphs. 3. Distinguish between misconceptions and not being able

to understand, but need to know WHY pupils are finding difficult. AKSIS is very useful at looking at what pupils get wrong, but not at why they get it wrong.

4. Have active learning5. Involve language and discussion6. Involve collaborative learning7. pupils have to use the graph to work out something, and

ideally this activity can be used to see if they have learnt and addressed any misconceptions they may have. Note, don’t start thinking that all pupils have misconceptions.

Background on AKSIS project and graphs

• The ASE and King’s College Science Investigations in Schools project was developed over a three year period (‘97-99) to help teachers to develop successful strategies for teaching science investigations which were required (called Sc1 Investigations). Many publications and articles were produced.

• Their research showed that over 75% of graphs were incorrectly constructed and most pupils regarded graphs as an end in themselves. And only a few pupils referred to their graphs when considering evidence.

• The AKSIS project designed materials to support teachers in the teaching of graphs. “Getting to grips with graphs”, ASE, Goldsworthy, Watson, Wood-Robinson

Activity1: Spot the mistakesAKSIS activities 3,8,18

• Work in pairs. You are provided with three charts, graphs etc. NOTE: these contain the answers so do NOT to look at the teacher’s notes on the first page

• Bar charts: find four mistakes • Line graphs: find two mistakes• Scales: find the mistake and redraw. Predict for

900 cm3 in both graphs.

• Why do these errors arise?

AKSIS Research: Graphs with and without errors

Percentage

Correctly constructed

21

Incorrectly constructed

77

Indecipherable 2

AKSIS Research: Error typesType of error No. of pupils

Labeling axes incorrectly 11

Putting dependent variable on horizontal axis

6

Labeling divisions on scales incorrectly 4

Writing numbers on horizontal axis with highest number on left and lowest on right

4

Writing numbers in spaces on axes rather than on line

6

Selecting inappropriate scale 9

Representing unequal intervals as equal intervals on scale

6

AKSIS Research: Errors types continued Drawing bar chart when data leads to line graphs or line graph when data leads to bar chart

6

Plotting points or bars incorrectly 15

Including the origin [0,0] as a point on line of best fit when not appropriate

Inappropriate lines of best fit drawn 3

Other errors 11

AKSIS Main learning objectives Yr9 Focus on drawing lines of best fit

• To know how to draw lines of best fit• To know how to use a line of best fit to

identify possible anomalous readings• To know that there may be several lines

of best fit and that we need to decide which is the most likely

• To understand and obtain information from the drawn graph

Teaching about graphs can help!Draw a line of best fit given a table

Year 7 Pre-test

N=35

Post-test

N=35

No attempt 10 0

Major faults 23 8

Minor faults 2 11

Correct 0 16

Teaching how to construct graphs: AKSIS activities 16,20,21,22

• 8 groups. Four groups do 16 and 22. Four groups do 20 and 21.

• Each group to evaluates 2 activities by trying them out as though they were pupils and then reading the teachers notes.

• Each group then selects an envoy who moves to another group to explain the activity they did to the other group.

• The envoy then returns to his/her group, who explains to the envoy what the other group did.

Working together

What is the difference between group work and collaborative learning?

Task• work in groups on a topic you are going

to teach that involves graphs. • devise a way of enabling pupils to learn

that involve the aspects covered in What do you need to plan into your lesson to help pupils learn?

• either focus on how you would find out the misconceptions about graphs, combined with how this relates to the science area, or a collaborative task to help the pupils understand the graph and what it represents.

Lesson materials (principles relevant to your SSA)

• Topic chosen• Names of people in group• A few sentences that explain what the exercise is

designed to achieve, including what year it is for• Collaborative exercise materials/ the questions to

tackle misconceptions• Details of how they are to be used and the

groupwork/collaborative learning built in, including any extra resources.

• A lesson plan. The framework of the lesson should follow either Orientation; elicitation; restructuring; application; review or the 5 Es.