Teaching approaches: Investigation
- Active learning
- Applying and consolidating
- Argumentation
- Assessment
- Classroom management
- Collaboration
- Curriculum development
- Curriculum planning
- Dialogue
- Differentiation
- Discussion
- Drama
- Exploring and noticing structure
- Games
- Group talk
- Group work
- Higher order
- Homework
- Inclusion
- Inquiry
- Introduction
- Investigation
- Language
- Learning objectives
- Mathematical thinking
- Modelling
- Narrative
- Open ended
- Planning
- Planning for interactive pedagogy
- Planning for professional development
- Posing questions and making conjectures
- Questioning
- Reasoning
- Reasoning, justifying, convincing and proof
- Scientific method
- Sharing practice
- The ORBIT Resources
- Thinking strategically
- Visualisation
- Visualising and explaining
- Whole class
- Working systematically
Investigations engage pupils in active learning to explore a particular topic or problem. Investigations may be related to enquiry based learning, and sometimes used synonymously, but we would normally consider enquiry based learning more open ended, involving higher order reasoning and perhaps high level dialogue in group work contexts, where in investigations such group talk might be more closely directed by the teacher.
Relevant resources
Biodiversity | Using Science to Support Biodiversity | |
A virtual field trip to study biodiversity. This is an investigation^{(ta)} in a virtual field trip to Dartmoor National Park. It involves research, designing a scientific investigation and analysing the results.
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Graph | Variation of human characteristics - Visualising Class data | |
A big survey of ourselves, measuring hands, feet and more The lesson offers the opportunity to explore measurement, relationships between measurement, and ways to visualise and summarise this data. The use of ICT^{(i)} allows the teacher to enter data and for pupils to immediately see the impact this has on the pie chart and frequency tables (which are automatically updated). This also allows the teacher to change the 'range' for the frequency counts, and discuss with pupils the impact of this on the pie chart, and whether this is a good representation - encouraging the use of mathematical language^{(ta)} and scientific method^{(ta)} throughout. In collecting the data pupils have opportunity for some self-directed group work^{(ta)} - to measure various lengths as described below - and the teacher could use whole class^{(ta)} questions^{(ta)} to explore the strategies taken to conduct this investigation^{(ta)}.
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ICT | Monsters using Scratch | |
Children using a computer programming language to create moving monsters This activity developed the specific e-skills^{(topic)} of programming and digital animation. It could be considered the first step towards enabling children to design and create their own games^{(tool)} using sprites and user-input controls. Computer programming helps to develop investigation^{(ta)} skills as it requires the use of a previously unknown language^{(ta)} to execute commands, which also develops the skills of mathematical thinking^{(ta)}. Computer programming also involves the use of modelling^{(ta)} and planning^{(ta)} techniques. Because Scratch is an open source programming language, this also creates opportunities for homework^{(ta)}, as the children are able to download the software for themselves at home.
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Investigation | Persuasive argument and evidence-based conclusions about the best car | |
Got a new motor? Talk about your investigation like a scientist This activity involving inquiry^{(ta)}aims to develop children’s ability to support their conclusions with evidence. The teacher will model^{(ta)} and encourage the use of the language^{(ta)} that children require to discuss or present their data. The teacher can explain their rationale using the lesson below.
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Investigation | Hypothesis and Variables | |
Prepare for ISA exams here... Students are required to make hypotheses and draw graphs for continuous and categoric data as part of their Individual Skills Assessment (ISA) for GCSE. This resource presents a hypothesis as a 'best guess' or proposal, intended to explain facts or observations available, prior to doing an investigation. Students work collaboratively to plan the following investigations, coming up with hypotheses and considering the variables:
They then plot graphs of data from similar contexts to their planned investigations deciding if the graphs should be bar charts or scatter plots/line graphs depending on whether or not the variables are continuous or categoric. | ||
Investigation | Consecutive Sums | |
Can all numbers be made in this way? For example 9=2+3+4, 11=5+6, 12=3+4+5, 20=2+3+4+5+6 By definition, a problem is something that you do not immediately know how to solve, so learning how to solve something unfamiliar is not straightforward. Tackling an extended problem is difficult.
This lesson gives pupils an opportunity to engage in mathematical thinking^{(ta)} and develop their higher order^{(ta)} thinking skills on a problem that is accessible but which has interest. For example, the problem is presented in diagrammatic and numerical ways. The plan suggests several visualisation^{(ta)} methods to present the same underlying task. It should be useful for teachers to compare these different presentations and either to select the one that they feel will be most useful for their pupils or explore ways for the pupils to see the links between the different methods. The assessment^{(ta)} ideas, using other pupils' solutions from the NRICH website are widely applicable to other problems too. | ||
Investigation | Scientific Definitions | |
Prepare for ISA exams here... Students are required to make use of a number scientific definitions as part of their Individual Skills Assessment (ISA) for GCSE. This resource uses the following activities in an attempt to liven up the teaching of these words:
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Language | Exploring shape and its mathematical language through sorting activities | |
Using mathematical language to discuss shapes of objects either printed or hidden in 'feely bags'. Can you feel the forks? The Investigation^{(ta)} of shapes and geometry can be very rewarding. A practical approach using objects from the pupils’ environment can increase their motivation and interest. In this unit, you will be using everyday objects to help pupils develop geometrical skills, such as recognising, visualisation^{(ta)}, describing, sorting, naming, classifying and comparing.
Through games^{(tool)} on the properties of shapes, the activity engages pupils in group talk^{(ta)}, mathematical thinking^{(ta)} and vocabulary^{(ta)}. This open ended^{(ta)} task encourages higher order^{(ta)} thinking, and could form the basis of whole class^{(ta)} discussion^{(ta)}/questioning^{(ta)} and inquiry^{(ta)} projects. It can be used as a lesson extension, or as a preliminary task. | ||
Standard Index Form | An Introduction to the Standard Index Form | |
Working out the rules according to which a calculator displays large numbers The Standard Index Form is a key idea for mathematicians and scientists. The notion that we choose to write numbers in this way requires some explanation. So in this activity, pupils take part in an investigation^{(ta)} on how standard index form works. This is a higher order^{(ta)} problem solving context where students are encouraged to engage in mathematical thinking^{(ta)}. They may be involved in whole class^{(ta)} or small group work^{(ta)} discussion^{(ta)}, so they have a good opportunity to practice using mathematical language^{(ta)} and questioning^{(ta)}.
This means that students do not need to be able to explain their ideas in full: they can use the calculator's feedback to discover whether their ideas are correct or not. This is also an exciting way for pupils to realise an initial idea that fits the data may need to be extended when new data arises. This resource therefore aims to develop investigative skills, as well as introduce pupils to standard index form in a memorable way. The pupils can later use their knowledge of indices in discussion^{(ta)} and group talk^{(ta)} as they explain what is happening. |