Teaching approaches: Visualisation
Visualisation can be a powerful tool in modelling various problems, writing approaches, activities, and so on. It can also be useful in helping pupils to reason, and engage in higher order thinking around problem solving, by using a variety of tools, for example brainstorms to plan essays, consider pros and cons, to address problems in enquiry learning, and so on. Argument mapping, concept mapping, brain storming, mind mapping, diagramming and mathematical modelling (including using tools like Geogebra), writing frames, visual narratives (for example using animation software), and many more provide excellent ways to use visualisation to support high quality reasoning which can be shared collaboratively.
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+6By 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.
|Modelling||Models in Science|
Teachers use models to help pupils make sense of their observationsAn opportunity for teachers to discuss the use of modelling(ta) and visualisation(ta) in Key stage 3 science
|Sampling||Sampling techniques to assess population size|
|Statistics||Cubic Equations and Their Roots|
To interactiviley explore and understand complex mathematics with GeoGebraThis lesson features a ‘real life’ example for students to explore using visualisation(ta) via GeoGebra. The focus on ‘real life’ increases student motivation.
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 encourages whole class(ta) discussion(ta)/questioning(ta) and inquiry(ta) projects.
|Visualisation||Perimeter of a rectangle.|
Interactive GeoGebra investigation that allows children (age 6-10) to explore an element of mathematics for themselves.
|Visualisation||Using visualisation in maths teaching|
Thinking about visualisation in education.This unit looks at visualisation(ta) as it relates to mathematics, focusing upon how it can be used to improve learning. It also identifies ways in which to make more use of visualisation within the classroom.