Teaching approaches: Visualisation
 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
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.
Relevant resources
CPD  Approaches to Reading  
Do we have to read it? Thinking about using 'reading' effectively in the classroom This resource highlights a range of approaches to reading in the classroom and the reasons we ask pupils to engage in reading activities, including the importance of subject language^{(ta)}, study skills^{(topic)}, and conceptual reasoning^{(ta)} and visualisation^{(ta)} arising from subject based reading activities.
 
CPD  Directed Activities Related to Text (DARTs)  
Developing good pedagogy in using text based activities for learning This resource covers a range of Directed Activities Related to Text, highlighting the importance of language^{(ta)} and visualisation^{(ta)} in activities, and their role in active learning^{(ta)} and study skills^{(topic)}.
 
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.  
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.  
Modelling  Models in Science  
Teachers use models to help pupils make sense of their observations An 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 GeoGebra This 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  Variety of perimeter with fixed area  
Interactive GeoGebra investigation that allows children (age 610) to explore an element of mathematics for themselves.
 
Visualisation  Circumference of a Circle.  
Interactive GeoGebra investigation that allows students to explore an element of mathematics for themselves.
 
Visualisation  Solar and Lunar Eclipse  
To show and explain how a Solar and Lunar eclipse occurs This 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 610) to explore an element of mathematics for themselves.
 
Visualisation  Number and representation game.  
Interactive GeoGebra investigation that allows children (age 610) to explore an element of mathematics for themselves.
 
Visualisation  Variety of areas with fixed perimeter.  
Interactive GeoGebra investigation that allows children (age 610) to explore an element of mathematics for themselves.
 
Visualisation  Radioactive Decay and Carbon Dating  
Using 'real life' data to explore exponential graphs This 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  Kepler's Third Law  
Using 'real life' data This lesson features a ‘real life’ example for students to explore GeoGebra. The focus on ‘real life’ increases student motivation.
The activity engages pupils in group talk(i), mathematical thinking(i) and vocabulary(i). This open ended(i) task encourages higher order(i) thinking, and encourages whole class(i) discussion(i)/questioning(i) and inquiry(i) projects.  
Visualisation  Flying paper planes  
Very visual and interactive and simple to understand This 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  GeoGebra STEM Exploration  
Develop 'real world' GeoGebra mathematical modelling applications which reach out to a wide range of users both students and teachers The halfterm activity consists of 3 halfday workshops interspersed with homeworking and online collaboration. Each workshop is part tutorial and help in GeoGebra, part development, presentation and feedback on their emerging work. The three halfday sessions become gradually less structured as students become more confident taking the initiative in developing their own work:
An initial GeoGebra tutorial session features ‘real life’ examples such as mathematical modelling^{(ta)} and visualisation^{(ta)} from photographs of patterns and structure in flowers and architecture; exercises such as “math aerobics” where students model algebraic functions kinaesthetically; and data analysis and exploration such as from astronomy (Kepler's 3rd law) and athletic performance (Usain Bolt’s 100m sprints). Realistic examples such as these, or from students’ previous work, are essential to get the ball rolling. Following this, the onus is very much on the student’s own initiative. The focus on ‘real life’ and student ownership of ideas and project development increases student motivation. The activity engages pupils in group talk^{(ta)}, mathematical thinking^{(ta)} and vocabulary^{(ta)}. This open ended^{(ta)} task develops higher order^{(ta)} reasoning^{(ta)}, and encourages whole class^{(ta)} discussion^{(ta)}/questioning^{(ta)} and inquiry^{(ta)} projects.  
Visualisation  ORBIT/GeoGebra Competion 2013  
The 2013 competition has generated five high quality openended activities that support interactive teaching and allow children (age 610) to explore an element of mathematics for themselves. The following guidance note are provided for each resource:
 
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.
 
Visualisation  Positioning fractions on the number line.  
Interactive GeoGebra investigation that allows children (age 610) to explore an element of mathematics for themselves.
