Teaching approaches: Higher order
- 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
It may seem slightly unusual that 'higher order' is given a special category here. Higher order thinking refers to thinking regarding critical problem solving and judgement skills, particularly those around novel situations. It is associated with the higher levels of Bloom's taxonomy. It is separated out here to give the spread of resources which explore higher order questioning, assessment, enquiry, and reasoning, for example. You could explore different sorts of task which probe these advanced thinking skills, and think about how to implement them in your own teaching.
Relevant resources
Acids | Forensic Science Investigation | |
A who-dunnit circus of activities This lesson introduces inquiry^{(ta)}-based learning through the topic of forensic science. It engages pupils in higher order^{(ta)} reasoning^{(ta)} solving a variety of forensic problems.
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Assessment | Changing KS3 Questions for Engaging Assessment | |
A large set of questions grouped by topic, paper, and national curriculum level Test questions are often seen as uninteresting and useful only to assess pupils summatively. This resource however allows questioning^{(ta)} to be used to support pupils’ revision, creativity and higher order^{(ta)} problem-solving in class. The tasks could be conducted via whole class^{(ta)} discussion^{(ta)} or assessment^{(ta)}, perhaps using mini-whiteboards^{(tool)}, or in small group work^{(ta)} situations.
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Astronomy | Recreating the Big Bang | |
An introduction to the creation of the Universe. This presentation offers a tour of the European Organization for Nuclear Research (CERN) and explains why it is worth spending money on one experiment. It then delves into particle physics, looking at sub-atomic particles to offer analogies for what these particles are. The session focuses on whole class^{(ta)} dialogue^{(ta)} and higher order^{(ta)} thinking skills as well as exploring scientific language^{(ta)}. This 4th session and the 5th are together the most theoretically complex and they present challenges to young peoples world views. As such they are led as much by their questions^{(ta)} as by the presentation.
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CPD | Questioning - Bloom's Taxonomy | |
Developing questioning through Bloom's taxonomy This resource discusses questioning^{(ta)} and Bloom's taxonomy - which, at the higher levels, can be linked to higher order^{(ta)} thinking skills and reasoning^{(ta)}.
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CPD | Using Thinking Skills | |
What do you think? Exploring thinking skills for the classroom This resource highlights higher order^{(ta)} reasoning^{(ta)} skills and activities to prompt their use in classroom contexts.
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CPD | Common Pitfalls in Questioning | |
Exploring problematic questions and ways to avoid them Questioning^{(ta)} is a key classroom practice, and skill, and can sometimes fall into the trap of focusing on lower levels, as opposed to higher order^{(ta)} reasoning^{(ta)} and discussion^{(ta)} skills. This resource covers some reasons why this - and other pitfalls - occur, with some practical advice for ensuring high quality questioning in your classroom.
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CPD | Understanding the Purposes of Explanations | |
Explaining why we explain - Thinking about how explanations are used in the classroom This resource focuses on 'explanation' in relation to learning objectives^{(ta)}, concept and process learning, and engaging higher order^{(ta)} reasoning^{(ta)} skills.
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Consecutive Sums | Using Prime and Square Numbers - How Old Am I? | |
Last year I was square, but this year I am in my prime. How old am I? This short activity offers opportunity for pupils to engage in mathematical thinking^{(ta)} and higher order^{(ta)} problem solving/reasoning^{(ta)}. They should be able to make links between different areas of mathematics and explore their ideas in whole class^{(ta)} discussion^{(ta)} and questioning^{(ta)}.
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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. | ||
Patterns | Exploring Pattern | |
Exploring patterns in mathematics Each chapter of this tutorial highlights the study skills^{(topic)} required to work through the real world examples and activities given. There are problems to be solved, some of which involve higher order^{(ta)} thinking skills (for example, being asked to correct a set of instructions), and all of which encourage the use of mathematical language^{(ta)} and mathematical thinking^{(ta)}. The resource could also be used in class, or as a useful homework^{(ta)} pack.
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Polygons | Exploring properties of rectangles: Perimeter and area. | |
Do two rectangles that have the same area also have the same perimeter? A problem to inspire higher order^{(ta)} questioning^{(ta)} especially in whole class^{(ta)} dialogic teaching^{(ta)} encouraging pupils to engage in mathematical thinking^{(ta)} and language^{(ta)}. You could use Geogebra^{(tool)} in this investigation, as an example of same-task group work^{(ta)}.
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Science | Primary Science Investigation | |
What is involved in 'doing a science investigation'? And what is there to assess? This resource describes the process of doing an investigation for inquiry^{(ta)}-based learning. Teachers could share practice^{(i)} and lesson planning^{(ta)} ideas using the list of pupil skills (e.g. observing). It also lists learning goals for investigation skills (e.g. observing, predicting, problem solving) and ideas for exploring different types of practical work^{(ta)} in science.
It could be used for discussion^{(ta)} or brainstorming on how to apply these skills to different content areas. The resource emphasises engaging pupils in the scientific method^{(ta)} - using higher order^{(ta)} thinking skills, group work^{(ta)} and dialogue^{(ta)} to facilitate knowledge building^{(ta)}/reasoning^{(ta)}. | ||
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. | ||
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 | 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 | 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 | 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 | GeoGebra STEM Exploration | |
Develop 'real world' GeoGebra mathematical modelling applications which reach out to a wide range of users both students and teachers The half-term activity consists of 3 half-day workshops interspersed with home-working and on-line collaboration. Each workshop is part tutorial and help in GeoGebra, part development, presentation and feedback on their emerging work. The three half-day 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. |