Skip Ribbon Commands
Skip to main content

Skip Navigation Linksnum2higherordermaths Higher order thinking skills in maths

Search the National Improvement Hub

Higher order thinking skills in maths

Last updated:
16 November 2017


What is this?

​This resource illustrates practical activities to improve learning and teaching skills. It will support improvement by utilising higher order thinking skills by tackling the following key areas:

  • problem solving:  seeking and identifying strategies and reasoning
  • comprehension and interpretation of statistics
  • flexibility of thinking
  • using and understanding appropriate mathematical vocabulary
  • identifying the steps and using a number of operation
  • realising the importance of accurate calculations
  • applying inverse operations

The resource specifically focuses on numeracy and mathematics, but the principles can be used across all curriculum areas. By focusing on Bloom's Revised Taxonomy of Learning, this resource provides a basis for:

  • extending knowledge and understanding of higher order thinking skills
  • planning learning and teaching
  • providing strategies to support learning
  • enabling opportunities for challenge

Who is this for?

​Explore the resource

Planning for learning and teaching

"One of the teaching approaches which contribute particularly well to successful learning in mathematics is - well planned opportunities for children and young people to learn through investigate, active approaches" Learning Together: Mathematics - HMIE

   The following questions may provide a stimulus for discussion:

  • When planning learning and teaching what type of activities provide opportunities for learners to work independently as well as collaboratively?
  • What steps are planned to review, improve and sustain these types of activities? See: Skills in Practice - Developing Thinking Skills

Well planned activities, incorporating Bloom’s Revised Taxonomy for Learning, are a useful tool for developing learners’ understanding and skills in numeracy and mathematics. The following activities have been developed to support staff to adopt the use of Bloom’s Revised Taxonomy in their planning:

 

  • Bloom’s Revised Taxonomy planning tool for numeracy and mathematics can be used to support quality questioning.
  • Bloom’s Higher Order Fans provide: Plenary questions to promote higher order thinking in the numeracy and mathematics classroom; exemplar activities which can be used to develop higher order thinking in numeracy and mathematics from early to fourth level in number and number process, fractions, decimal fractions and percentages and measurement.

Downloads

Word file: Bloom's Fans - A Brief Overview (1.2 MB)

Word file: Bloom's Fans - Blank template (34 KB)

Word file: Bloom's Fans – Plenary Questions (47 KB)

Word file: Blooms Revised Taxonomy Planning Tool (32 KB)

Word file: Bloom's Fans - Number and number processes (62 KB)

Word file: Bloom's Fans - Fractions, decimal fractions and percentages (79 KB)

Word file: Bloom's Fans - Measurement (71 KB)

Activities to support learning and teaching

This section is designed to support staff and learners by providing practical activities for the numeracy and mathematics classroom:

Practical activity 1 - Hinge questions

The Mathematics Excellence Group advocates strongly the planning of questions into lesson preparation. Such questions have been called 'hinge questions'. The idea is that the teacher plans every lesson with a 'hinge'; a point in the lesson when the teacher can check on student understanding, and then decide what to do next.  'Hinge' questions are typically designed to test learners' understanding of one important concept in a lesson—one that is critical for pupils to comprehend before the teacher moves on in the lesson.

Word file: Hinge Questions - Overview (168 KB)

Practical activity 2 - Starter and stand-alone activities

Putting a different ‘spin’ on lesson starters is one way to stimulate thinking and problem solving and also generates some very interesting discussions between learners and staff. Longer starters could be used as stand-alone activities during lessons.

PowerPoint file: HOT Starters and Standalone activities (3.7 MB)

Word file - HOT Starters - Teacher notes (28 KB)

Practical activity 3 - Self and peer assessment

Peer assessment makes greater demands on dialogue between learners. It encourages learners to externalise their thinking, explaining their understanding to others. In endeavouring to support others in their understanding, the learner is involved in utilising higher order thinking skills.

Word file: Think Pair Share - Teacher notes (134 KB)

Practical activity 4 - Using incorrect answers

Through their use of effective questioning and discussion, teachers will use misconceptions and wrong answers as opportunities to improve and deepen children’s understanding of mathematical concepts.

Word file: Using wrong answers - Teacher notes (169 KB)

Practical activity 5 - Using summative assessment formatively

Using summative assessments in a meaningful way to raise learners’ awareness of their strengths and development needs is vital in promoting understanding in mathematics. High quality discussion and debate from analysing summative tests provides an opportunity for learners to further develop higher order thinking and questioning skills.

Word file: Assessment in Mathematics (287 KB)

Reflective questions

  • What kind of techniques and activities do you find are useful and effective for evaluating learners' progress informally?
  • What kind of opportunities do you already provide for learners to discuss their progress?

About the author(s)

This resource was created within Education Scotland’s Numeracy team in conjunction with Scottish Government.




Tags:

Numeracy; Learning and assessment