Continuous Professional Development in Mathematics

What are�Higher Order�Thinking Skills?

Higher order thinking involves the learning of complex judgmental skills such as critical thinking and problem solving.

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Higher order thinking is more difficult to learn or teach but also more valuable because such skills are more likely to be usable in new and unfamiliar situations.

Higher order questions require answers that go beyond simple information and as such both the language and thinking behind them is more complex. They take learners into abstract language functions, such as giving and justifying opinions, speculation and hypothesising.

Higher Order Thinking

Higher Order Questioning

What are higher order skills?

Higher order skills are skills involving analysis, evaluation and synthesis (creation of new knowledge). These are thought to be of a ‘higher order’, requiring different learning and teaching methods than the learning of facts and concepts.

Higher Order Skills

Are you already doing some of these?

To set the scene, watch this clip on a classroom practitioner talking about how to create more independent problem solvers.

[ Dan Meyer: Math class needs a makeover ]

In practice: Problem solving using Higher Order Skills

Video clip on TED Talks website

The backbone for all of this is Bloom’s Taxonomy…

Creating

Generating new ideas, products, or ways of viewing things

Designing, constructing, planning, producing, inventing.

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Evaluating

Justifying a decision or course of action

Checking, hypothesising, critiquing, experimenting, judging

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Analysing

Breaking information into parts to explore understandings and relationships

Comparing, organising, deconstructing, interrogating, finding

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Applying

Using information in another familiar situation

Implementing, carrying out, using, executing

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Understanding

Explaining ideas or concepts

Interpreting, summarising, paraphrasing, classifying, explaining

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Remembering

Recalling information

Recognising, listing, describing, retrieving, naming, finding

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Higher order thinking (HOT) skills

BLOOM’S TAXONOMY

Using knowledge of fractions, write a question given a context/problem.

Creating

Generating new ideas, products, or ways of viewing things

Designing, constructing, planning, producing, inventing.

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Evaluating

Justifying a decision or course of action

Checking, hypothesising, critiquing, experimenting, judging

​

Analysing

Breaking information into parts to explore understandings and relationships

Comparing, organising, deconstructing, interrogating, finding

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Applying

Using information in another familiar situation

Implementing, carrying out, using, executing

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Understanding

Explaining ideas or concepts

Interpreting, summarising, paraphrasing, classifying, explaining

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Remembering

Recalling information

Recognising, listing, describing, retrieving, naming, finding

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In context, compare fractions with a variety of different denominators and come to a decision.

Given a fraction of a quantity, find the total amount.

Find the fractions of a quantity.

Order the fractions you know.

List all the fractions you know.

Higher order thinking (HOT) skills

BLOOM’S TAXONOMY

Topic:

3D Shape

E&O:

MTH 2-16a

1. Range of 3D objects
2. Their properties

Skills:

1. Explored
2. Use mathematical language
3. Describe
4. Investigation
5. Discuss where and why particular shapes are used in the environment

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Having explored a range of 3D objects and 2D shapes, I can use mathematical language to describe their properties, and through investigation can discuss where and why particular shapes are used in the environment.

MTH 2-16a

Practice:

1. 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
2. using relevant contexts and experiences, familiar to young people
3. Mathematics is at its most powerful when the knowledge and understanding that have been developed are used to solve problems

1. Effective Questioning
2. Discussion
3. Use misconceptions
4. Use wrong answers
5. Relevant contexts
6. Experiences familiar to young people
7. Solve problems

E& O

Principles and Practice

How do I know what knowledge and skills to involve in my planning?

Knowledge:

Topic:

3D Shape

E&O:

MTH 2-16a

1. Range of 3D objects
2. Their properties

Skills:

1. Explored
2. Use mathematical language
3. Describe
4. Investigation
5. Discuss where and why particular shapes are used in the environment

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Practice:

1. Effective Questioning
2. Discussion
3. Use misconceptions
4. Use wrong answers
5. Relevant contexts
6. Experiences familiar to young people
7. Solve problems

How do I know what knowledge and skills to involve in my planning?

Knowledge:

Planning using Bloom’s Taxonomy

Exemplars and guides on these three tools are provided in this pack

Creating

Generating new ideas, products, or ways of viewing things

Designing, constructing, planning, producing, inventing.

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Evaluating

Justifying a decision or course of action

Checking, hypothesising, critiquing, experimenting, judging

​

Analysing

Breaking information into parts to explore understandings and relationships

Comparing, organising, deconstructing, interrogating, finding

​

Applying

Using information in another familiar situation

Implementing, carrying out, using, executing

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Understanding

Explaining ideas or concepts

Interpreting, summarising, paraphrasing, classifying, explaining

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Remembering

Recalling information

Recognising, listing, describing, retrieving, naming, finding

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Curriculum for Excellence: Higher Order Skills

Topic:

Related E&O:

3D Shape

MTH 2-16a

Create an item that includes all, or part of your shape. Draw and label your design.

Tell us why your shape is used in the places it is.

Identify where the shape is found in the classroom and the school

Draw a diagram or take a photograph of the shape.

Find items that you can use to show the shape

List the attributes of your shape.

1. Look through three of the sample mini grids provided
• Look at the differences between the LOT and the HOT skills
2. In group(s) complete a grid for a topic using the blank grids provided.

‘Bloom’s mini grid’

Activity 1: Using the mini grids

We can take these handy ‘mini’ grids a bit further and use more detailed grids (shown below) as a CPD activity to support understanding and use of Higher Order Skills in the maths learning environment.

Taking it further…

Using the detailed grids

Activity 2: Using the detailed Grids

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Part 1

In a group(s), have a look through the exemplar detailed grids supplied in this pack.

Discuss:

• When you use similar Higher Order Skills (top 3 rows) in your classroom
• The benefits of using these higher order approaches with pupils
• Other topics these skills and approaches could transfer too
• Ideas you could use immediately in your classroom

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Activity 2

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Part 2

• In a group(s), decide on a topic to focus on.
• Using the E&O(s) and Principles and Practice paper decide on the knowledge, skills and practice that will be involved
• Complete a blank grid for this topic
• Can you add a few more keywords?
• Create questions/questioning approaches for each level

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• Share your grid with other groups

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Reflection

• Why are higher order skills (the upper three rows) so beneficial in the classroom?
• Individually, share how you plan to incorporate some of these higher order skills into your classroom…immediately? Over the longer term?

Further materials supplied in this pack

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In this pack

This pack includes materials to increase focus on Higher Order Skills that can be used:

1. By a department as CPD
2. By a teacher in their classroom
3. By pupils in the course of their learning

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Be creative with the materials as they can be used in a multitude of ways. Feel free to edit, amend, change and improve materials to best suit your learners.

Hinge Questions

+CPD

Self and peer assessment

+CPD

Using wrong answers

+CPD

Starter/Stand alone activities

+CPD

Using summative formatively

+CPD

CPD Session

Overview of H.O.S.

Scene setting

Summary of attached materials

(EG)

Brief overview of whole resource

Planning Learning and Teaching

using Bloom’s

1. Detailed grids + CPD
2. Mini grids + CPD
3. Fans + CPD (stand-alone)

Learning and Teaching - Everyday strategies

This PowerPoint!

Further materials supplied in this pack

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Planning using Bloom’s Taxonomy

Hinge Questions

Self & Peer Assessment

Think-Pair -Share

Beat the Class

Foldy

Starters and Stand Alone Activities

Making Summative Formative

Using wrong answers

Learning and Teaching – Everyday strategies