Continuous Professional Development in Mathematics

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

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.

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.

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…

CreatingGenerating new ideas, products, or ways of viewing things

Designing, constructing, planning, producing, inventing.

EvaluatingJustifying a decision or course of action

Checking, hypothesising, critiquing, experimenting, judging

AnalysingBreaking information into parts to explore understandings and relationships

Comparing, organising, deconstructing, interrogating, finding

ApplyingUsing information in another familiar situationImplementing, carrying out, using, executing

UnderstandingExplaining ideas or concepts

Interpreting, summarising, paraphrasing, classifying, explaining

RememberingRecalling information

Recognising, listing, describing, retrieving, naming, finding

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

CreatingGenerating new ideas, products, or ways of viewing things

Designing, constructing, planning, producing, inventing.

EvaluatingJustifying a decision or course of action

Checking, hypothesising, critiquing, experimenting, judging

AnalysingBreaking information into parts to explore understandings and relationships

Comparing, organising, deconstructing, interrogating, finding

ApplyingUsing information in another familiar situationImplementing, carrying out, using, executing

UnderstandingExplaining ideas or concepts

Interpreting, summarising, paraphrasing, classifying, explaining

RememberingRecalling information

Recognising, listing, describing, retrieving, naming, finding

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.

BLO

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Topic: 3D Shape E&O: MTH 2-16a

1. Range of 3D objects2. Their properties

Skills:1. Explored2. Use mathematical language3. Describe 4. Investigation5. Discuss where and why particular

shapes are used in the environment

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 people3. Mathematics is at its most powerful when the knowledge and

understanding that have been developed are used to solve problems

1. Effective Questioning2. Discussion3. Use misconceptions4. Use wrong answers5. Relevant contexts6. Experiences familiar to young

people7. 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 objects2. Their properties

Skills:1. Explored2. Use mathematical language3. Describe 4. Investigation5. Discuss where and why particular

shapes are used in the environment

Practice:

1. Effective Questioning2. Discussion3. Use misconceptions4. Use wrong answers5. Relevant contexts6. Experiences familiar to young

people7. Solve problems

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

Knowledge:

Bloom’s Detailed Grid

Bloom’s Mini Grid

Bloom’s Fan

Planning using Bloom’s Taxonomy

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

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

Part 1In 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

Activity 2

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

Further materials supplied in this pack

In this packThis pack includes materials to increase focus on Higher Order Skills that can be used:1.By a department as CPD2.By a teacher in their classroom3.By pupils in the course of their learning

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 SessionOverview of H.O.S.

Scene settingSummary of attached materials

(EG)

Brief overview of whole resource

Planning Learning and Teaching using Bloom’s1.Detailed grids + CPD2.Mini grids + CPD 3.Fans + CPD (stand-alone)

Learning and Teaching - Everyday strategies

This PowerPoint!

Further materials supplied in this pack

Bloom’s Detailed Grid

Bloom’s Mini Grid

Bloom’s Fan

Planning using Bloom’s TaxonomyHinge Questions

Self & Peer Assessment

Think-Pair -Share Beat the Class Foldy

Starters and Stand Alone Activities

Making Summative FormativeUsing wrong answers

Learning and Teaching – Everyday strategies