Continuous Professional

Development in Mathematics
 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 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.

Are you already doing some of these?

In practice: Problem solving using Higher Order Skills

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 ]

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.

Evaluating
Justifying a decision or course of action
Checking, hypothesising, critiquing, experimenting, judging

Analysing
BLOOM’S TAXONOMY

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

Understanding
Explaining ideas or concepts
Interpreting, summarising, paraphrasing, classifying, explaining

Remembering
Recalling information
Recognising, listing, describing, retrieving, naming, finding
 Creating Using knowledge of
Generating new ideas, products, or ways of viewing things fractions, write a question
Designing, constructing, planning, producing, inventing. given a context/problem.

In context, compare
Evaluating fractions with a variety of
Justifying a decision or course of action different denominators
Checking, hypothesising, critiquing, experimenting, judging
and come to a decision.

Analysing
BLOOM’S TAXONOMY

Given a fraction of a
Breaking information into parts to explore understandings and relationships quantity, find the total
Comparing, organising, deconstructing, interrogating, finding amount.

Applying Find the fractions of a

Using information in another familiar situation
Implementing, carrying out, using, executing
quantity.

Understanding Order the fractions you

Explaining ideas or concepts
know.
Interpreting, summarising, paraphrasing, classifying, explaining

Remembering
Recalling information List all the fractions you
Recognising, listing, describing, retrieving, naming, finding know.
How do I know what knowledge and skills to involve in my planning?
Topic: 3D Shape E&O: MTH 2-16a

Knowledge: E& O
Having explored a range of 3D
1. Range of 3D objects objects and 2D shapes, I can use
2. Their properties mathematical language to describe
their properties, and through
investigation can discuss where and
Skills: why particular shapes are used in the
environment.
1. Explored
MTH 2-16a
2. Use mathematical language
3. Describe
4. Investigation
5. Discuss where and why particular
shapes are used in the environment
Practice:
1. Effective Questioning
Principles and Practice
2. Discussion 1. Through their use of effective questioning and discussion, teachers
3. Use misconceptions will use misconceptions and wrong answers as opportunities to
4. Use wrong answers improve and deepen children’s understanding of mathematical
5. Relevant contexts concepts
6. Experiences familiar to young 2. using relevant contexts and experiences, familiar to young people
people 3. Mathematics is at its most powerful when the knowledge and
7. Solve problems understanding that have been developed are used to solve problems
How do I know what knowledge and skills to involve in my planning?
Topic: 3D Shape E&O: MTH 2-16a

Knowledge:
1. Range of 3D objects Planning using Bloom’s Taxonomy
2. Their properties G r id
a il e d
’ s D et
Bloom
Skills:
1. Explored
2. Use mathematical language
Bloom’s Mini Grid
3. Describe
4. Investigation
5. Discuss where and why particular
shapes are used in the environment
o o m’s Fan
Bl
Practice:
1. Effective Questioning
2. Discussion
3. Use misconceptions
4. Use wrong answers
5. Relevant contexts
6. Experiences familiar to young
people Exemplars and guides on these three tools are provided in this pack
7. Solve problems
 Activity 1: Using the mini grids

‘Bloom’s mini grid’

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.
 Taking it further…
Using the detailed 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.
Activity 2: Using the detailed Grids

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
 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 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

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.
 Brief overview of whole resource

CPD Session This Powe

r Point!
Overview of H.O.S.
Scene setting
Summary of attached materials
Planning Learning
(EG) and Teaching

using Bloom’s
1.Detailed grids + CPD
2.Mini grids + CPD
3.Fans + CPD (stand-alone)

Learning and Teaching - Everyday strategies

Starter/Stand Using
Hinge Self and peer Using wrong
alone summative
Questions assessment answers
activities formatively
+CPD +CPD +CPD
+CPD +CPD
 Further materials supplied in this pack

Planning using Bloom’s Taxonomy Learning and Teaching – Everyday strategies

rid Hinge Questions Starters and Stand Alone Activities
i l ed G
’s Deta
Bloom

Bloom’s Mini Grid Self & Peer Assessment

o m’ s F an
Blo Think-Pair -Share Beat the Class Foldy

Making Summative Formative

Using wrong answers