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…
Generating new ideas, products, or ways of viewing things
Designing, constructing, planning, producing, inventing.
O
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
Understanding
Explaining ideas or concepts
Interpreting, summarising, paraphrasing, classifying, explaining
O
O
M
’
S
T
A
X
O
Evaluating
N
M
Y
Creating
B
L
Remembering
Recalling information
Recognising, listing, describing, retrieving, naming, finding
Generating new ideas, products, or ways of viewing things
Designing, constructing, planning, producing, inventing.
Using knowledge of
fractions, write a question
given a context/problem.
O
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
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.
Understanding
Explaining ideas or concepts
Interpreting, summarising, paraphrasing, classifying, explaining
Order the fractions you
know.
O
O
M
’
S
T
A
X
O
Evaluating
N
M
Y
Creating
B
L
Remembering
Recalling information
Recognising, listing, describing, retrieving, naming, finding
List all the fractions you
know.
How do I know what knowledge and skills to involve in my planning?
Topic: 3D Shape
E&O: MTH 2-16a
E& O
Knowledge:
1. Range of 3D objects
2. Their properties
Skills:
1.
2.
3.
4.
5.
Explored
Use mathematical language
Describe
Investigation
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.
2.
3.
4.
5.
6.
7.
Effective Questioning
1.
Discussion
Use misconceptions
Use wrong answers
Relevant contexts
Experiences familiar to young 2.
3.
people
Solve problems
Principles and Practice
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
using relevant contexts and experiences, familiar to young people
Mathematics is at its most powerful when the knowledge and
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
2. Their properties
Planning using Bloom’s Taxonomy
Skills:
1.
2.
3.
4.
5.
Explored
Use mathematical language
Describe
Investigation
Discuss where and why particular
shapes are used in the environment
Bloom’s Mini Grid
Practice:
1.
2.
3.
4.
5.
6.
7.
Effective Questioning
Discussion
Use misconceptions
Use wrong answers
Relevant contexts
Experiences familiar to young
people
Solve problems
Exemplars and guides on these three tools are provided in this pack
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
• Share your grid with other groups
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
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
Overview of H.O.S.
Scene setting
Summary of attached materials
(EG) and Teaching
Planning Learning
using Bloom’s
1. Detailed grids + CPD
2. Mini grids + CPD
3. Fans + CPD (stand-alone)
Learning and Teaching - Everyday strategies
Hinge
Questions
+CPD
Self and peer
assessment
+CPD
Using wrong
answers
+CPD
Starter/Stand
alone
activities
+CPD
Using
summative
formatively
+CPD
Further materials supplied in this pack
Planning using Bloom’s Taxonomy
Learning and Teaching – Everyday strategies
Hinge Questions
Bloom’s Mini Grid
Starters and Stand Alone Activities
Self & Peer Assessment
Think-Pair -Share
Using wrong answers
Beat the Class
Making Summative Formative