1. Continuous Professional Development in Mathematics
What are Higher Order Thinking Skills?

2. Higher Order Questioning
What are higher order skills?
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
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 Questioning
This is a PowerPoint that can be used to introduce Higher Order Skills in maths with a department. All or part of this powerpoint may be used. Either as a presentation itself or as a prompt or support for the PT. Feel free to edit and amend this as suits. It has deliberately been kept brief and any attached notes are for guidance only and are not prescriptive.
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?

3. [ Dan Meyer: Math class needs a makeover ]
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 ]
The following video (or part thereof) may be interesting group viewing or pre-meeting viewing.
Video clip on TED Talks website

4. The backbone for all of this is Bloom’s Taxonomy…
This is a visual representation of Bloom’s Taxonomy that can be useful for both teachers and learners.
The aim is be as far out in the wingspan as possible with classroom activities and thinking, but the earlier stages are also required to be in place beforehand.

5. Higher order thinking (HOT) skills
Creating
Generating new ideas, products, or ways of viewing things
Designing, constructing, planning, producing, inventing.
Higher order thinking (HOT) skills
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
BLOOM’S TAXONOMY
Applying
Using information in another familiar situation
Implementing, carrying out, using, executing
Understanding
Explaining ideas or concepts
Interpreting, summarising, paraphrasing, classifying, explaining
This slide breaks down the 6 stages of Bloom’s Taxonomy and separates these stages into ‘LOT’ skills and ‘HOT’ skills.
‘LOT’ skills happen a lot in our classrooms and ‘HOT’ skills are what we are aiming to increase.
Just rewording a question or taking a different approach on an activity can make the difference between a LOT and a HOT skill or move something up another step.
It’s important to stress how much of this we already do and how one small change can take it even further.
Remembering
Recalling information
Recognising, listing, describing, retrieving, naming, finding

6. Higher order thinking (HOT) skills
Creating
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.
Higher order thinking (HOT) skills
In context, compare fractions with a variety of different denominators and come to a decision.
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
Given a fraction of a quantity, find the total amount.
BLOOM’S TAXONOMY
Applying
Using information in another familiar situation
Implementing, carrying out, using, executing
Find the fractions of a quantity.
Understanding
Explaining ideas or concepts
Interpreting, summarising, paraphrasing, classifying, explaining
Order the fractions you know.
Bloom’s Planning: Mini Grid
This is one example of building up a topic using Bloom’s Taxonomy. We have referred to this format as a Bloom’s mini-grid.
Encourage staff to amend, improve, discuss and debate this grid and see the differences between stages.
Each topic or outcome can have lots of different steps, depending on the areas you choose to focus on.
Remembering
Recalling information
Recognising, listing, describing, retrieving, naming, finding
List all the fractions you know.

7. 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 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
Range of 3D objects
Their properties
Skills:
Explored
Use mathematical language
Describe
Investigation
Discuss where and why particular shapes are used in the environment
Practice:
Principles and Practice
This page provides a reminder of the knowledge, skills and practice that is expected nationally and suggests a strategy for involving this in your planning.
It is helpful to remind teachers of the guidance set out in the Mathematics Principles and Practice document.
Effective Questioning
Discussion
Use misconceptions
Use wrong answers
Relevant contexts
Experiences familiar to young people
Solve problems
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

8. How do I know what knowledge and skills to involve in my planning?
Topic:
3D Shape
E&O:
MTH 2-16a
Knowledge:
Planning using Bloom’s Taxonomy
Range of 3D objects
Their properties
Bloom’s Detailed Grid
Skills:
Explored
Use mathematical language
Describe
Investigation
Discuss where and why particular shapes are used in the environment
Bloom’s Mini Grid
Bloom’s Fan
Practice:
This slide shows how the knowledge, skills and practice (once identified and selected) can then feed into the three formats for Planning using Bloom’s (Bloom’s Detailed Grid, Bloom’s Mini Grid and Bloom’s Fan) which are provided in this pack.
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

9. H.O.T Curriculum for Excellence: Higher Order Skills Topic: 3D Shape
Related E&O:
MTH 2-16a
Creating
Generating new ideas, products, or ways of viewing things
Designing, constructing, planning, producing, inventing.
H.O.T
Create an item that includes all, or part of your shape. Draw and label your design.
Step-up Question
Evaluating
Justifying a decision or course of action
Checking, hypothesising, critiquing, experimenting, judging
Tell us why your shape is used in the places it is.
Step-up Question
Analysing
Breaking information into parts to explore understandings and relationships
Comparing, organising, deconstructing, interrogating, finding
Identify where the shape is found in the classroom and the school
Step-up Question
Applying
Using information in another familiar situation
Implementing, carrying out, using, executing
Draw a diagram or take a photograph of the shape.
Step-up Question
Understanding
Explaining ideas or concepts
Interpreting, summarising, paraphrasing, classifying, explaining
Find items that you can use to show the shape
Step-up Question
Remembering
Recalling information
Recognising, listing, describing, retrieving, naming, finding
List the attributes of your shape.

10. Activity 1: Using the mini grids
‘Bloom’s mini grid’
Blooms Mini Grid: Staff CPD activity
This slide takes you step by step through using the Bloom’s Mini Grid to support staff discussion and pupil learning.
Look through three of the sample mini grids provided
Look at the differences between the LOT and the HOT skills
In group(s) complete a grid for a topic using the blank grids provided.

11. Using the detailed grids
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.
Staff CPD Activity: Bloom’s Detailed Grid
This and the following 2 slides introduce the Bloom’s Detailed Grid as a form of Planning using Bloom’s.
Again the purpose of this activity is to support staff discussion about questioning approaches and extending work into the ‘HOT’ skills levels.
Staff should be encouraged to discuss what they already do in the ‘HOT’ levels as well as topics that can be extended up into the ‘HOT’ levels.
There are sample grids provided is this pack to support discussion.

12. The benefits of using these higher order approaches with pupils
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
Staff CPD Activity: Bloom’s Detailed Grid
You can follow this activity with staff as a CPD activity

13. In a group(s), decide on a topic to focus on.
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
Staff CPD Activity: Bloom’s Detailed Grid
You can follow this activity with staff as a CPD activity
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?

14. Further materials supplied in this pack
This pack includes materials to increase focus on Higher Order Skills that can be used:
By a department as CPD
By a teacher in their classroom
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.
Staff CPD Activity: Bloom’s Detailed Grid
You can follow this activity with staff as a CPD activity

15. Brief overview of whole resource Planning Learning and Teaching
CPD Session
Overview of H.O.S.
Scene setting
Summary of attached materials
(EG)
This PowerPoint!
Planning Learning and Teaching
using Bloom’s
Detailed grids + CPD
Mini grids + CPD
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

16. Further materials supplied in this pack
Planning using Bloom’s Taxonomy
Learning and Teaching – Everyday strategies
Starters and Stand Alone Activities
Hinge Questions
Bloom’s Detailed Grid
Bloom’s Mini Grid
Self & Peer Assessment
Bloom’s Fan
Think-Pair -Share
Beat the Class
Foldy
Making Summative Formative
Using wrong answers
Staff CPD Activity: Bloom’s Detailed Grid
You can follow this activity with staff as a CPD activity