Understanding
How do we know whether pupils have really understood?
ALTA Education · Mathematics CPD Tour 2026/27
Developing mathematical understanding without lowering ambition.
Four-session professional learning programmes for Primary and Secondary mathematics, led by Kieran Mackle and Stuart Welsh.
Practical mathematics CPD in Dublin, Belfast, Cardiff and Glasgow.
Why attend?
Better decisions in the mathematics classroom.
Scaffold
How do we support pupils without making them dependent on adult guidance?
Expectations
How do we respond when pupils struggle without lowering expectations?
Assessment
How do we turn what we see in pupil work into precise next steps?
The programme
Explore the programme.
Each programme contains four sessions. Open any session to see the detailed content.
Primary Programme
09:30–11:30Session 1Explicit InstructionHow do we explain new mathematics so more pupils understand it first time?
In this session
- what should actually be made explicit
- modelling mathematical thinking
- examples and non-examples
- representations
- sequencing examples
- checking understanding
- moving from concrete experience towards abstraction
- the difference between explaining a procedure and teaching an idea
Session 2ScaffoldingHow much help is too much help?
In this session
- task versus instructional scaffolding
- representations
- worked and partially worked examples
- prompts
- sentence structures
- reducing extraneous demand
- fading
- when manipulatives help
- when manipulatives become another thing to process
- the difference between support and simplification
Session 3ChallengeBeyond bigger numbers and extra questions.
In this session
- challenge versus acceleration
- difficulty versus complexity
- variation
- comparison
- explanation
- generalisation
- missing information
- multiple representations
- when problem solving becomes appropriate
- maintaining high expectations while managing cognitive demand
Session 4The Foundations of NumberWhich early gaps in number cause problems years later?
In this session
- counting principles
- cardinality
- subitising
- composition
- comparison
- additive structures
- multiplicative structures
- place value
Secondary Programme
13:00–15:00Session 1DiagnosisWhen pupils get stuck, how do we know what they actually don’t understand?
In this session
- distinguishing errors from misconceptions and knowledge gaps
- prerequisite knowledge
- diagnostic questions
- error analysis
- hinge questions
- curriculum dependency
- deciding what genuinely requires reteaching
- responding within normal classroom instruction rather than endlessly removing students for “intervention”
Session 2Explicit InstructionHow do we teach complex mathematics without overwhelming pupils?
In this session
- selecting the first example
- sequencing examples
- worked examples
- completion problems
- example/non-example
- representations
- variation
- mathematical language
- exposing mathematical structure
- checking for understanding
- guided practice
- independent practice
- fading support
Session 3From Number to AlgebraWhich gaps in number make algebra harder than it needs to be?
In this session
- equivalence and transformation
- additive versus multiplicative relationships
- fractions as numbers rather than pieces of pizza
- ratio and proportion
- distributivity
- seeing structure
- moving from numerical examples to general statements
- symbols as expressions of relationships rather than strange new objects
Session 4Problem SolvingHow do we get pupils thinking for themselves without leaving them to flounder?
In this session
- when students are ready for non-routine problems
- knowledge versus problem solving
- productive difficulty
- varying problems rather than simply making numbers bigger
- reasoning from examples
- generalising
- comparing methods
- removing scaffolds
- problem-solving prompts that preserve the problem
- keeping the mathematical destination constant while varying the support required to reach it
Dates & pricing
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Venues are currently being confirmed.
Select a location to view programme dates and pricing.
Primary 09:30–11:30Secondary 13:00–15:00
Programme dates
Programme dates
Cycle 1
Cycle 2
Pricing
Pricing
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Led by
Kieran Mackle & Stuart Welsh
Mathematics professional learning built around classroom decisions: what pupils need to understand, how to teach it clearly, and how to maintain ambition when learning becomes difficult.
ALTA Education
More than a one-off event.
The tour is also an opportunity to meet ALTA, explore our wider professional learning and teaching resources, and talk about support for your school or organisation.