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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.

01

Understanding

How do we know whether pupils have really understood?

02

Scaffold

How do we support pupils without making them dependent on adult guidance?

03

Expectations

How do we respond when pupils struggle without lowering expectations?

04

Assessment

How do we turn what we see in pupil work into precise next steps?

Explore the programme Register interest
The programme

Explore the programme.

Each programme contains four sessions. Open any session to see the detailed content.

Primary Programme

09:30–11:30
Session 1Explicit Instruction
How 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 2Scaffolding
How 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 3Challenge
Beyond 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 Number
Which 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

13:00–15:00
Session 1Understanding & Retention
What don’t pupils understand, and what have they simply forgotten?
In this session
  • distinguishing errors, misconceptions, missing prerequisites and forgotten knowledge
  • working memory, long-term memory and prior knowledge
  • diagnostic questions and hinge questions
  • retrieval practice for learning and next steps
  • feedback that improves learning
  • spacing and interleaving
  • deciding between more practice, a brief recap and full reteaching
  • using evidence to plan what happens next
Session 2Explicit Instruction & Representations
How do we make complex mathematics understandable without doing the thinking for pupils?
In this session
  • managing cognitive demand
  • selecting and sequencing examples
  • worked and partially worked examples
  • examples, non-examples and boundary cases
  • variation and exposing mathematical structure
  • manipulatives and visual representations
  • connecting concrete, pictorial and symbolic mathematics
  • guided practice and fading support
Session 3Mixed Attainment
How do we teach one ambitious lesson when pupils start from very different places?
In this session
  • whole-class teaching without one-size-fits-all instruction
  • using responsive checks to decide what happens next
  • differentiating support rather than mathematical goals
  • identifying missing prerequisite knowledge
  • Tier 1, Tier 2 and Tier 3 support
  • scaffolding as temporary support
  • maintaining high expectations and a shared mathematical destination
  • challenge through depth rather than simply acceleration
Session 4Mathematical Thinking
How do we help pupils think mathematically when the route isn’t obvious?
In this session
  • making sense of unfamiliar problems
  • identifying the mathematics beneath the surface
  • specialising and working systematically
  • conjecturing, testing and refining
  • generalising from examples and cases
  • goal-free problems and open mathematical exploration
  • purposeful prompts that preserve the thinking
  • justification, counterexamples and proof
Dates & pricing

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Venues are currently being confirmed.

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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.

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