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Grounded in the world's most successful primary mathematics methodology. Aligned with the New Primary Mathematics Curriculum 2023. Department of Education and Youth Inspectorate approved and EPV eligible (3 days). Built for every learner in every Irish primary classroom. Develop deep conceptual understanding through the Concrete-Pictorial-Abstract approach — the proven Singapore methodology that has produced world-leading mathematical outcomes for over four decades. Build confident, flexible mathematical thinkers through multiple solution pathways, structured variation and bar modelling. Support every learner — including those with special educational needs and diverse learning profiles — through genuinely inclusive teaching strategies aligned with NCSE Guidelines and Universal Design for Learning. This is mathematics teaching that changes what children believe about themselves. Paddy Teacher strives to offer affordable, practical training that immediately produces increased teacher competency and directly supports improved pupil outcomes. Comparable teacher training is currently priced at over €900 through other providers. This is among the first courses of its type to be facilitated in Ireland. Limited spaces are available. Secure your enrolment today. Please note: This course is open to teachers and NQTs currently teaching or residing in the Republic of Ireland. A separate international course is available for EU, US, and Canadian teachers — contact us for details.

Conceptual Mastery

Develop deep understanding of number through CPA, ensuring pupils grasp the “why” behind mathematical processes, not just the method.

Flexible Strategies

Equip pupils with multiple solution pathways, including decomposition and compensation, to build confidence, fluency and adaptable thinking.

Practical Impact

Implement ready-to-use classroom approaches that improve assessment, address misconceptions and enhance pupil outcomes immediately.

About the course

This practical, classroom-focused course is designed to enhance your mathematics teaching by strengthening pedagogical content knowledge, refining instructional strategies and deepening your approach to assessment — in full alignment with the New Primary Mathematics Curriculum 2023 and Ireland's national commitment to inclusive education for every child. You will learn how to apply the Concrete-Pictorial-Abstract progression to build secure conceptual understanding before introducing formal written methods. The course explores structured variation, multiple solution pathways and Singapore computational strategies — including decomposition, compensation and left-to-right approaches — to develop flexibility, fluency and mathematical reasoning. You will also build expertise in bar modelling to support problem-solving, enabling pupils to visualise relationships and represent unknown quantities with clarity and confidence. Directly supporting the Number strand of the New Primary Mathematics Curriculum 2023, this course affirms that every child is mathematical. Through flexible number strategy, multiple solution paths and multiple entry points grounded in the CPA approach, Singapore Mathematics makes genuine mathematical understanding accessible to every learner — including those with special educational needs, English as an additional language, and diverse learning profiles — in full alignment with NCSE Guidelines, Universal Design for Learning and the Cosán Framework for Teachers' Learning. By the end of this course, you will have a clear, structured and evidence-based approach to teaching addition and subtraction - empowering you to improve pupil confidence, conceptual understanding and mathematical achievement across your school. This 20-hour synchronous summer course has been formally evaluated and approved by the Inspectorate of the Department of Education and Youth and results in qualified teachers receiving a certificate of course completion and eligibility for 3 EPV days. The course is structured across five modules, totalling 20 hours of professional learning: 15 hours of course content (including pre-recorded video instruction, reading, structured activities and one mandatory live synchronous online event/webinar) and 5 hours of independent study and reading. Each module is to be completed sequentially, building knowledge and pedagogical skill progressively across the programme. COURSE DATES COHORT 1 Sunday, 12th of July – Saturday, 26th of July, 2026 Live Webinar Event (mandatory course completion requirement) Thursday 24th of July 2026 - Morning session: 10:00am – 12:00pm - Lunch break: 12:00pm – 1:15pm - Afternoon session: 1:15pm – 3:15pm

Patrick Griffin - Course Trainer

Patrick Griffin is a highly experienced primary educator with 22 years of classroom teaching, special education and school leadership experience. A fully registered teacher in Ireland, Scotland and the United States, he has spent 17 years mentoring Newly Qualified Teachers across multiple education systems. Patrick holds a Master’s Degree in Primary Education. He has been selected by education authorities in the US and Scotland to share best practice in Mathematics and Science, and contributed to Scotland’s Curriculum for Excellence. Patrick brings deep expertise in curriculum development, inclusive practice and high-impact teaching methods, with a particular focus on Singapore Mathematics methodology and its transformative impact on pupil outcomes.

Curriculum

30 Chapters · 162 Lessons

1
1. (Included in full purchase)
  Academic Integrity Policy
2. (Included in full purchase)
  Overview
3. (Included in full purchase)
  Course Aims
4. (Included in full purchase)
  Promoting Inclusivity
5. (Included in full purchase)
  Intellectual Property and Copyright Notice
6. (Included in full purchase)
  Key Reference Documents
7. (Included in full purchase)
  Course Reading List
8. (Included in full purchase)
  Self-Directed Reading Guide and Reading Log
9. (Included in full purchase)
  Assessment and Completion Criteria Assignment
10. (Included in full purchase)
  Discussion Forum Protocol
2
1. (Included in full purchase)
  Module 1 Overview
2. (Included in full purchase)
  Module 1 Learning Outcomes
3
1. (Included in full purchase)
  M1-S1.1: From Crisis to Global Model
2. (Included in full purchase)
  M1-S1.2: Two Key Decisions: Language and Depth
3. (Included in full purchase)
  M1-S1.3: The Pentagon Model
4. (Included in full purchase)
  M1-S1.4: From the Bottom to the Summit
5. (Included in full purchase)
  M1-S1.5 One Generation Is All It Takes
6. (Included in full purchase)
  Module 1: Section 1 - Participant Attention Check
4
1. (Included in full purchase)
  M1-S2.1: Conceptual Understanding and Metacognition
2. (Included in full purchase)
  M1-S2.2: Inquiry-Based Learning and Mathematical Reasoning
3. (Included in full purchase)
  M1-S2.3: Mathematical Communication and Problem Solving Competency
4. (Included in full purchase)
  M1-S2.4: Promoting Inclusivity: Approaches to Teaching and Learning
5. (Included in full purchase)
  M1-S2.5: Promoting Inclusivity: Learning Diversity and Inclusion
6. (Included in full purchase)
  M1-S2.6: Collaborative Reflective Inquiry
7. (Included in full purchase)
  M1-S2.7: Ongoing School Improvement
8. (Included in full purchase)
  Module 1: Section 2 - Participant Attention Check
5
1. (Included in full purchase)
  M1-S3.1: What is the CPA (Concrete-Pictorial-Abstract) Approach?
2. (Included in full purchase)
  M1-S3.2: Why not Rote Learning and Assessment for Accuracy only?
3. (Included in full purchase)
  M1-S3.3: Origins of the CPA Approach: Jean Piaget
4. (Included in full purchase)
  M1-S3.4: Origins of the CPA Approach: Zoltán Dienes
5. (Included in full purchase)
  M1-S3.5: Origins of the CPA Approach: Jerome Bruner
6. (Included in full purchase)
  M1-S3.6: Origins of the CPA Approach: Lev Vygotsky
7. (Included in full purchase)
  M1-S3.7: Conceptual Understanding vs. Procedural Understanding: Richard Skemp
8. (Included in full purchase)
  M1-S3.8: Variation Theory: Conceptual Variation and Procedural Variation
9. (Included in full purchase)
  M1-S3.9: Modelled Progression: CPA-based example of Addition
10. (Included in full purchase)
  M1-S3.10: Reflective Discussion Forum Assignment
11. (Included in full purchase)
  Module 1: Section 3 - Participant Attention Check
6
1. (Included in full purchase)
  M1-S4.1: What is Number Sense? Define Mathematical Relationships.
2. (Included in full purchase)
  M1-S4.2: What is Relational Understanding?
3. (Included in full purchase)
  M1-S4.3: Counting, Number Conservation and Subitising
4. (Included in full purchase)
  M1-S4.4: Representing Number, Combining and Partitioning
5. (Included in full purchase)
  M1-S4.5: Why Number Bonds support Fluency, Flexibility and Understanding
6. (Included in full purchase)
  M1-S4.6: Flexibile Thinking and Mental Strategy: Decomposition (Partitioning) - Addition and Subtraction
7. (Included in full purchase)
  M1-S4.7: Flexibile Thinking and Mental Strategy: Compensation - Addition and Subtraction
8. (Included in full purchase)
  M1-S4.8: Why Multiple Representations are Important (Supporting Connections through CPA)
9. (Included in full purchase)
  Module 1: Section 4 - Participant Attention Check
7
1. (Included in full purchase)
  M1-S5.1: Ensuring Equitable Access through Differentiated Instruction
2. (Included in full purchase)
  M1-S5.2: What is Cognitive Load? What is Linguistic Demand?
3. (Included in full purchase)
  M1-S5.3: Reducing Cognitive Load and Linguistic Demand
4. (Included in full purchase)
  M1-S5.4: Overcoming Directionality Challenges
5. (Included in full purchase)
  M1-S5.5: Improving Performance and Attainment
6. (Included in full purchase)
  M1-S5.6: CPA Lesson Reflective Discussion Forum Assignment
7. (Included in full purchase)
  M1-S5.7: Reflective Discussion Forum Assignment
8. (Included in full purchase)
  Module 1: Section 5 - Participant Attention Check
8
1. (Included in full purchase)
  Module 2 Overview
2. (Included in full purchase)
  Module 2 Learning Outcomes
9
1. (Included in full purchase)
  M2-S1.1: The Singapore Approach to Addition and Its Alignment With the New Primary Mathematics Curriculum 2023
2. (Included in full purchase)
  M2-S1.2 Singapore Approach: Importance of Addition Language and Maths Talk
3. (Included in full purchase)
  M2-S1.3 Properties of Addition: Identity Property (Zero Property)
4. (Included in full purchase)
  M2-S1.4 Properties of Addition: Commutative Property
5. (Included in full purchase)
  M2-S1.5: Properties of Addition: Associative Property
6. (Included in full purchase)
  M2-S1.6: Multiple Addition Structures
7. (Included in full purchase)
  M2-S1.7: Importance of Part-Part-Whole Relationship
10
1. (Included in full purchase)
  M2-S2.1: The Concrete–Pictorial–Abstract (CPA) Sequence of Addition (Teaching and Learning)
2. (Included in full purchase)
  M2-S2.2: Concrete Stage: Using manipulatives to support representation and communication
3. (Included in full purchase)
  M2-S2.3: Pictorial Stage: Using visual models to support representation and communication
4. (Included in full purchase)
  M2-S2.4: Abstract Stage: Using abstract symbols to support representation and communication
5. (Included in full purchase)
  M2-S2.5: Advantages of Multiple Solution Paths for Deep Conceptual Understanding of Addition
6. (Included in full purchase)
  Module 2: Section 2 - Participant Attention Check
11
1. (Included in full purchase)
  M2-S3.1: Base Ten Place Value System and Addition through Partitioning
2. (Included in full purchase)
  M2-S3.2: Singapore Addition Approach: Dynamic Compensation (Concrete-Pictorial-Abstract)
3. (Included in full purchase)
  M2-S3.3: Singapore Addition Approach: Number Bonds - Horizontal Orientation (Concrete-Pictorial)
4. (Included in full purchase)
  M2-S3.4: Singapore Addition Approach: Number Bonds - Horizontal Orientation (Abstract 1-3 digit addends)
5. (Included in full purchase)
  M2-S3.5: Singapore Addition Approach: Left to Right Vertical Orientation (1 digit addends)
6. (Included in full purchase)
  M2-S3.6: Singapore Addition Approach: Left to Right Vertical Orientation (2 digit addends)
7. (Included in full purchase)
  M2-S3.7: Singapore Addition Approach: Left to Right Vertical Orientation (3+ digit addends)
8. (Included in full purchase)
  M2-S3.8: Singapore Addition Approach vs Traditional Algorithm (Vertical Column Addition)
12
1. (Included in full purchase)
  M2-S4.1: Defining Structured Variation within Addition
2. (Included in full purchase)
  M2-S4.2: Designing Differentiated Addition Tasks: Multiple Entry Points
3. (Included in full purchase)
  M2-S4.3: Mathematical Language of Addition and Visualisation (Multilingual Learners)
4. (Included in full purchase)
  M2-S4.4: Scaffolded Learning of Addition: Revisiting Stages to Support Understanding
5. (Included in full purchase)
  Module 2: Section 4 - Participant Attention Check
13
1. (Included in full purchase)
  M2-S5.1: Identifying and Analysing Common Misconceptions in Addition
2. (Included in full purchase)
  M2-S5.2: Applying Formative Assessment Strategies for Addition
3. (Included in full purchase)
  M2-S5.3: Strengthening Pupil Understanding: Evidence-Based Responsive Teaching
4. (Included in full purchase)
  M2-S5.4: Why is Addition Competency Critical?
5. (Included in full purchase)
  M2-S5.5: Reflective Discussion Forum Assignment
6. (Included in full purchase)
  Module 2: Section 5 - Participant Attention Check
14
1. (Included in full purchase)
  Module 3 Overview
2. (Included in full purchase)
  Module 3 Learning Outcomes
15
1. (Included in full purchase)
  M3-S1.1: The Singapore Approach to Subtraction and Its Alignment With the New Primary Mathematics Curriculum 2023
2. (Included in full purchase)
  M3-S1.2: Singapore Approach: Importance of Subtraction Language and Maths Talk
3. (Included in full purchase)
  M3-S1.3: Properties of Subtraction: Identity Property (Zero Property)
4. (Included in full purchase)
  M3-S1.4: Properties of Subtraction: Non-Commutative Property
5. (Included in full purchase)
  M3-S1.5: Properties of Subtraction: Non-Associative Property
6. (Included in full purchase)
  M3-S1.6: Multiple Subtraction Structures
7. (Included in full purchase)
  M3-S1.7: Importance of Part-Part-Whole Relationship (Inverse of Addition)
8. (Included in full purchase)
  Module 3: Section 1 - Participant Engagement Check
16
1. (Included in full purchase)
  M3-S2.1: The Concrete–Pictorial–Abstract (CPA) Sequence of Subtraction (Teaching and Learning)
2. (Included in full purchase)
  M3-S2.2: Concrete Stage: Using manipulatives to support representation and communication
3. (Included in full purchase)
  M3-S2.3: Pictorial Stage: Using visual models to support representation and communication
4. (Included in full purchase)
  M3-S2.4: Abstract Stage: Using abstract symbols to support representation and communication
5. (Included in full purchase)
  M3-S2.5: Advantages of Multiple Solution Paths for Deep Conceptual Understanding of Subtraction
17
1. (Included in full purchase)
  M3-S3.1: Base Ten Place Value System and Subtraction through Partitioning
2. (Included in full purchase)
  M3-S3.2: Singapore Subtraction Approach: Dynamic Compensation (Concrete-Pictorial-Abstract)
3. (Included in full purchase)
  M3-S3.3: Singapore Subtraction Approach: Number Bonds - Horizontal Orientation (Concrete-Pictorial)
4. (Included in full purchase)
  M3-S3.4: Singapore Subtraction Approach: Number Bonds - Horizontal Orientation (Abstract 1-3 digit minuends and subtrahends)
5. (Included in full purchase)
  M3-S3.5: Singapore Subtraction Approach: Left to Right Vertical Orientation (1 digit Singapore Subtraction Approach: Left to Right Vertical Orientation (1 digit minuends and subtrahends)
6. (Included in full purchase)
  M3-S3.6: Singapore Subtraction Approach: Left to Right Vertical Orientation (2 digit minuends and subtrahends)
7. (Included in full purchase)
  M3-S3.7: Singapore Subtraction Approach: Left to Right Vertical Orientation (3+ digit minuends and subtrahends)
8. (Included in full purchase)
  M3-S3.8: Singapore Subtraction Approach vs Traditional Algorithm (Vertical Column Subtraction)
9. (Included in full purchase)
  Module 3: Section 3 - Participant Engagement Check
18
1. (Included in full purchase)
  M3-S4.1: Defining Structured Variation (Subtraction)
2. (Included in full purchase)
  M3-S4.2: Designing Differentiated Subtraction Tasks: Multiple Entry Points
3. (Included in full purchase)
  M3-S4.3: Mathematical Language of Subtraction and Visualisation (Multilingual Learners)
4. (Included in full purchase)
  M3-S4.4: Scaffolded Learning of Subtraction: Revisiting Stages to Support Understanding
5. (Included in full purchase)
  Module 3: Section 4 - Participant Engagement Check
19
1. (Included in full purchase)
  M3-S5.1: Identifying and Analysing Common Misconceptions in Subtraction
2. (Included in full purchase)
  M3-S5.2: Applying Formative Assessment Strategies for Subtraction
3. (Included in full purchase)
  M3-S5.3: Strengthening Pupil Understanding: Evidence-Based Responsive Teaching
4. (Included in full purchase)
  M3-S5.4: Why is Subtraction Competency Critical?
5. (Included in full purchase)
  M3-S5.5: Reflective Discussion Forum Assignment
6. (Included in full purchase)
  Subtraction Misconception Analysis Task (Sample-Based)
20
1. (Included in full purchase)
  Module 4 Overview
2. (Included in full purchase)
  Module 4 Learning Outcomes
21
1. (Included in full purchase)
  M4-S1.1: What is Bar Modelling?
2. (Included in full purchase)
  M4-S1.2: Alignment with PMC Priorities: Problem Solving
3. (Included in full purchase)
  M4-S1.3: Alignment with PMC Priorities: Reasoning
4. (Included in full purchase)
  M4-S1.4: Alignment with PMC Priorities: Representation and Communication
5. (Included in full purchase)
  M4-S1.5: Part-Whole Bar Model
6. (Included in full purchase)
  M4-S1.6: Comparison Bar Model
7. (Included in full purchase)
  Module 4-Section 1: Participant Engagement Check
22
1. (Included in full purchase)
  M4-S2.1: What are Problem-Solving Heuristics?
2. (Included in full purchase)
  M4-S2.2: Common Addition Problem-Solving Heuristics
3. (Included in full purchase)
  M4-S2.3: Common Subtraction Problem-Solving Heuristics
4. (Included in full purchase)
  M4-S2.4: Word Problem Sequencing: Recommended Progression for Addition and Subtraction
5. (Included in full purchase)
  M4-S2.5: Importance of Teaching Strategic Thinking and Growth Mindset
6. (Included in full purchase)
  Module 4 - Section 2: Participant Engagement Check
23
1. (Included in full purchase)
  M4-S3.1: Use of the Concrete–Pictorial–Abstract (CPA) approach within Word Problem Solving
24
1. (Included in full purchase)
  M4-S4.1: Inclusive Teaching: Multiple Entry Points for Problem Solving
2. (Included in full purchase)
  M4-S4.2: The Importance of Visualisation and Reducing Linguistic Complexity
3. (Included in full purchase)
  M4-S4.3: Restating the Problem and Forming Representations
4. (Included in full purchase)
  M4-S4.4: Procedure for Step-by-Step Reasoning
5. (Included in full purchase)
  M4-S4.5: Simplifying the Problem - Identifying Necessary Operations to Solve
6. (Included in full purchase)
  Module 4 - Section 4: Participant Engagement Check
25
1. (Included in full purchase)
  M4-S5.2: Reflective Discussion Forum Assignment
2. (Included in full purchase)
  Course Summative Singapore Methodology Proficiency Task
26
1. (Included in full purchase)
  Module 5 Overview
2. (Included in full purchase)
  Module 5 Learning Outcomes
27
1. (Included in full purchase)
  M5-S1.1: Opportunities for Teaching Singapore Mathematics Methodologies Within the Irish Primary Curriculum Framework
28
1. (Included in full purchase)
  M5-S3.1: Final Course Reflection Assignment
29
1. (Included in full purchase)
  M5-S4.1: Enhanced Teacher Practice = Improved Pupil Achievement
2. (Included in full purchase)
  M5-S4.2: Collaborative Planning and Reflection — Singapore Mathematics Integration in Irish Primary Schools
3. (Included in full purchase)
  M5-S4.3: Pupil Records Review: Pace and Challenge, Opportunities, Knowledge Gaps
4. (Included in full purchase)
  M5-S4.4: Embedding CPA in Daily Instruction in the Irish Primary Mathematics Classroom
5. (Included in full purchase)
  M5-S4.5: Ongoing Assessment for Learning and Responsive Teaching
30
1. (Included in full purchase)
  M5-S5.1: Mapping the Curriculum
2. (Included in full purchase)
  M5-S5.2: Establishing Baseline
3. (Included in full purchase)
  M5-S5.3: Timelines
4. (Included in full purchase)
  M5-S5.4: Building Teacher Pedagogical Capacity
5. (Included in full purchase)
  M5-S5.5: Reflective Implementation
6. (Included in full purchase)
  Paddy Teacher Course Participant Evaluation Form

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