Best AI for Number Sense and Mathematics Foundations in 2026

Quick Answer: AI for number sense and mathematics foundations generates Dehaene-aligned number line and approximate number system activities; Kamii constructivist logico-mathematical knowledge building sequences; Clements and Sarama learning trajectory-based lesson progressions from counting through operations; Fosnot and Dolk problem-centered mathematics investigations; Boaler mathematical mindsets growth-oriented classroom structures; Skemp relational understanding lesson designs that build conceptual before procedural knowledge; and Van de Walle three-part lesson structures for conceptual development. EduGenius (edugenius.app) supports K-9 educators with research-based mathematics instruction content.

Mathematics education has a persistent and well-documented achievement problem that is distinct from general educational underperformance: enormous numbers of students who succeed reasonably well in other academic domains experience profound difficulty with mathematics, developing mathematical anxiety, avoidance, and disidentification that persist into adulthood and constrain their educational and occupational choices. This pattern is not evenly distributed — it disproportionately affects girls, students from lower-income families, and students from racial and ethnic minority groups — and it is substantially created by school mathematics instruction rather than by any genuine incapacity in these students.

The research on what school mathematics instruction does wrong is convergent: most school mathematics instruction focuses on procedures (the steps for getting the right answer) at the expense of concepts (what is actually happening mathematically and why the procedures work). Students who learn procedures without concepts become dependent on memorization; cannot apply their knowledge flexibly to novel problems; feel that mathematics is arbitrary and mysterious; and are highly vulnerable to forgetting or confusing the procedures they have memorized when they cannot fall back on understanding. This produces the well-documented "brittle" mathematical knowledge that characterizes many students: confident performance on familiar problem types; complete collapse when the problem type changes even slightly.

The research on what effective mathematics instruction looks like — instruction that produces durable, flexible, and genuine mathematical understanding — is equally convergent: it begins with concrete, contextual mathematical sense-making; develops students' intuitive understanding of quantity, magnitude, and relationship; connects procedures to the conceptual understanding that makes them meaningful; and treats mathematical thinking as a sense-making activity rather than a rule-following activity.

Research Foundations of Number Sense and Mathematics Education

Stanislas Dehaene: The Neuroscience of Number Sense

Stanislas Dehaene (Collège de France, Paris), in The Number Sense: How the Mind Creates Mathematics (1997, revised 2011) and numerous subsequent publications in cognitive neuroscience, established the neurological foundations of numerical cognition — providing the most rigorous account of what number sense is, where it comes from, and how mathematical instruction can support or undermine it:

The Approximate Number System (ANS): Dehaene's most foundational finding is that humans — and many other animals — possess an innate "number sense" in the form of the Approximate Number System: a core cognitive capacity, present from birth and operative across cultures without formal instruction, for perceiving and comparing numerical magnitudes approximately. Infants as young as four days old demonstrate sensitivity to changes in numerical quantity (Antell & Keating, 1983); by five months, infants show surprise when a small number of objects is changed (Wynn, 1992). This is not learned from instruction; it is a biological endowment.

The ANS is approximate (not exact) and operates according to Weber's Law: the ability to discriminate between two quantities decreases as the ratio between them approaches 1. We can instantly and accurately perceive that ten objects is more than three objects (large ratio), but have difficulty perceiving that eleven objects is more than ten (ratio approaching 1). Individual differences in ANS acuity — how well people can discriminate between quantities — are significantly correlated with formal mathematical achievement (Halberda et al., 2008): students with more precise ANS perform better at mathematics even controlling for other cognitive factors.

The Triple-Code Model: Dehaene proposes that the brain processes numbers in three distinct representational formats:

1. Visual Arabic numerals: The written symbols "3," "47," "π" — processed primarily in visual cortex
2. Verbal number words: The spoken/heard words "three," "forty-seven" — processed in language areas
3. Analog magnitude representation (the "number line" in the brain): The intuitive sense of how big a number is, its place in a continuum of magnitude — associated with the parietal cortex, particularly the intraparietal sulcus (IPS)

The Mental Number Line: Perhaps Dehaene's most influential educational contribution is his characterization of the internal "mental number line" — the spatial representation of numerical magnitude in which smaller numbers are mentally mapped to the left and larger numbers to the right (in Western left-to-right reading cultures). This representation is not merely metaphorical; neuroimaging shows systematic spatial activation patterns corresponding to numerical magnitude. Crucially, young children's mental number line is initially logarithmic (numbers feel more compressed at the large end); with development and instruction, it becomes linear (evenly spaced from 1 to any given upper bound). Training that helps children develop a linear number line — through number line estimation tasks; counting and quantity activities; and board games with linear spatial layouts (Ramani & Siegler, 2008) — produces measurable improvements in arithmetic and number sense.

Implications for Mathematics Education: Dehaene's research has several direct implications for early mathematics instruction:

• The approximate number system is a foundation for formal mathematics, and instruction should deliberately connect formal symbolic arithmetic to the ANS (developing intuitive magnitude sense alongside procedural facility)
• Number line activities are particularly powerful for developing the linear magnitude representation associated with mathematical achievement
• Mathematical instruction that focuses only on symbolic manipulation (procedures with numerals) without connecting to the underlying magnitudes risks creating "math without number sense" — procedural performance disconnected from intuitive understanding

Constance Kamii: Constructivist Mathematics

Constance Kamii (University of Alabama at Birmingham), building on Piaget's framework, in Young Children Reinvent Arithmetic (1985, second edition 2000), Young Children Continue to Reinvent Arithmetic: 2nd Grade (1989), and related volumes, developed a constructivist approach to mathematics education grounded in the distinction between different types of knowledge:

Piaget's Three Types of Knowledge:

1. Physical knowledge: Knowledge of observable properties of objects — that a rubber ball bounces; that ice is cold. Developed by acting on objects and observing the result; the source of knowledge is the object.
2. Social (conventional) knowledge: Knowledge that is arbitrary social convention — that symbols are called "letters"; that 3 is written with a specific squiggle; that Tuesday comes after Monday. The source of knowledge is social convention; it must be transmitted.
3. Logico-mathematical knowledge: The most important type for mathematics education. Logico-mathematical knowledge is neither in the object nor in the social convention but is constructed by the mind through reflective abstraction — through mentally comparing, relating, and organizing. The number "two" is not a property of two objects (physical knowledge) nor just a word we've agreed to use (social knowledge) but a relationship that the mind constructs by comparing quantities — the same relationship that holds between any two pairs of objects, regardless of what those objects are.

The Critical Implication: Logico-mathematical knowledge cannot be transmitted — it can only be constructed by the learner through active engagement. This means that telling children the facts of arithmetic, or demonstrating procedures, does not build mathematical understanding; it builds knowledge of social conventions (how we write numbers; what symbols we use) and physical knowledge (what happens when I add objects) but not the logico-mathematical relationships that constitute genuine mathematical understanding.

Constructivist Mathematics Classroom: Kamii's constructivist mathematics classroom is organized around activities that require children to construct logico-mathematical relationships:

• Children are presented with genuine mathematical problems (not practice exercises with predetermined methods)
• Children work through problems using their own invented methods, reasoning, and strategies
• Children share and discuss their methods — explaining their reasoning to each other
• Multiple methods are compared and evaluated for efficiency and generalizability
• The teacher's role is to facilitate sense-making through questioning, not to demonstrate correct procedures

Critique of Standard Algorithms: Kamii's most controversial (and most research-supported) position is that teaching standard algorithms for arithmetic too early — before children have constructed genuine understanding of number relationships and place value — actually harms children's mathematical development by replacing their own logical reasoning with memorized procedures. Children who are given the standard addition algorithm before they genuinely understand place value stop thinking about what they are doing and start following steps — a regression from logical reasoning to mechanical procedure-following.

Douglas Clements and Julie Sarama: Learning Trajectories

Douglas Clements (University of Denver) and Julie Sarama (University of Denver), through decades of research culminating in Learning and Teaching Early Math: The Learning Trajectories Approach (2009, third edition 2021) and the Building Blocks curriculum, developed the most carefully researched account of the developmental progression of mathematical understanding in early childhood:

The Learning Trajectory Model: Clements and Sarama define a learning trajectory as consisting of three components:

1. Goal: A specific, significant mathematical objective — "understand cardinality" or "compare and order numbers"
2. Developmental progression: The sequence of levels of thinking through which children typically develop toward the goal — described in enough detail to be diagnostically useful
3. Instructional sequence: The types of experiences and activities that are most effective for helping children move from each level to the next

Sample Learning Trajectory: Counting: The counting trajectory illustrates the approach's power. Rather than treating "counting" as a single skill to be taught at once, Clements and Sarama identify ten developmental levels, from "Pre-Explicit Number" (0-1 year; no explicit number sense beyond very small quantities) through successive levels of counting competence, including:

• Level 1 — Chanter: Recites number words in sequence but without meaningful reference to quantities
• Level 3 — Reciter: Can count up to 5 with one-to-one correspondence
• Level 5 — Counter: Can reliably count up to 10 objects with one-to-one correspondence; cardinality (the last number reached is the count)
• Level 7 — Counter and Producer: Can count up to 30 and produce sets of given quantity
• Level 9 — Counter Backward from 10: Can count backward and understands number relationships
• Level 10 — Counter from N (N+1, N-1): Counts on from any number; beginning of addition and subtraction as operations on number sequences

Each level has specific characteristics (what children can and cannot do) and specific instructional activities that help children develop from that level to the next. The trajectory is diagnostic: a teacher who knows where each student is on the trajectory knows specifically what instruction will be most productive.

The Building Blocks Curriculum: Building Blocks is a comprehensive PreK-K mathematics curriculum grounded in the learning trajectory approach, with activities precisely calibrated to specific developmental levels and with embedded assessment that tracks students' progress through the trajectories. Research on Building Blocks shows consistent effects on mathematical learning, particularly for students from lower-income backgrounds.

Cathy Fosnot and Maarten Dolk: Young Mathematicians at Work

Cathy Fosnot (City College of New York) and Maarten Dolk (Freudenthal Institute, Netherlands), in the four-volume series Young Mathematicians at Work (Constructing Number Sense, Addition, and Subtraction, 2001; Constructing Multiplication and Division, 2001; Constructing Fractions, Decimals, and Percents, 2002; Algebra, 2005), developed the most complete pedagogical framework for building genuine mathematical thinking in K-5 classrooms:

Landscapes of Learning: Fosnot and Dolk reject the linear progression model of mathematics education (teach skill A, then skill B, then skill C) in favor of what they call "landscapes of learning" — nonlinear descriptions of the strategies, big ideas, and models that develop as children engage in genuine mathematical problem-solving. The landscape metaphor is deliberate: learners do not all travel the same path to mathematical understanding; they may approach from different directions, develop different strategies first, and reach the same destination by different routes.

Big Ideas vs. Procedures: Fosnot and Dolk emphasize "big ideas" — the fundamental organizing concepts of mathematics — over procedures. Big ideas in number: quantity; unitizing (ten ones can be treated as one ten); equivalence; compensation (if you add to one addend, you must subtract from the other to maintain the sum). These big ideas emerge from genuine mathematical problem-solving and provide the conceptual scaffolding within which procedures make sense.

The Minilessons and Investigations: Fosnot and Dolk's instructional approach involves two primary forms:

• Investigations: Extended open-ended problem contexts (often lasting multiple class periods) that allow children to explore mathematical ideas through genuine problem-solving — producing diverse strategies that are then shared, discussed, and compared in class conferences. The investigations are carefully designed to be mathematically rich: they open into multiple problem-solving approaches; they develop the target big ideas; and they are genuinely engaging.
• Minilessons: Shorter, more focused sessions using specific computational strings or number talks to develop specific strategies and relationships. A computational string is a series of related problems designed to draw attention to mathematical relationships: 4+4; 4+5; 4+6; 14+6; 24+6 — the relationships among these problems help students develop strategies based on number relationships rather than isolated memorization.

Jo Boaler: Mathematical Mindsets and Growth in Mathematics

Jo Boaler (Stanford University), in Mathematical Mindsets: Unleashing Students' Potential Through Creative Math, Inspiring Messages, and Innovative Teaching (2015) and Limitless Mind: Learn, Lead, and Live Without Barriers (2019), applied Carol Dweck's growth mindset research specifically to the endemic problem of mathematical anxiety, underperformance, and disidentification:

Mathematical Mindset Research: Boaler documents the specific ways in which school mathematics instruction, as typically practiced, creates fixed mindsets about mathematical ability: the emphasis on speed (timed tests; flash cards) communicates that mathematical ability is about quick retrieval; the emphasis on correct procedures (one right way to solve each problem) communicates that mathematical thinking is about rule-following rather than reasoning; and the persistent cultural myth that mathematical ability is a genetic gift that some people have and others don't creates a fixed-ability narrative that students who struggle early accept about themselves.

Mathematics as Creativity, Visualization, and Connection: Boaler's most important positive contribution is her documentation — through classroom research, student interviews, and review of neuroscience research — that high mathematical performance is associated with: connecting mathematical ideas across representations (visual, symbolic, contextual, tabular, graphical); making unexpected connections between apparently unrelated mathematical domains; approaching problems from multiple directions; and being comfortable with ambiguity and productive struggle — not with fast procedural retrieval. This understanding of mathematical excellence as multi-representational, connected, and creative has direct implications for what classroom mathematics instruction should look like.

Five Principles of Mathematical Mindsets Teaching:

1. Everyone can learn math at the highest levels
2. Mistakes are valuable (struggle activates brain growth; error analysis deepens understanding)
3. Questions are valued and curiosity is celebrated
4. Depth matters more than speed
5. Mathematics is visual, creative, and connected — not linear, procedural, and isolated

Mathematical Conversations and Number Talks: Boaler advocates strongly for mathematical discussion — specifically number talks (Parrish, 2010, developed from Kathy Richardson's work) in which students share and compare their mental computation strategies, making the diversity of mathematical approaches visible and valued. Number talks are particularly powerful for developing number sense because they make students' flexible, non-algorithmic reasoning about numbers visible and celebrated.

Richard Skemp: Relational and Instrumental Understanding

Richard Skemp (1919-1995, University of Warwick), in the enormously influential paper "Relational Understanding and Instrumental Understanding" (Mathematics Teaching, 1976) — described by many mathematics educators as the most important short paper in mathematics education — made a fundamental distinction that continues to organize the debate about mathematics instruction:

Instrumental Understanding: Knowing what rule to apply and how to apply it, without understanding why the rule works. 'Ours is not to reason why, just invert and multiply.' Instrumental understanding can produce correct answers on familiar problems quickly and efficiently. It does not support transfer to new problem types; it does not support mathematical reasoning; and it is highly fragile — a single confusion about which rule applies produces complete failure.

Relational Understanding: Knowing both what to do AND why — understanding the mathematical relationships that the rule expresses. Relational understanding develops a mental map of mathematical territory rather than a set of rules for specific routes. Relational understanding is slower to build but produces durable, flexible, transferable mathematical knowledge that supports genuine problem-solving.

The Teaching Dilemma: Skemp identifies a genuine teaching dilemma: instrumental understanding is faster to teach, easier to assess (by testing rule-application), and produces immediate success (students get the right answers). Relational understanding takes longer to develop, is harder to assess (genuine understanding is often expressed in imprecise, exploratory, partially correct reasoning), and produces apparent confusion and error in the short term. As a result, pressured teachers, pressured by coverage demands and assessment requirements, consistently choose instrumental over relational instruction — with the long-term result that students who can follow procedures cannot think mathematically.

Relational Teaching Principles: Skemp's implicit instructional principles include: allow and encourage multiple methods; require explanation of why, not just what; use problems that make the mathematical relationship visible; accept and explore incorrect approaches rather than quickly redirecting to the correct procedure; and assess for understanding, not just correct answers.

AI Applications in Number Sense and Mathematics Foundations

Number Sense and Conceptual Development

"Design a complete Grade 2 Number Sense unit — 'Understanding Addition and Subtraction: Building a Mathematical Mind, Not a Calculation Machine' — grounded in Kamii's constructivist approach, Clements and Sarama's learning trajectory framework, and Skemp's relational understanding principles. This unit explicitly develops relational understanding before procedural efficiency. Duration: 6 weeks. Goals: Students will understand addition and subtraction as relationships between quantities (not just as procedures for getting answers); will develop flexible, multiple strategies for computation rather than a single algorithm; will be able to explain and justify their reasoning; and will extend their counting-on and decomposition strategies to larger numbers. Learning Trajectory Starting Points: Teacher diagnostic assessment (day 1-2): Using brief individual interviews (3-4 minutes each) and observational tasks, identify where each student is on the addition/subtraction learning trajectory. Key questions: Can they count on from any number (or do they count from 1 every time)? Do they understand the commutative property intuitively (do they start with the larger addend)? Do they decompose numbers flexibly (e.g., seeing 9+7 as 10+6)? Can they subtract by counting up (on a number line or mentally) as well as by removing? Week 1 — Building the Number Line: Students work with physical number lines (floor-length masking tape number line walked on; individual number lines drawn to scale). Key activities: Estimating where numbers belong on a 0-100 number line; playing 'where am I?' games; constructing physical groups of objects and placing them on the number line; comparing quantities (how much more?; how much less?; how far apart?). Goal: Develop intuitive linear number sense — the mental representation of numbers as continuous magnitudes in sequence. Week 2-3 — Strategies Rather Than Algorithm: Students are explicitly NOT shown the standard addition algorithm. Instead: multiple sessions of 'number talks' (5-7 minutes daily): teacher writes a problem (e.g., 47+28); students solve mentally; each student shares their strategy. Teacher records all strategies on board: 'I added 47+30=77 then subtracted 2 to get 75.' 'I decomposed: 40+20=60; 7+8=15; 60+15=75.' 'I started with 48+27=75 (moving 1 off the 28 onto the 47).' Students evaluate strategies: 'Which is most efficient? Which can you explain? Which makes you less likely to make errors?' Investigation: 'The store problem' — given a store with items priced between 10¢ and 99¢ and a budget of $1.50, how many different combinations of items can you buy? Students must add and subtract flexibly to solve; teacher facilitates discussion of strategies. Week 4-5 — Understanding Subtraction: Subtraction as distance vs. subtraction as removal: these are different mental models. Distance model (how far is it from 38 to 63?) vs. removal model (if I have 63 and spend 38, how many remain?). Activities that make both models visible. Counting-up strategy for subtraction: 63-38 is 'how much do I add to 38 to get to 63?' — students use number lines to develop this strategy, which is often more efficient and less error-prone than 'borrowing.' Week 6 — Application and Consolidation: Open-ended problem contexts that require flexible addition and subtraction in realistic settings; partner games that build fluency; individual reflection: 'What is your most reliable strategy? What strategy are you still developing?' Full unit with: diagnostic interview protocol; number talk facilitation guide; all investigation descriptions; number line activity materials; strategy recording templates; formative assessment tools; final assessment with both procedural and conceptual dimensions."

"Design a complete Grade K-1 Number Sense instructional sequence — 'Counting, Quantity, and the Number Line: Building the Foundation of All Mathematics' — for early childhood educators, grounded in Dehaene's neuroscience of numerical cognition and Clements and Sarama's learning trajectories for counting and cardinality. The sequence should be appropriate for young children (ages 5-6) and should be hands-on, playful, and embedded in rich mathematical contexts. Foundation Principle: Before children can do arithmetic, they need a robust sense of quantity — the ability to perceive, estimate, compare, and represent numerical magnitudes. This is distinct from being able to count (recite numbers in sequence) and is more fundamental. Research-based activities for developing each level of the counting learning trajectory: Level 3 — Reciter (count to 5 with correspondence): Songs with objects (five little ducks; five green frogs); counting physical objects with one-to-one correspondence; making sets of 1-5 objects on request. Level 5 — Counter (count to 10 objects reliably): Counting collections — bags of small objects (10-20 items; students count and record); count and compare — whose collection has more?; the cardinality principle — 'how many?' after counting and pointing to the whole set (not the last item). Level 7 — Counter and Producer (count to 30; make sets): 'Show me twelve beans' (producing set of specific quantity); counting games (Ten Frame; Rekenrek / arithmetic rack); dot card quick looks — brief exposure to dot patterns (1-10); students identify quantities without counting (subitizing). Subitizing Development (Clements): Perceptual subitizing: instantly recognizing quantities 1-4 without counting (innate). Conceptual subitizing: perceiving larger quantities (5-10) as composed of smaller subgroups (e.g., seeing 7 as a group of 5 and a group of 2 on a domino). Activities for conceptual subitizing: 'How did you see it?' discussions after dot card quick looks; dice games; dominoes. Number Line Games (Dehaene-inspired): The physical number line walk: students stand on floor number line (0-20); teacher calls a number; students walk to it; students estimate ('between which two numbers is 13?'). Number line board games (linear): research (Ramani & Siegler, 2008) shows that linear board games (like Chutes and Ladders) significantly develop number line representation and arithmetic readiness in young children, particularly those from lower-income households who have had less exposure to these games. Student-made number lines (0-10; 0-20; 0-100 as the year progresses). Full sequence with: learning trajectory diagnostic for K-1; activity descriptions with materials needed; number talk formats adapted for ages 5-6; daily routine suggestions; family connection activities."

Mathematical Mindsets and Productive Struggle

"Design a complete math classroom culture sequence for Grade 5 — 'What Is Math Really? Rebuilding Mathematical Identity and Confidence' — grounded in Boaler's mathematical mindsets research and Skemp's relational understanding principles, for a class where many students have developed math anxiety or fixed mindsets about mathematics. Opening Week — Reorienting to Mathematics: Day 1: 'What is math?' — collaborative discussion. Most students answer: rules; answers; times tables; formulas. Teacher introduces evidence from Boaler's research: 'At the highest levels of mathematics, mathematicians say math is creative, visual, and connected. Let me show you.' Multiple representations of the same mathematical idea: the number 16 shown as a square (4×4 arrangement of dots), a rectangle (2×8), a double-square (two squares of 4), a number on a number line (between 15 and 17, between 10 and 20, close to the square root of 256) — students see that sixteen has a rich visual and relational identity, not just a position in a counting sequence. Day 2: Mistake of the Day. Teacher shows their own work on a problem, including mistakes: 'I tried this first. It was wrong. Here's what I was thinking. Here's what went wrong. Here's what I learned from the mistake.' Students respond: 'What was useful about this mistake?' Research discussion: 'When you make a mistake in math and correct it, which part of your brain activates? Your prefrontal cortex — the part responsible for reasoning and understanding. Mistakes literally build your brain.' Day 3-4: Open Middle problems (problems with constrained starts and ends but multiple solution paths in between) — problems where there is no single method; students explore and compare. Day 5: Number Talk series — students share mental computation strategies and realize that there are multiple valid approaches; 'fastest' is not 'best.' Weeks 2-6 — Relational Mathematics: Each week's investigation is designed to reveal mathematical relationships rather than practice procedures. Sample Week 3 Investigation: 'The Multiplication Square' — students fill in a 10×10 multiplication grid, but rather than memorizing facts, they use the structure of multiplication: commutativity (3×7 = 7×3; so once you know one fact, you know another); distributivity (6×7 = 6×5 + 6×2; use facts you know to derive facts you don't); square numbers (which numbers appear only on the diagonal? why? what's special about them?); the nines trick (why does it work? what does it reveal about our base-ten system?). Students complete the grid using relationships and strategies rather than memorized facts — and discuss: 'What mathematical relationships make this possible?' Growth Mindset Assessment Protocol: In this unit, assignments are evaluated on reasoning quality, not just answer correctness. Each assignment includes: 'Show your thinking' (partial credit for productive reasoning even if the final answer is wrong); 'What did you learn?' (reflection on process); 'What question does this raise?' (extension and curiosity). Full unit with: opening week daily lesson plans; open middle problem bank; growth mindset reflection templates; relational assessment rubric; teacher facilitation guide."

Classroom Scenario: A Maths Class in Wales

Say you teach Year 4 (equivalent to Grade 3-4) at a community primary school in Cardiff, the capital city of Wales — a nation of approximately 3.2 million people in the southwest of the island of Great Britain, with its own Parliament (the Senedd), its own distinctive culture, and its own language, Welsh (Cymraeg), which is now co-official with English and is spoken as a first language by approximately 29% of the population (concentrated in the north and west) and as a second language by hundreds of thousands more. Wales's educational system is distinct from England's: since the devolution of education powers to the Welsh Government in 1999, Wales has developed its own educational policy, and the 2022 implementation of the new Curriculum for Wales represents one of the most significant educational reforms in the country's history — replacing the old prescriptive National Curriculum with a more flexible, skills-based framework organized around six Areas of Learning and Experience (AoLE), with significant local flexibility for schools and teachers.

Wales's Educational Context: Cardiff is a diverse, cosmopolitan city — Wales's largest and most ethnically diverse, with significant communities of South Asian, Caribbean, Somali, and Eastern European background alongside the longstanding Welsh and English communities. You might teach in a school where approximately 40% of students come from families where English is an additional language, including significant numbers of recently arrived Welsh learners — a status that intersects interestingly with the national commitment to Welsh language education (all Welsh state schools offer Welsh-medium or Welsh-English bilingual education to some degree). The Curriculum for Wales's emphasis on creative, connected, and skills-based learning — including its explicit inclusion of Numeracy as one of three Cross-Curricular Skills that apply across all AoLEs — aligns well with a relational mathematics approach.

A Relational Approach: You might become an advocate for relational mathematics instruction after seeing the pattern Skemp described play out in your own classroom: students who could follow algorithms accurately but were immediately helpless when any problem varied from the familiar form. You could shift toward number talks (a daily 5-10 minute routine in which students share mental computation strategies), investigation-based units, and explicit discussion of mathematical reasoning. Many teachers find that the most important shift is the classroom culture one: students' initial resistance to showing their thinking and sharing imperfect strategies gives way, over weeks, to genuine engagement with the idea that there are multiple valid ways to think about a mathematical problem.

EduGenius for Mathematics: EduGenius (edugenius.app) can generate number talk problem strings aligned to your current unit; investigation designs that connect to Welsh curriculum contexts; learning trajectory diagnostic tools; and relational assessment tasks that evaluate conceptual understanding as well as procedural accuracy.

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