By Professor Hamsa Venkatakrishnan, Numeracy Research and Development (NRD) programme
Across the world, inequalities in foundational numeracy can be seen through what might be called the “80/20 problem.” In much of the global North, around 80% of children achieve minimum grade-level proficiency in mathematics. In many parts of the global South, the reverse is true — 80% of children do not. While there has been significant global progress in foundational literacy, progress in numeracy has been slower and more uneven.
Why might this be? One explanation lies in the hierarchical nature of mathematics learning. Even at the earliest stages, progress depends on connected clusters of knowledge and skills.
Consider a simple example such as 9 + 7 = ?. In many classrooms across sub-Saharan Africa, the most common approach is to count out bottle tops or draw tally marks — first for nine, then for seven — and then count the total again from one. This works, but it is time-consuming and becomes increasingly error-prone as numbers get larger.
There are more efficient approaches to solving this problem. We can break 7 into 1 and 6, add 9 and 1 to make 10, then 10 and 6 to make 16. However, this approach relies on several pre-requisite fluencies:
- Knowing instantly that 9 + 1 = 10
- Knowing that 7 can be partitioned into 1 and 6
- Knowing that 10 + 6 = 16
Without these fluencies, children must revert to counting in ones — and that limits progress. This example illustrates a broader truth: numeracy learning builds cumulatively, and missing pieces at early stages make later concepts harder to grasp.
Understanding What Children Can Do
Most countries now have early-grade mathematics curricula in place, so the challenge is not what we want children to learn but how to ensure they actually do. Despite large gains in access to schooling, data from national, regional, and international assessments show that many learners continue to struggle with foundational mathematical concepts.
The Critical Early Numeracy Outcomes (CENOs), developed under a Gates Foundation-funded Numeracy Research and Development (NRD) programme by a Technical Panel of international experts in mathematics education, responds to this gap. They provide a practical framework for identifying and supporting the key early number skills and concepts that underpin later success in mathematics.
A Backward Design Approach
The CENOs were created using a “back-fill” process. Starting with Grade 3 outcomes outlined in national curricula and the Global Proficiency Framework, the team worked backward to identify what children should be able to do by the ends of Grades 1 and 2. This creates a clear pathway of progression across the early grades — a roadmap for what it takes to reach minimum proficiency by Grade 3.
For example, in Grade 1, one expected fluency is to recall doubles of numbers 1–5. In Grade 2, children should begin to manipulate place value to add and subtract efficiently. By Grade 3, these foundational fluencies support more complex problem-solving and flexible calculation.
Figure 1: Grade 1 Addition and Subtraction CENOs.
Fluency and Problem-Solving: Building Together
The CENO specifications include fluency and problem-solving outcomes in all three grades. Fluencies are skills that children should acquire at the level of near automaticity in each grade. This usually means being able to state an answer within 4 seconds without needing to count or work out on paper.
Fluency and problem-solving are intertwined. Fluencies — skills performed automatically within seconds — don’t develop in isolation. They are first encountered and practised in the context of problem-solving. Over time, as fluencies strengthen, they enable children to solve more complex problems efficiently and confidently.
The CENOs therefore integrate both fluency and problem-solving outcomes for each grade. They encourage teachers to design activities that reinforce both — helping learners move beyond counting to develop strategies based on number relationships and place value understanding.
Using the CENOs in Practice
The CENO report presents the outcomes in a simple, accessible format designed for teachers, curriculum specialists, programme developers, and policymakers. Each outcome is illustrated with exemplar classroom tasks.
For teachers, the framework supports diagnostic reflection:
- What can my learners already do?
- Which fluencies or concepts might be missing?
- How can I scaffold learning to strengthen those building blocks?
For programme developers and policymakers, CENOs offer a common reference point for monitoring progress across diverse education systems. They can help align curriculum, assessment, and intervention design — ensuring that efforts at different levels work towards shared learning goals.
From Ambition to Attainment
Bridging the gap between curriculum ambitions and actual learning outcomes remains one of the biggest challenges in global education. By specifying the critical early steps towards numeracy proficiency, the CENOs provide a practical tool to support teachers and systems alike.
When used effectively, they can help us move beyond broad statements about “improving mathematics learning” to a clearer understanding of how this can happen — and what progress looks like in the early years.