Research has shown the importance of building strong foundations for learning, as the development of cognitive skills in preschool and early primary years is predictive of later mathematical achievement. This article examines the national curriculum for mathematics and learning materials used in three states and finds that state textbooks do not always follow the prescribed content and there is a lack of continuity between the curriculum followed during preschool and early years of primary school.
India’s National Education Policy (NEP) 2020 calls for a ‘foundational’ stage of education for children between the ages of three and eight (Ministry of Human Resource Development, 2020). This structure aligns with international research underlining the importance of building strong foundations for learning by ensuring continuity and integration across the preschool and early primary years, a key period in young children’s development. Specifically, global research shows that mathematics achievement in primary school and beyond is strongly related to children’s acquisition of pre-numeracy and early numeracy skills before entering school (see Jordan et al. 2007, Desoete et al. 2009).
A new curriculum spanning the proposed foundational stage is currently under development. The need for a revised curriculum is underlined by the available national evidence on children’s mathematics learning, which shows that large proportions of children begin to fall behind from the very first year of formal schooling. This suggests that their early preparation to handle formal mathematics content is insufficient. Once they have fallen behind, children have few opportunities to catch up (Kaul et al. 2017, ASER Centre, 2020). This evidence also suggests the converse: children with emergent and early numeracy skills have a significant advantage at the primary stage.
In a recent study we examined continuity and coherence within and across the existing national frameworks for early mathematics content, as well as workbooks and textbooks currently used in government schools in Assam, Rajasthan and Telangana. The analysis focused on:
- Learning domains and expected learning outcomes for early mathematics in national curricular frameworks (for preschool years as well as grade 1 of primary school, which collectively span ages 3-6)
- The degree of alignment between national frameworks and state curricular materials for preschool and the first grade
- The extent to which a continuum of learning opportunities for early mathematics is visible across preschool years, as well as from preschool to primary school.
Approach and methodology
A comparative analysis of national curricular frameworks was conducted alongside learning materials (workbooks at the pre-primary stage, and textbooks from primary school onwards) of three large and geographically diverse states.
The analysis of national frameworks was based on two key National Council of Educational Research and Training (NCERT) publications: The Preschool Curriculum (NCERT 2019), which sets out key concepts and skills to be taught, processes to be used, and expected outcomes for each of the three prescribed years of pre-primary education; and Learning Outcomes at Elementary Stage (NCERT 2017), which was developed two years earlier, and set out the content that children are expected to master for each of grades 1-8, separately for each subject.
The state-level analysis focused on government-issued workbooks (for pre-primary years) and mathematics textbooks (for grade 1) as mandated by each state.1 In total, across Assam, Rajasthan and Telangana, we examined 11 books for pre-primary and grade 1, all published within the last five years.
To accurately compare, our analytical framework was developed from the content of the material itself, going back and forth between the state-level learning materials and the national-level policy documents. The analysis focused on the following four mathematics domains and topics within these:
- Concept Identification (includes concepts like colours, identification of objects, things, and missing parts)
- Pattern and Seriation (includes patterns, seriation, classification, and functional association)
- Spatial Thinking and Measurement (includes understanding shapes, spatial position and location, and measurement).
- Number Concepts and Arithmetic (includes topics such as quantity comparison, counting, number recognition, and sequences and operations)
National curricular expectations
Our analysis reveals that the pre-primary and elementary frameworks show substantial discontinuities in learning expectations for children across the envisaged foundational stage. A review of the nationally prescribed learning outcomes for preschool and grade 1 in these two documents reveals gaps and inconsistencies rather than a clear progression of topics between the two stages (see Table 1).
Table 1. Early mathematics topics and specification of learning outcomes in preschool and grade 1
Several domains that are key to children’s early numeracy acquisition are addressed only at the preschool stage. Their absence in the first grade learning outcome specifications suggests that children are expected to have acquired these skills prior to entering primary school. This assumption is not supported by data on children’s learning.
Given that preschool education is not compulsory, and is not covered under India’s Right to Education Act, the focus on numbers in the first grade curriculum, together with the lack of attention to key pre-numeracy and cognitive domains once children begin formal school, may help to explain why children begin to fall far behind official curriculum expectations as soon as they enter school.
Approaches to early numeracy across states
We find that the three states covered in this study treat early mathematics topics and domains differently in each preschool year and in grade 1 (Figure 1).
Figure 1. Distribution of early numeracy and mathematics domains in preschool and grade 1 learning materials across sampled states, in percentage
Differences are observed with respect to the amount of exposure given to each topic and domain, as well as to the pace at which new topics are introduced, which in turn influence the scope for revisiting topics that were introduced earlier.
For example, in both Assam and Rajasthan, activities for younger children focus largely on non-number related topics and domains. In Telangana, on the other hand, workbooks for these children focus more on the number domain, along with topics related to spatial thinking and measurement.
For the number concept and arithmetic domain, the jump in available learning material between the last year of preschool and grade 1 textbooks is substantial across all states. Mathematics textbooks leap from seven to 75 pages of content in Assam, from 19 to 82 pages in Rajasthan, and from 55 to 114 pages in Telangana. As a consequence, there is far less attention to concept identification, pattern, seriation, and other topics and domains in early mathematics, with 71% of the grade 1 textbook chapters in Assam, 79% in Rajasthan and 85% in Telangana covering number and arithmetic related topics.
Preschool workbooks in different states also cover similar topics differently, but once formal schooling begins, fewer differences are visible across states. Grade 1 mathematics textbooks in all three states focus heavily on number concepts and arithmetic, with far less attention to other dimensions of early numeracy (see Table 2).
Table 2. Grade 1 textbook content in relation to topics covered at the preschool stage, by state
Notes: i) ‘Revision’ indicates that the textbook begins by revisiting concepts covered in the year immediately preceding grade 1. ii) ‘Continuation’ indicates that the textbook does not revise previous content but builds on content covered at the preschool stage (that is, it presumes learners have acquired adequate familiarity with the topic. iii) ‘Gap’ indicates that the topic is addressed in the textbook after a gap of one or more years, indicating some exposure at the preschool stage but not in the year immediately preceding grade 1. iv) ‘Missing’ indicates that the topic is not addressed in the grade 1 textbook, but is addressed at the preschool stage. v) ‘New’ indicates that the topic in the textbook was not introduced in any preschool year.
In summary, our analysis suggests that states have different ways of envisioning the best approach to building early mathematics skills among preschool children, although there is broad consensus that formal mathematics should be the focus as soon as children enter primary school.
Although the materials reviewed here form only a part of the learning and teaching process, they provide evidence of considerable variations in how states approach early numeracy teaching and learning. Differences are observed in relation to the age at which topics are introduced; how topics progress across years, both within the preschool stage as well as at the point of transition to primary school; and the pacing of topics, which in turn shape the available opportunities for revision and recap.
By first grade, the focus on numbers and formal mathematics is clear. But prior to this point, children’s level of preparation for this transition is uneven across the country– even among those children who are able to enrol in preschool for the nationally prescribed three years. States vary in terms of ensuring that there is scope to revisit or reinforce key pre-numeracy concepts and mathematical skills when children enter primary school.
Alignment of state-level materials with national learning outcomes
A comparison across states for each domain and topic covered in early mathematics shows that while most learning outcomes on the topics of numbers, shapes, and functional association are fully addressed in preschool, many learning outcomes for other topics are either not addressed or only partially addressed. There are also examples of content that goes beyond the level of difficulty specified in the national framework, raising concerns about including content that is not age appropriate, and the effects of doing so on children’s foundational mathematical understanding and its later development.
Three key findings from our analysis are summarised below.
- State material do not always incorporate the learning outcomes specified in the national framework: for example, the specification of early numeracy outcomes for grade 1 requires that children be able to “estimate and measure short lengths using non-uniform units like a finger, hand span, length of a forearm etc.” While grade 1 mathematics textbooks in Assam and Telangana contain activities designed to achieve this outcome, the textbook in Rajasthan does not. There are also instances where the learning outcomes are clearly specified but are not fully covered in the books. For example, preschool learning outcomes for age four specify that children should be able to classify objects on the basis of two categories, but both the Assam and Rajasthan workbooks for this age only cover classification on the basis of one category and the topic is missing altogether in the Telangana workbook. There are many other similar examples.
- State material sometimes introduces content that is more difficult than the level specified in the national framework: for example, the location-position topic is not mentioned in the NCERT preschool curricular outcomes, (but is covered explicitly in preschool workbooks in all three states. Similarly, while the topic of one-to-one correspondence mentions numbers up to five, workbooks in Telangana and Assam cover this topic for numbers up to nine and ten respectively, which is higher than the national curriculum expectation.
- The specification of learning outcomes in the national framework is, on occasion, overly generic, inviting varying interpretations: for example, under ‘measurement’, the NCERT preschool learning outcomes include “concept formation of distance, measurement, size, length, weight, height, time, etc.” for preschool ages 3-6. In the absence of greater specificity regarding what children should understand at (for example) age three versus age six, state workbooks vary in how they interpret this outcome. Similarly, for the topic of shapes, while the national document only specifies one outcome for all three preschool years, the workbooks in the focal states show considerable variation in the types of shapes covered at different stages.
The learning continuum for early years mathematics
The NEP’s ideation of a ‘foundational’ stage is an important first step in the provision of a continuum of learning for young children in India. A new curriculum for this first stage of education can remove some existing barriers to continuity in early mathematics content across this stage. Our analysis shows that intended pre-mathematics and early mathematics learning outcomes specified at the national level for the years and grades covered by the foundational stage are not always clearly defined, nor do they consistently build upwards from the envisaged abilities of the youngest children. Moreover, states vary considerably in the extent to which they follow national guidelines and the ways in which these are interpreted, sometimes exceeding the national framework and at other times failing to address all of the specifications. The range of topics in key learning domains for mathematics is differentially addressed, and does not ensure that all learners are exposed to the full range of skills and knowledge needed to establish firm foundations in mathematical thinking and problem-solving.
Most importantly, regardless of the diverse ways in which state materials differ from national frameworks and also from each other, in all three states included in this study, we see large gaps between the content taught in preschool years and the learning expectations for the first grade. A focus on formal mathematics teaching takes place abruptly, as soon as children enter primary school.
Conclusions and recommendations
International evidence on early mathematics learning shows that development of cognitive skills and pre-number concepts such as non-symbolic quantity, patterning and spatial skills, and measurement, is predictive of later mathematical achievement. Recent evidence from India, both from large-scale measurements of early learning across the country (ASER Centre, 2020) as well as from longitudinal research that tracked children’s early learning over a five-year period (Kaul et al. 2017) substantiate these findings.
However, translating these general principles into a set of clear, specific set of materials and activities for children at each age and in each grade is not a simple task. Guidelines in terms of approach, planning, and suggestive activities are available in several documents, including those forming the basis for the current analysis. Additional frameworks (such as the Ministry of Women and Child Development’s National Early Childhood Care and Education Curriculum Framework (2014), Save the Children’s Emergent Literacy and Math toolkit (2016), and most recently UNICEF’s Guidelines for the Design and Implementation of Early Learning Programmes (2019)) differ in terms of detail, but broadly agree on principles and practices to be followed in early years classrooms.
Incorporating these conceptual ideas into a set of age and grade specific curricula for the new foundational stage of education proposed by the NEP 2020 requires three key general principles to be followed. First, curricular design should map onto a set of clearly specified learning and teaching expectations that fully and coherently reflect the proposed continuum, beginning from the abilities of the youngest children and building upwards. Second, learning and teaching materials should map coherently and consistently onto this curricular framework. And third, these design principles should be contextualised to reflect the enormous diversity in children’s age and home background (including linguistic differences). Further, given that at present, many children do not attend pre-primary grades for the envisaged three years, building in opportunities for frequent review and revisiting of topics in different ways is essential, rather than establishing a linear pathway through the content to be covered.
This analysis draws on the research conducted under the study Pathways to Numeracy in Rural India: Policies, Patterns and Perceptions. The study was funded by the UK’s Economic and Social Research Council under its GCRF NGO Secondary Data Analysis 2019 programme (# ES/T010479/1).
- Because of different norms for age of entry to the first grade, Assam and Rajasthan each have separate pre-primary workbooks for ages 3-5; whereas Telangana has these materials only for ages 3 and 4.
- ASER Centre (2020), ‘Annual Status of Education Report (Rural) 2019 ‘Early Years’’, ASER Centre.
- Desoete, Annemie, Pieter Stock, Annimie Schepens, Dieter Baeyens and Herbert Roeyers (2009), “Classification, seriation, and counting in grades 1, 2, and 3 as two-year longitudinal predictors for low achieving in numerical facility and arithmetical achievement?”, Journal of Psychoeducational Assessment, 27(3): 252-264.
- Ministry of Human Resource Development (2020), ‘National Education Policy’, Ministry of Human Resource Development, Government of India.
- Jordan, Nancy C, David Kaplan, Maria N Locuniak and Chaitanya Ramineni (2007), “Predicting first-grade math achievement from developmental number sense trajectories”, Learning Disabilities Research and Practice, 22(1): 36-46.
- Kaul, V, S Bhattacharjea, AB Chaudhary, P Ramanujan, M Banerji and M Nanda (2017), ‘The India Early Childhood Education Impact Study’, UNICEF.
- NCERT (2017), ‘Learning outcomes at the Elementary Stage’, National Council of Educational Research and Training.
- NCERT (2019), ‘The Preschool Curriculum’, National Council of Educational Research and Training.