Technical Appendix


Early numeracy approaches aim to develop number skills and capability to improve young children’s knowledge and understanding of early mathematical concepts which will provide a secure foundation for mathematical learning in school. Activities in this area might be structured, for example through programmes designed to develop children’s ‘number sense’ (their developing understanding of quantity and number), or more informal, for example, using mathematical games, board games and computer games (see also Digital technology), or pretend activities involving counting or using other mathematical language.

Search Terms: early childhood mathematics, mathematics, math achievement, mathematics concepts, arithmetic, addition, counting, enumeration, numerical reasoning

Evidence Rating

There are three meta-analyses suggesting that the impact of early numeracy approaches tends to be moderate or high. There is some variation between approaches, which suggests that the choice of approach and the way in which strategies are introduced are important. Approaches tended to produce larger effects when they were focused on particular mathematical content (such a counting or estimating), committed a regular amount of time to developing mathematics (between two and three hours per week), designed the approach for the early years setting involved, and included some specific individual interaction. Early numeracy approaches appear to benefit all groups of children, including children from low-income families. There is some evidence that targeted early numeracy approaches, including small group activities, can help children from disadvantaged backgrounds catch up with their peers by the beginning of formal schooling, though not all approaches appear to be equally effective.

Commonly, the most effective early numeracy approaches include small group work and balance guided interaction with direct teaching and child-led activities. A number of studies also indicate that it is important for early years professionals to understand young children’s mathematical development (such as the typical stages in learning to count) and to understand how to assess this development. This understanding will support the provision of more effective activities. A challenge for evaluations to date has been that numeracy approaches often have multiple elements, meaning that it is hard to definitively state the essential features of an effective programme. Findings are consistently positive, but there is some variation between approaches.

There is extensive evidence related to early numeracy approaches. The evidence base includes three meta-analyses and a number of high-quality single studies, mainly from the USA but also from Greece, the Netherlands, New Zealand and Sweden. Overall the evidence is rated as extensive.

Additional Cost Information

Overall the costs are estimated as very low. Research indicates that knowledge of mathematics, knowledge of children’s development and development trajectories in mathematics and understanding of the kinds of activities which support early mathematical learning are all important for practitioners. As a result, professional development is likely to be particularly beneficial in supporting early numeracy approaches, and some assessment and professional development costs are included in this estimate. Additional equipment to support mathematical experiences such as counting, measuring and using money is also likely to be beneficial.


Aubrey, C., Godfrey, R., & Dahl, S.
Early mathematics development and later achievement: Further evidence. open_in_new
Mathematics Education Research Journal, 18(1), 27-46.
Clements, D. H., & Sarama, J.
Experimental evaluation of the effects of a research-based preschool mathematics curriculum. open_in_new
American Educational Research Journal, 45 (2), 443-494.
Clements, D. H., Sarama, J., Farran, D., Lipsey, M., Hofer, K. G., & Bilbrey, C.
An Examination of the Building Blocks Math Curriculum: Results of a Longitudinal Scale-Up Study. open_in_new
Paper presented at the Society for Research on Educational Effectiveness.
Clements, D. H., Sarama, J., Spitler, M. E., Lange, A. A., & Wolfe, C. B.
Mathematics learned by young children in an intervention based on learning trajectories: A large-scale cluster randomized trial. open_in_new
Journal for Research in Mathematics Education, 42(2), 127-166.
Dyson, N. I., Jordan, N. C. & Glutting, J.
A number sense intervention for low-income kindergartners at risk for mathematics difficulties. open_in_new
Journal of learning disabilities, 46(2), 166-181.
Ebin, H. R.
Growth in Math Skills and Response to Math Intervention in Kindergarten. open_in_new
Doctoral dissertation, (Order No 10113650), Available from ProQuest Dissertations & Theses Global.(1801725326)
Elofsson, J., Gustafson, S., Samuelsson, J., & Träff, U.
Playing number board games supports 5-year-old children’s early mathematical development. open_in_new
The Journal of Mathematical Behavior, 43, 134-147.
Foster, M. E., Anthony, J. L., Clements, D. H., Sarama, J., & Williams, J. M.
A Randomized Control Trial Evaluating the Effectiveness of Computer Assisted Instruction in Numeracy on Math Outcomes for Monolingual English Speaking Kindergartners from Title 1 Schools. open_in_new
Paper presented at the Society for Research on Educational Effectiveness.
Jordan, N. C., Glutting, J., Dyson, N., Hassinger-Das, B., & Irwin, C.
Building kindergartners' number sense: A randomized controlled study. open_in_new
Journal of Educational Psychology, 104(3), 647
Klein, A., Starkey, P., DeFlorio, L., & Brown, E. T.
Establishing and Sustaining an Effective PreKindergarten Math Intervention at Scale. open_in_new
Paper presented at the Society for Research on Educational Effectiveness.
Malofeeva, E. V. (Abstract arrow_downward)
Meta-analysis of mathematics instruction with young children. open_in_new
Doctoral Thesis Graduate School of the University of Notre Dame.
Park, J., Bermudez, V., Roberts, R. C., & Brannon, E. M.
Non-symbolic approximate arithmetic training improves math performance in preschoolers. open_in_new
Journal of Experimental Child Psychology, 152, 278-293.
Ramani, G. B., Siegler, R. S., & Hitti, A.
Taking it to the classroom: Number board games as a small group learning activity. open_in_new
Journal of Educational Psychology, 104(3), 661.
Sarama, J., Lange, A. A., Clements, D. H., & Wolfe, C. B.
The impacts of an early mathematics curriculum on oral language and literacy. open_in_new
Early Childhood Research Quarterly, 27(3), 489-502.
Sood, S., & Jitendra, A. K.
An exploratory study of a number sense program to develop kindergarten students’ number proficiency. open_in_new
Journal of Learning Disabilities, 46(4), 328-346.
Starkey, P., Klein, A., & Wakeley, A
Enhancing young children’s mathematical knowledge through a pre-kindergarten mathematics intervention. open_in_new
Early Childhood Research Quarterly, 19(1), 99-120.
What Works Clearing House (Abstract arrow_downward)
SRA Real Math Building Blocks Pre-K. open_in_new
What Works Clearing House Intervention Report
Young-Loveridge, J. M.
Effects on early numeracy of a program using number books and games. open_in_new
Early Childhood Research Quarterly, 19(1), 82-98.
Zaranis, N.
The use of ICT in kindergarten for teaching addition based on realistic mathematics education. open_in_new
Education and Information Technologies, 21(3), 589-606.

Summary of effects

Meta-analyses Effect size FSM effect size
Malofeeva, E. V. , (2005)
0.47 -
Wang, A. H., Firmender, J. M., Power, J. R., & Byrnes, J. P. , (2016)
0.62 -
What Works Clearing House, (2007)
0.36 -
Single Studies Effect size FSM effect size
Ebin, H. R. (2014)
0.61 -
Elofsson, J., Gustafson, S., Samuelsson, J., & Träff, U. (2016)
0.12 -
Foster, M. E., Anthony, J. L., Clements, D. H., Sarama, J., & Williams, J. M. (2016)
0.43 -
Klein, A., Starkey, P., DeFlorio, L., & Brown, E. T. (2012)
0.45 -
Park, J., Bermudez, V., Roberts, R. C., & Brannon, E. M. (2016)
0.41 -
Toll, S. W., & Van Luit, J. E. (2014)
0.20 -
Weiland, C., & Yoshikawa, H. (2013)
0.50 -
Zaranis, N. (2016)
0.46 -
Effect size (median) 0.49  

The right hand column provides detail on the specific outcome measures or, if in brackets, details of the intervention or control group.

Meta-analyses abstracts

Malofeeva, E. V. (2005)

On average, the mean weighted effect size for the difference between the experimental and control groups was .467. A combination of direct and guided instruction was the most beneficial instructional approach followed by guided instruction. In addition, interventions including controlling task difficulty, additional explanations provided about taught concepts, sequencing activities, and small group games showed larger effect sizes than interventions not including these techniques. The magnitude of mean weighted effect size was lower for skill-specific than for standardized measures of math performance. Weighted regression analyses indicated that such variables as the year of publication, sample size, whether a study was published or not, length of treatment, age, type of the control group, type of design, type of population employed, and percentage of attrition did not predict effect size estimates. Implications of the findings and future directions in this field are discussed.

Wang, A. H., Firmender, J. M., Power, J. R., & Byrnes, J. P. (2016)

The early childhood years are critical in developing early mathematics skills, but the opportunities one has to learn mathematics tend to be limited, preventing the development of significant mathematics learning. By conducting a meta-analysis of 29 experimental and quasi-experimental studies that have been published since 2000, this study extends beyond prior evaluations of early mathematics programs for prekindergarten and kindergarten environments by quantifying program effectiveness in terms of effect sizes and examining 6 aspects of these programs. We found an overall moderate to large effect size. There was a tendency for programs to produce larger effects when they (a) targeted a single content strand, (b) presented content 120 to 150 min per week, (c) designed programs for the prekindergarten environment, (d) presented content individually to children, and (e) used researcher-made mathematics assessments. Practice or Policy: Early mathematics programs can be designed to be both developmentally appropriate and highly effective. The goal of this meta-analysis was to reveal these programs to early development and education professionals so that they understand some of the factors that might explain why some produced stronger effects than others.

What Works Clearing House (2007)

SRA Real Math Building Blocks PreK (also referred to as Building Blocks for Math) is a supplemental mathematics curriculum designed to develop preschool children’s early mathematical knowledge through various individual and small- and large-group activities. It uses Building Blocks for Math PreK software, manipulatives, and print material. Building Blocks for Math embeds mathematical learning in children’s daily activities, rang­ing from designated math activities to circle and story time, with the goal of helping children relate their informal math knowledge to more formal mathematical concepts.