Does Non-symbolic Math Practice in Young Children Improve Symbolic Mathematics Ability in Later Life?
Last registered on August 04, 2017


Trial Information
General Information
Does Non-symbolic Math Practice in Young Children Improve Symbolic Mathematics Ability in Later Life?
Initial registration date
October 04, 2013
Last updated
August 04, 2017 6:33 PM EDT
Primary Investigator
Other Primary Investigator(s)
PI Affiliation
Harvard University
PI Affiliation
Harvard University
PI Affiliation
Additional Trial Information
Start date
End date
Secondary IDs
While most children in developing countries now receive a primary education, the performance of primary schools is weak, especially for the poor (Banerjee & Duflo, 2011). Part of the problem is that many poor children are neither prepared for nor receive support with schoolwork, and initial gaps in performance are reinforced by a tendency for teachers to focus on “high – performers.” There is very little evidence of effective school-readiness curricula for poor children to combat this issue. If effective curricula could be devised, the achievement gap in mathematics between rich and poor children could be dramatically reduced as learning school mathematics depends on the exercise of numerical and geometric concepts that emerge in infancy and that are equally accessible to children of all cultures (Dehaene et al., 2006) across the socioeconomic spectrum (Gilmore et al., 2010). These early-developing mathematical concepts are greatly enhanced by exercise, which leads to measurable gains in school math performance (Griffin & Case, 1997).

This project aims to develop and evaluate a game-based preschool curriculum to enhance children's: (1) core numerical and geometric abilities in relation to the symbol systems of elementary school mathematics; (2) awareness of their own mathematical abilities and of the growth of those abilities with exercise; (3) appreciation of the link between everyday cognition and school-based skills. The ultimate goal is to prepare disadvantaged children – cognitively and motivationally – for success in school.

We will evaluate the games together as a curriculum, by introducing them to children in Indian preschools in the framework of a randomized controlled trial (RCT) to assess whether the group of games together produces changes in children's mathematical competence or motivation both at the end of preschool and for at least one year later.

To asses the effect of the mathematical games themselves, in contrast to simply playing games in school, we will be introducing "social games", which could develop skills that are also by-product of the math games (attention to rules, ability to stay on task, etc) without a focus on mathematics. There are thus 3 groups: control, social games, and math games.
External Link(s)
Registration Citation
Banerji, Rukmini et al. 2017. "Does Non-symbolic Math Practice in Young Children Improve Symbolic Mathematics Ability in Later Life?." AEA RCT Registry. August 04.
Experimental Details
The proposed innovation is a battery of games that will be organized in a curriculum and implemented in preschools run by Pratham in Delhi. We will focus on children aged 5 years, and run the games for four months (Nov. 18, 2013 – Mar. 7, 2014), in three weekly one-hour sessions. The "math games" will be played in the math games treatment group, and the social games will be played in the social games treatment group.

A group of Pratham staff will be specially trained to conduct the games.
Our experience from piloting is that working with a group of approximately 10 children for one hour (with two games played for 30 minutes each) keeps children entertained and focused. Four months will be enough to play all the games at progressively higher levels of difficulty. In April, these children will join primary school, where they will be exposed to the traditional curriculum in mathematics.
Intervention Start Date
Intervention End Date
Outcomes (end points)
Performance in Mathematics, performance in other subjects
Outcomes (explanation)
Short run: test of mathematical competencies to be performed on computers (adapted from pyschology test); tests of executive functions.

Long run: Performance in mathematics will be quantified using test score of students in basic tests of numeracy after they have joined school,
Experimental Design
Experimental Design
We will test the impact of our intervention using a randomized controlled trial. We will form three groups of 70 preschools operating in schools in the slums of Delhi. These preschools are operated by Pratham, our partner, either in premises rented in the community, or inside the government schools (if we use both types of schools, we will stratify the randomization by type of school).
(1) In the first group (status quo), Pratham will implement its regular curriculum.
(2) In the second group (math games), Pratham will implement its regular curriculum, with the same type of teachers, but three hours per week, the math games assistant will play the math games with the older children, who would be gearing up to attend school that spring (the teacher will be free to play the math games with the younger children as well, so those children may be indirect beneficiaries of the intervention, but they will not be part of the formal study).
(3) In the third group (social games), a trained assistant will implement “social games.” Six social games, each equivalent in gameplay and teacher/peer engagement to one math game but lacking in numerical or geometric content, will be introduced to classrooms following the same schedule as the math games. Social games aim to enhance children's pedagogical learning by training basic communicative skills such as evaluating emotions on a face or determining the object of a person's attention. This condition will allow us to distinguish the impact of structured play from the focus on non-symbolic mathematics per se. To minimize halo effects, social and math games will be presented as equally beneficial (as, indeed, they may be).
Experimental Design Details
Randomization Method
Randomization done by a computer program.
Randomization Unit
Was the treatment clustered?
Experiment Characteristics
Sample size: planned number of clusters
Sample size: planned number of observations
Sample size (or number of clusters) by treatment arms
70 pre-schools control, 70 pre-schools Math Games, 70 pre-schools Social Games
Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
IRB Name
MIT Committee on the use of Human as Experimental Subjects
IRB Approval Date
IRB Approval Number
Analysis Plan
Analysis Plan Documents
First Endline Analysis - Making Learning Count

MD5: 52d73adddff8f198a8a2fb0908e1696f

SHA1: 76e83e1c75c8b4c91ddcf698eb06484593b64e7d

Uploaded At: July 21, 2014

Second Endline Analysis - Every Child Counts_1_27_2015

MD5: 889c305e5b27580fb16cee6a0cde9e84

SHA1: e0a15b67e076e5039ef7d43925ff20e095c03aa4

Uploaded At: January 28, 2015

Third Endline Analysis - Every Child Counts_7_08_2015

MD5: f479ba9f5005d9263c435d7df2334291

SHA1: 648f813352c1ded5c12e1b4e8f180a27e031126d

Uploaded At: July 13, 2015

Post Trial Information
Study Withdrawal
Is the intervention completed?
Intervention Completion Date
April 01, 2014, 12:00 AM +00:00
Is data collection complete?
Data Collection Completion Date
September 01, 2015, 12:00 AM +00:00
Final Sample Size: Number of Clusters (Unit of Randomization)
214 preschools
Was attrition correlated with treatment status?
Final Sample Size: Total Number of Observations
1540 were observed at baseline, 1452, 1339 and 1300 were observed at endline 1, endline 2, and endline 3 respectively.
Final Sample Size (or Number of Clusters) by Treatment Arms
72 control, 71 math treatment, and 71 social treatment
Reports and Papers
Preliminary Reports
Relevant Papers
Many poor children are underprepared for demanding primary school curricula. Research in cognitive science suggests that school achievement could be improved by preschool pedagogy in which numerate adults engage children’s spontaneous, nonsymbolic mathematical concepts. To test this suggestion, we designed and evaluated a game-based preschool curriculum intended to exercise children’s emerging skills in number and geometry. In a randomized field experiment with 1540 children (average age 4.9 years) in 214 Indian preschools, 4 months of math game play yielded marked and enduring improvement on the exercised intuitive abilities, relative to no-treatment and active control conditions. Math-trained children also showed immediate gains on symbolic mathematical skills but displayed no advantage in subsequent learning of the language and concepts of school mathematics.
Dillon, M. R., Kannan, H., Dean, J. T., Spelke, E. S., & Duflo, E. (2017). Cognitive science in the field: A preschool intervention durably enhances intuitive but not formal mathematics. Science, 357(6346), 47-55.