Mathematical Reasoning (re-grant)

The Mathematical Reasoning programme aims to improve mathematical attainment by developing pupils’ understanding of the logical principles underlying mathematics. The Literacy and Morphemes programme aims to improve pupils’ spelling and reading comprehension. Both programmes are delivered to year 2 pupils during normal lesson time. 


Key Stage 1

Key stage




EEF Summary

Previous studies suggested both programmes offered affordable approaches to improving pupil outcomes. Based on this, the EEF funded a trial (Improving Literacy and Numeracy in KS1) to test the impact of the two programmes under developer-led conditions. Pupils receiving Mathematical Reasoning made an additional three months’ progress in maths compared to other pupils in comparison schools. There was no evidence that Literacy and Morphemes improved spelling or reading outcomes.

The EEF then funded a follow-up evaluation which examined the impact of a scalable version of Mathematical Reasoning in a larger number of schools and with less involvement from the original developer (co-funded by the Worshipful Company of Actuaries). The National Centre for Excellence in the Teaching of Mathematics (NCETM) helped to develop the training model, and coordinated its delivery through its national network of ‘Maths Hubs’ (partnerships of schools focused on maths education). In this second, larger trial, pupils who received Mathematical Reasoning made the equivalent of one additional month’s progress in maths, on average, compared to other children.

There are some differences between the two projects which may explain the smaller impact in the second trial. First, it used a different delivery model. Rather than doing the teaching training directly, the programme developers (the University of Oxford) trained Maths Hub teachers who then delivered the teacher training to participating schools. This may have affected how faithfully the programme was delivered in the classroom. Also, although a precise comparison is difficult, there was evidence that the comparison schools in the second trial were more likely than in the first trial to provide alternative support for children’s reasoning in maths. This may have reduced the difference seen between Mathematical Reasoning pupils and other pupils.

Together, these trials provide evidence for the effectiveness of Mathematical Reasoning. The project will remain on the EEF’s Promising Projects list and we will explore the potential for bringing it to more schools.

Research Results

Were the schools in the trial similar to my school?

  • There were 160 schools in the trial, located in eight Maths Hub areas throughout the country.
  • 26% of the pupils in the trial had ever been eligible for free school meals.
  • On average, the schools had 74% of their pupils working at the expected standard or above at Key Stage 1 in 2016.
  • 12% of the pupils in the trial spoke English as an additional language. 

Could I implement this in my school?

  • There is one initial day of training for teachers, and one support visit during programme delivery
  • Teachers receive lesson plans and powerpoint slides to deliver the intervention.
  • Learning is supported by online games, which can be used by pupils both at school and at home.

Eight maths hubs were trained to train teachers to deliver the programme. These Maths Hubs could offer training and support for schools interested in the programme:

  • Archimedes (North East, Durham and Tees Valley region)
  • Central (Birmingham)
  • GLOW (Gloucestershire, Oxfordshire, Worcestershire)
  • Kent and Medway
  • London South East
  • North West Three
  • Salop and Herefordshire
  • Sussex


Delivered by


Whole Class

Participant group


15 Weeks

Intervention length

How much will it cost?

The average cost of Mathematical Reasoning for one school was around £1,073, or £8 per pupil per year when averaged over 3 years. 



Cost per pupil



No. of Teachers/TAs


1 Day

Training time per staff member

Evaluation info





Key Stage

Key Stage 1

Start date

October 2015

End date

July 2017

Type of trial

Effectiveness Trial

Evaluation Conclusions

  1. Pupils who received Mathematical Reasoning made the equivalent of one additional month’s progress in maths, on average, compared to children who did not. This result has high security. 

  2. Among pupils eligible for free school meals, those who received Mathematical Reasoning made an average of one additional month’s progress compared to those who did not. This result may have lower security than the overall finding because of the smaller number of pupils.

  3. There was some evidence that the programme also had a positive impact on mathematical reasoning.

  4. The intervention was generally well received by schools. Teachers reported positive experiences with the training and materials, and were positive about the programme’s focus on fundamental mathematical principles. 

  5. The process evaluation found that there was some variation in how schools implemented aspects of the programme, particularly in relation to the use of the online games.

  1. Updated: 28th March, 2019

    Printable project summary

    1 MB pdf - EEF-mathematical-reasoning.pdf

  2. Updated: 13th December, 2018

    Evaluation report

    1 MB pdf - Mathematical_Reasoning.pdf

  3. Updated: 16th November, 2016

    Project Protocol

    355 KB pdf - EEF_Project_Protocol_Maths_and_Reasoning_effectivness_trial.pdf

Full project description

The Mathematical Reasoning programme aims to improve the mathematical attainment of pupils in Year 2 by developing their understanding of the logical principles underlying maths. The programme was previously tested in an EEF-funded efficacy trial (Improving Numeracy and Literacy in Key Stage 1) which suggested that it had a positive impact. The efficacy trial examined the programme under developer-led conditions. This report describes a follow-up effectiveness trial which examined the impact of the programme under everyday conditions in a large number of schools and with less involvement from the original developer.

Mathematical Reasoning lessons focus on developing pupils’ understanding of number and quantitative reasoning. They cover principles such as place value and the inverse relation between addition and subtraction. The programme consists of ten units delivered to pupils by their teachers as part of their usual mathematics lessons. It is designed to be taught over a 12- to 15-week period, with each unit taking approximately one hour. Learning is supported by online games, which can be used by pupils both at school and at home. The intervention was originally developed by a team at the University of Oxford, led by Professor Terezinha Nunes and Professor Peter Bryant. The National Centre for Excellence in the Teaching of Mathematics (NCETM) contributed to the development of the training model used in this trial and coordinated the delivery of the training through the network of Maths Hubs (partnerships of schools created to lead improvements to maths education).

In this trial, the teacher training was delivered using a ‘train-the-trainers’ model through eight Maths Hubs. Each Maths Hub was asked to recruit two ‘Work Group Leads’. The University of Oxford programme developers trained these Work Group Leads who then trained the teachers in participating schools to deliver the programme. To prepare them to train the teachers, Work Group Leads received an initial day of training, used the materials in their own teaching, and then received a further two days’ training. Teachers delivering the programme then received one day of training from a Work Group Lead as well as a visit from the Work Group Lead during programme delivery. They were also able to seek additional support directly from the Work Group Lead or ask questions through an online Maths Hub community.

The impact of the programme on maths attainment was evaluated using a randomised controlled trial involving 160 schools. Schools were randomly allocated either to receive Mathematical Reasoning or to be in the control group, the latter having the opportunity to take part in the programme in the following school year. A process evaluation used observations of training sessions, teacher interviews, lesson observations, and an online survey of treatment and control schools to examine implementation and the factors influencing impact. The trial began in August 2015 and analysis and reporting of the trial completed in December 2018. The project was co-funded by the Worshipful Company of Actuaries.