Mathematical Reasoning (second effectiveness trial)

University of Oxford
Implementation costThe cost estimates in the Toolkits are based on the average cost of delivering the intervention.
Evidence strengthThis rating provides an overall estimate of the robustness of the evidence, to help support professional decision-making in schools.
Impact (months)The impact measure shows the number of additional months of progress made, on average, by children and young people who received the intervention, compared to similar children and young people who did not.
+1
months
Project info

Independent Evaluator

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NFER

A maths programme that develops Year 2 pupils’ mathematical reasoning through teacher training, teaching assistant support, structured lessons, and computer games.

Pupils: 6480 Schools: 240 Grant: £599,736
Participating settings: 240

Introduction

Mathematical Reasoning is a maths programme for Year 2 pupils developed by the University of Oxford. It aims to improve pupils’ maths attainment by promoting depth of knowledge, strengthening their mathematical reasoning, number sense, and quantitative reasoning.

Over 12 to 15 weeks, teachers replace one maths lesson each week with structured sessions that combine whole-class teaching, group activities, and computer games.

Teachers and teaching assistants complete online training and attend webinars before and during delivery.

This evaluation tested whether the programme improved pupils’ maths attainment when delivered at scale, compared with usual Year 2 maths teaching practice.

It was tested through a large randomised controlled trialAn RCT is used evaluate an educational programme by assigning settings to one of two groups: the intervention group, who receive the programme or the control group, who continue with business as usual. This ensures that any differences in outcomes can be confidently attributed to the programme, providing a robust estimate of the impact and contributing to the evidence for what works in improving educational outcomes., under everyday conditions.

Why did the EEF fund this project?

Strong maths foundations are associated with later educational success. Mathematical Reasoning was developed because research suggests that children’s understanding of quantitative reasoning and number sense predict later mathematics attainment.
The EEF previously funded two randomised controlled trialsAn RCT is used evaluate an educational programme by assigning settings to one of two groups: the intervention group, who receive the programme or the control group, who continue with business as usual. This ensures that any differences in outcomes can be confidently attributed to the programme, providing a robust estimate of the impact and contributing to the evidence for what works in improving educational outcomes. of the programme. The first trial, conducted under ideal conditions, found an impact of three additional months’ progress. A second larger trial, conducted under everyday conditions found a smaller impact of one additional month’s progress.

This second effectiveness trial tested whether an online training model, with modules delivered by the programme designers, improved implementation and retained more of the impact seen in the earlier efficacy trial.

What did the evaluation find?

  • Pupils in Mathematical Reasoning schools made the equivalent of one additional month of progress in maths, on average, compared with pupils in schools delivering usual practice. This finding has a high security rating, which means we have confidence in it.
  • Pupils eligible for Free School Meals made the equivalent of two additional months of progress, on average, compared with similar pupils in schools delivering usual practice. This finding should be interpreted more cautiously because it is based on a smaller group of pupils.
  • Exploratory analysis suggested that pupils with lower prior attainment may have benefited more than pupils with higher prior attainment.
  • Teachers reported that the programme improved their understanding of and confidence in teaching mathematical reasoning. Most teachers also felt the programme had a positive impact on pupils’ mathematical reasoning, arithmetic skills, confidence, and enjoyment of maths.
  • Teachers reported that support from teaching assistants during programme sessions was important for delivering the programme as intended. Some schools reported that the training requirements and demands of delivering the programme made it challenging to implement.

How should I interpret these findings?

  • This evaluation provides strong evidence that Mathematical Reasoning can improve maths attainment for Year 2 pupils.
  • The overall impact was modest but positive and was observed in a large trial conducted under everyday school conditions. The high security rating means we have confidence in the main finding.
  • The programme appears particularly promising for pupils eligible for Free School Meals and pupils with lower prior attainment, although these findings are less secure than the overall result.
  • The findings also suggest that implementation matters. Some schools did not always deliver the full programme as intended, particularly where time, staffing, or teaching assistant capacity were limited. Despite these challenges, the programme still produced a positive overall impact.
Outcome/​Group
ImpactThe size of the difference between pupils in this trial and other pupils
SecurityHow confident are we in this result?
Maths attainment (all pupils)
+1
Months' progress
(Effect size 0.09)
Maths attainment (pupils eligible for FSM)
+2
Months' progress
(Effect size 0.14)

Were the settings in the trial similar to mine?

Project type: Effectiveness level evidenceKey Stage: Key Stage 1Subject: Maths
  • The evaluation involved 238 primary schools
    and 6,443 pupils across England.
  • Schools were recruited nationally and all state primary schools in England were eligible, except those involved in overlapping maths trials or the earlier pilot of the revised training model.
  • Trial schools were somewhat more likely than the national school population to be urban and to serve higher proportions of pupils eligible for Free School Meals.
  • Most participating schools were rated Good by Ofsted, with a smaller proportion rated Outstanding.

Could I implement this in my setting?

Delivered by: Teachers & Teaching AssistantsParticipant group: Whole ClassIntervention length: 15 week(s)
  • Mathematical Reasoning is delivered by the class teacher to the whole class with support from a teaching assistant. Schools replace one maths lesson each week for 12 to 15 weeks with a programme session that combines whole-class teaching, group activities, and computer games.
  • Schools need access to programme materials, classroom display technology, devices for pupils to play the computer games, and manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods). such as counters and blocks.
  • Teachers and teaching assistants need time to complete online training and webinars.
  • The implementation and process evaluationAn IPE is used to understand how and why an intervention has (or has not) been successful. Data is analysed to explore programme quality, reach, adaptation and differentiation, as well as setting fidelity and responsiveness to the trial design. found that some schools faced challenges relating to staff time, training completion, teaching assistant availability, and technology. However, most schools were able to deliver the programme successfully.

How much will it cost?

Cost per pupil: £19No. of teachers/TAs: -Staff training duration: unknown days
  • The average cost of Mathematical Reasoning is approximately £652 per class per year, equivalent to around £19 per pupil per year when averaged over three years.
  • Most of the cost relates to training and programme materials. Schools also need access to classroom technology, pupil devices, and manipulativesobjects that educators and children can move and interact with to represent mathematical ideas (including fingers, everyday objects, such as buttons or pine cones, and mathematical resources such as Numicon, Cuisenaire rods)., such as counters, blocks and coins.
  • Schools can register their interest in the programme, or find out how to purchase it, through the EEF Promising Programmes Page.

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