Education Endowment Foundation:Mathematical Reasoning

Mathematical Reasoning

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.
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months

Mathematical Reasoning is a whole class programme to develop pupils’ understanding of the logical principles underlying mathematics.

Mathematical Reasoning (MR) is a 12 to 15 week programme developed by the University of Oxford for pupils in Year 2. The programme aims to improve mathematical attainment by developing pupils’ understanding of the logical principles underlying mathematics, primarily:

  • Quantitative Reasoning – the ability to reason about quantities and relations between quantities with or without numbers; and
  • Arithmetic – the ability to reason about relations between numbers using the four operations, with a specific focus on additive composition and the inverse relation between addition and subtraction.

The programme consists of twelve teaching units, with children receiving approximately one hour of content per week as part of their normal mathematics lessons. The programme is fully resourced and includes online games for pupils to use.

The MR programme was developed by academics at the University of Oxford based on evidence showing that abilities to reason about mathematics were predictive of later mathematic attainment.

EEF has conducted two trials of the Mathematical Reasoning approach, both of which showed positive impacts on pupil attainment in maths. In the EEF funded efficacy trial, where the teacher training was led by the programme developers, pupils receiving the programme made an additional three months’ progress in maths compared to children in comparison schools (5 padlocks). The EEF then funded a follow-up effectiveness trial evaluation which examined the impact of a version of Mathematical Reasoning in a larger number of schools and with less involvement from the original developer, with support from the National Centre for Excellence in the Teaching of Mathematics (NCETM). In this second trial, pupils who received Mathematical Reasoning made the equivalent of one additional month’s progress in maths, on average, compared to other children (4 padlocks). In this trial, rather than delivering the training directly, the programme developers trained Maths Hub teachers who then delivered the teacher training to participating schools. The result was similar when looking only at children eligible for free school meals.

Taken together, these positive results have led EEF to designate this as a Promising Programme’.

The developers have considered how they can scale Mathematical Reasoning, in a way that is closer to its original form, which led to the development of an online teacher training course to train teachers in the Mathematical Reasoning approach. EEF ran a short pilot evaluation of this training and is now re-trialling the programme at effectiveness level to assess the impact of the programme as delivered in this way at scale.

  • The latest published effectiveness trial took place in 160 schools, located in eight Maths Hub areas throughout the country.
  • 26% of the pupils in the trial schools were eligible for FSM, which is around national average.
  • 93% of the schools involved were Ofsted-rated Good or Outstanding schools. This is slightly higher than national average.

The programme consists of 12 units that are delivered by the teacher, with TA support, across 12 – 15 sessions. Learning is supported by mathematical computer games that are accessed by children in the lessons. Each session comprises a whole-class component and a group component. For the whole class teaching component, teachers receive lesson plans and PowerPoint slides to deliver the intervention, as well as pupil workbooks, which include written activities and extension worksheets, as well as cut-out shapes to be used as manipulatives. For the group component, the teacher divides the class into two groups. Group 1 consists of pupils for whom the teacher feels additional support could be beneficial, while Group 2 is for pupils perceived by the teacher to be ready for further learning. These groupings are intended to be flexible according to perceived pupil need in response to each topic covered, on a session-by-session basis. The groups alternate between teacher-led activities and playing the computer games, according to the allocation provided for each unit in the handbook.

In the effectiveness trial, there was one initial day of face-to-face training for teachers, and one in person support visit during programme delivery. Schools are expected to provide the necessary IT equipment, including access to computers or tablets for pupils to play computer games during the group component of the sessions. In addition, schools are expected to provide additional manipulatives for pupil use, such as counters, blocks and coins.

Teachers reported positive experiences with the training and materials and were positive about the programme’s focus on fundamental mathematical principles. In the latest trail there was some variation in how schools implemented aspects of the programme, particularly in relation to the use of the online games, with access to IT equipment highlighted as a potential barrier for some schools.

For the programme as trialled in the latest evaluation, the average cost of Mathematical Reasoning for one school was around £1,073, or £8 per pupil per year when averaged over 3 years.

This is an estimate of holistic school costs to implement the programme at the time of the evaluation. Schools will need to check the current purchase cost of the programme through Home | Reasoning First.

The Mathematical Reasoning programme is available to schools nationally from the academic year 25/26 onwards, with some limited availability for a smaller number of schools to participate in the 2024/25 academic year whilst the effectiveness trial takes place (delivery starting Spring 2024).

The version of the programme available is with fully online teacher training and support, including an online course for the initial training, and access to remote implementation support using webinars and an online forum. This is the same model EEF are currently trialling. There is also the option for schools to access tests that they can use to monitor their pupils’ progress in mathematical reasoning, as part of the programme offer.

Schools can express an interest to take part in the programme either in AY24/25 or AY25/26 using this form.