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1. 0Maths - Theory of Change

Every learner should have the opportunity to develop mathematical confidence, regardless of prior attainment, learning difficulty or educational background.

0Maths exists to reduce barriers to mathematical learning by applying insights from psychology, cognitive science and inclusive design. By helping pupils experience success, build secure foundations and develop confidence, we aim to improve both mathematical attainment and long-term life opportunities.

The Challenge

Despite high-quality classroom teaching, many pupils continue to struggle with mathematics.

For these learners, difficulty is often caused by a combination of cognitive and emotional factors rather than a lack of effort or motivation. As learning gaps widen, pupils may lose confidence, become increasingly anxious and avoid mathematical tasks, making future learning progressively more difficult.

These barriers are particularly common amongst pupils with SEND/ASN, those with interrupted learning, and those who have experienced repeated failure in mathematics.

Common barriers include:

Without effective intervention, these barriers reinforce one another, leading to widening attainment gaps over time.

Our Theory of Change

We believe mathematical success depends upon addressing the underlying barriers that prevent learning, rather than simply providing more practice.

Each element of 0Maths is designed to influence a specific psychological or educational mechanism known to affect mathematical learning.

The pathway can be summarised as:

Barrier
↓
Psychological mechanism
↓
0Maths intervention
↓
Behaviour change
↓
Learning outcome
↓
Long-term impact

By strengthening each stage of this pathway, we expect sustained improvements in both mathematical attainment and learners' confidence.

Psychological Barriers and Our Response_

Mathematics Anxiety

Barrier

Fear of failure reduces engagement and consumes working memory needed for mathematical thinking.

0Maths response

Expected change

Pupils attempt more questions, persist for longer and develop greater confidence in their mathematical ability.

Weak Number Representations

Barrier

Some learners struggle to develop secure mental representations of quantity and number relationships.

0Maths response

Expected change

Learners develop stronger numerical intuition, supporting later arithmetic and reasoning.

Gaps in Prior Knowledge

Barrier

Later mathematical topics often depend upon knowledge that has never become secure.

0Maths response

Expected change

Secure foundations enable successful learning of increasingly complex mathematical ideas.

Forgetting

Barrier

Previously learned material is forgotten without sufficient retrieval and reinforcement.

0Maths response

Expected change

Improved long-term retention and increased mathematical fluency.

Low Confidence

Barrier

Repeated failure reduces willingness to engage with mathematics.

0Maths response

Expected change

Greater self-efficacy, resilience and willingness to tackle unfamiliar problems.

Teacher Visibility

Barrier

Teachers cannot always identify misconceptions or individual learning needs quickly enough within busy classrooms.

0Maths response

Expected change

Earlier intervention and more effective use of teacher time.

From Design to Impact_

Inputs

0Maths provides:

Teachers provide:

Schools provide:

Activities

Pupils:

Teachers:

Outputs

For pupils:

For teachers:

Short-Term Outcomes

Medium-Term Outcomes

Long-Term Impact

By reducing barriers to mathematical learning rather than expecting learners simply to overcome them, we believe more pupils can experience success and develop positive lifelong relationships with mathematics.

Assumptions

2. Foundational Evidence

A 2022 UCL study found that only 1 of the top 25 maths apps on the Apple store and Play stores was effective. At 0Maths, we began with the goal of making the most effective maths platform possible. We've used findings from Educational Psychology as the basis for every aspect of its design:

Gamification

Gamification in maths platforms is often interpreted as a narrative (eg slay the dragon / race your friend / dog with your numeracy skills).

Outside of maths platforms, gamification is much broader and more sophisticated. It is intrinsic to everything from banking apps to the dark design of gambling apps and social media. It simply means utilizing design that taps into the brain's reward pathways. This is the approach we've adopted.

Gamification on 0maths is not:

Motivation

The rewards on 0maths are crafted to be intrinsic and informational (ie emphasising what they have done well). This contrasts with some other platforms where rewards are extrinsic and controlling (ie a bribe for doing well). Studies show that such extrinsic controlling rewards actually reduce intrinsic motivation [Ledford, Fang and Gerhart, 2013]. Learners may enjoy time on such platforms, but they enjoy maths less as a result.

Question format

Adrenaline vs dopamine

On many maths platforms, adrenaline provides the addictive element by racing against peers or some sort of ticking bomb.

If you search Google images for "stress performance" you get a curve known as the Yerkes-Dodson curve.

This is a misinterpretation of their results. Their actual (1906) paper "The Relation of Strength of Stimulus to Rapidity of Habit-Formation" looks at the effect of electric shocks on which route Japanese dancing mice would take through a maze.

There was a simple discernment task (white box vs black box) and a difficult discernment task (same black and white boxes, misleading lighting). Notably, the mice did not require working memory (which is inhibited by adrenaline) and had no other motivation (ie no 'cheese' for getting it right). To interpret their research as the popular "Yerkes-Dodson curve" you have to assume that trials to completion corrleates to cognitive capacity, that the mice wanted to solve the maze, and that the strength of an electric shock correlates to arousal.

A simpler explanation is that in the solitary data point from which the entire left hand side of the curve is drawn (ie where low arousal = low performance), the mice weren't too bothered about the electric shock.

There are many modern studies that have added a bit of nuance here. We can break down stress into 3 physiological responses:

Back to maths:

By eschewing time based failure, peer-to peer competition, and even wrong answers, we decrease adrenaline levels (which are in any case elevated for many students when doing maths, and have a bigger impact on autistic learners). Instead, because answers on 0maths are never wrong, and multi stage problems are often broken down with marked workings, the constant stream of correct answers triggers dopamine* release. * dopamine levels can also be increased through exposure to sunlight, getting sufficient sleep, healthy diet (especially protein: turkey, eggs, beef, legumes, and dairy) and exercise. That's out of our remit but it would be remiss to not mention the broader picture.

The colour scheme

Typing versus handwriting

If appropriately equipped (ie using an ipad and an apple pen) it is possible to use 0maths with handwritten, as opposed to typed, answers so we can happily sit on the fence for this issue. It makes for an interesting discussion though, as the popular interpretation of the research is not at all related to what the research tested.

Several well publicisized studies (i.e. Handwriting but not typewriting leads to widespread brain connectivity: a high-density EEG study with implications for the classroom, Van der Weel, Van der Meer, 2023) have demonstrated increased and more interconnected brain activity when writing by hand as opposed to typing. This in itself is not especially surprising; handwriting requires more muscles, moving more intricately, in a more coordinated manner than typing. It would be surprising if handwriting did not induce more brain activity.

However, such studies have often been interpreted to mean writing things by hand leads to better retention, but it's important to note that they did not test for this. Their own wording, not directly supported by their research, is qualified ("Thus, the ongoing substitution of handwriting by typewriting in almost every educational setting may seem somewhat misguided as it could affect the learning process in a negative way"). I'll say it again: they did not test for this conclusion and provided no direct evidence for it.

An alternative interpretation of the same study (not presented by its authors) is that cognitive load increases more with handwriting than with typing. This is directly supported by the conclusion of another study that handwriting deteriorates with cognitive load - ie handwriting utilises cognitive capacity. (A legibility scale for early primary handwriting: Authentic task and cognitive load influences [Staats, Oakley and Marais, 2019] ). As a large part of the task of teaching maths is to reduce cognitive load as much as possible, this would seem to imply that typing would be better than handwriting.

Straying from maths, there are several studies looking at college performance when typing notes versus handwriting and they all seem to have different conclusions - here's a good discussion on the subject. The study alluded to in the above article looked at student exam results and how they took notes (ie typed or by hand). This got much more emphatic results (in favour of handwriting) than previous studies. However, the key difference is likely to be the students' ability to add diagrams and mind maps into their notes rather than the mechanism for forming words.

The optimal solution may not be the same for all students. My own writing can be neat when I'm writing without thinking, but it deteriorates rapidly if I have to think while writing.

3. Case Study

0Maths helped intervention groups to build confidence, work independently, and achieve National 3 numeracy.

Case Study: Supporting Low-Attaining Learners in Secondary Maths with 0Maths

School: Elgin Academy
Role: Maths Teacher
Cohort: First and second year (S2) pupils with low prior attainment in numeracy

The Challenge

Like many secondary settings, Elgin Academy faces the challenge of supporting pupils who arrive with limited numeracy and low confidence in maths. These learners often require significant support, can struggle to work independently, and may rely heavily on calculators rather than developing core skills.

The Approach

0Maths was introduced for S1 & S2 intervention groups, in class, for up to 2 lessons per week. The platform was used primarily to reinforce numeracy skills alongside normal classroom teaching.

The Impact on Pupils

“My second year class are more confident in trying calculations without a calculator and the majority of the class have achieved Nat3 numeracy. ”

The Impact on Teaching

Better support for struggling learners
0Maths enabled targeted support during lessons:

“When I find that they are struggling with something I have used 0Maths to help support them in their areas of weakness.”

Fewer repeated errors
After working through topics on 0Maths, pupils were less likely to repeat the same mistakes, suggesting stronger understanding and consolidation.

Supports independent learning
The platform fit easily into lessons and helped pupils continue working productively without constant teacher intervention.

Teacher Workload & Usability

Quick and easy to implement

Time savings during lessons

Flexible classroom use
0Maths integrated smoothly into existing teaching without requiring major changes to lesson structure.

Teacher Summary

“I have used 0Maths mainly for improving numeracy skills and I would say the practice has helped support the work I have been doing in class.

[0Maths makes it] Easier to support learners who have come into secondary with a low level of numeracy.

My second year class are more confident in trying calculations without a calculator and the majority of the class have achieved Nat3 numeracy.”

Conclusion

This pilot demonstrates that 0Maths can play a valuable role in supporting lower-attaining secondary pupils, helping to:

At the same time, it enables teachers to use their time more effectively, particularly in differentiating work and targetting interventions.

Would the teacher continue using 0Maths?
Yes
The school have broadened the use of 0Maths

Full responses

Download the full teacher's feedback questionaire, here.

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