Students spending more time doing maths online would be fantastic if this complemented a reasonable minimum amount of written work. In many cases, however, students are doing online work at the expense of written work, and teachers are sometimes complicit. Many maths platforms exploit gamification and use extrinsic motivation to incentivise students to rack up scores, virtual trophies, stars, and hours of learning—all online.

Of course, schools do use fantastic online platforms and students do make progress, but publicly available GCSE results show that using a platform doesn’t automatically ensure a school’s students make good progress: teachers have to use the platform correctly to ensure it works as desired. So, we asked ourselves, for four main reasons, whether a platform designed to encourage a wholesale culture change could make it easier for teachers to use correctly and see students making even greater progress.

Firstly, many schools benefit more in the year they launch a new platform than in subsequent years. This may be down to the enthusiasm of teachers and students for a new platform, and also because of culture changes encouraged by the makers of the platform. In many ways, however, the platforms don’t best promote culture change through their own design, and put the onus on teachers to do so. This is fine as long as the teachers can do this. When the effort required by teachers to sustain a culture becomes too great, however, the benefits that were down to that culture are lost. This becomes an issue when a platform’s success is based more on sustaining a culture than on the intrinsic design and quality of the platform itself.

Secondly, the nature of online questions is currently better suited to testing isolated skills than application and synthesis of skills. In exams, we would often see students struggle to present clear mathematical arguments on the longer-form questions, despite the fact they had all the individual skills they needed. Clearly these students would have benefited from more written practice.

Thirdly, we also see in many schools a pattern of students heavily using a maths platform, performing well at GCSE, choosing to continue with Maths into the Sixth Form, but then struggling at A-Level—partly because they have not developed the skills needed for longer questions.

Finally, we found that while lower-achieving students benefit the most from the online platforms, the highest-achieving students benefited most from exposure to challenging—and invariably written—work that was either found online or created from scratch. It is interesting to note the differences in take-up of the major platforms between comprehensive schools on one hand and selective schools on the other. The major platforms tend to be so obsessively focused on specifications and examinations that they shackle bright and curious students if their teachers do not otherwise provide for them.

For these reasons, we have created BossMaths—a website with plenty of longer-form exercises suitable for written work, and with material that goes beyond the narrow focus of examinations.

Maths is the subject most often taught in ability-based sets—often for valid reasons—and the subject also continues to have examination tiers of entry. Nevertheless, one consequence is that it is all too easy for both teachers and students to subconsciously lower their expectations as a result of setting and examination tier. The resources we choose often reinforce such expectations—we may eschew difficult topics because we think that students cannot cope. While this may be perfectly true, students who are not even exposed to more challenging material don’t know what they are missing out on.

BossMaths lessons include differentiated content and “challenge” questions embedded into every lesson. It is up to teachers to choose the appropriate range of content within each lesson. However, we made the design choice to include ever more challenging content just a scroll to the right in order to increase students’ exposure to the existence of more challenging material—so that they become aware that there is more to learn, even if they are not yet ready to learn about it straight away.

In some schools, teachers spend a significant proportion of their time monitoring students, collecting data, inputting this data elsewhere, generating personalised documents for pupils, targeting interventions at particular students, and refining and delivering an exam-focussed curriculum.

In some others schools, teachers spend a very low proportion of their time collecting data. They spend more of their time developing their curriculum and creating an environment that encourages students to become more responsible for themselves—while maintaining strict boundaries.

Both of these types of schools can and do achieve excellent examination results—but examination results do not completely illustrate the quality of education provided. Students with identical GCSE grades can perform very differently at A-Level, university and in the workplace. While many factors can influence this divergence, we believe that schools can play a powerful role in ensuring students are well-equipped to cope with the challenges they will face in further education, the workplace and their personal lives.

As Craig Barton notes in How I Wish I’d Taught Maths, students asking when they’ll need to use a particular bit of maths in real life is often a sign that they don’t understand rather than a genuine interest in real-world applications. He also notes that poorly-conceived real-life problems can be pointless, confusing and sometimes dangerous. We have all seen uninspiring, contrived “real-life” applications. For example, whilst it is possible to use trigonometry to solve problems involving placing a ladder against a wall, this is neither exciting nor something that real users of ladders are likely to do!

On the other hand, Mathematics is used in many genuinely mind-blowing ways in real life, but the level of knowledge required to appreciate these is out of reach for most students. Given this fact, our In the real world featurettes are not designed to instruct students through real-life contexts or to present contrived problems for them to solve. These featurettes contain curated articles and videos about how Maths is used in fascinating contexts—and are accessible because they don’t get bogged down into mathematical technicalities. Our aim through these is to inspire students, broaden their horizons and increase the likelihood of their choosing a STEM subject in Sixth Form and beyond.

Online textbooks are often formatted identically to their physical counterparts. While identical formatting has the advantage of consistency, it can result in a frustrating experience for teachers and students. Ostensibly, many online textbooks are designed for front-of-class use; they even include pen and highlighter tools. In practice, the material can be very difficult to present on interactive whiteboards. Even students using tablets with high-resolution screens constantly need to zoom and pan across textbook pages.

That’s why we have ensured that BossMaths lessons look good on all devices, and don’t require a username or password to access. We are also going a step further by producing an eBook. Therefore, unlike the major publishers, our offering will include an eBook that works offline and only requires a single purchase as opposed to an annual subscription.

At BossMaths, we include GeoGebra applets in our lessons where we can. This dynamic content is more helpful for teachers and students than static illustrations or passively-watched videos alone. Here, for example is one of the applets from our lesson on circle theorems. Note that by moving point P to the 3-o’clock position (just above point B), we can illustrate, live, how the angle at the circumference is double the angle at the centre even in cases where a chord intersects a radius. We can also move points A and B so that the angle at the centre is reflex, and show that the theorem still holds. A single textbook illustration cannot convey all of this at a glance.