Adaptivity in Mathematics – Your Own Learning Path

Adaptivity is one of the biggest trends in education technology – and rightfully so! It allows students to walk their own learning path, perfectly tailored to their needs. Adaptive systems work by analyzing the performance of the students, and subsequently choose to make the material harder or easier. In other words, it adapts the path the students takes through the content so that it fits their level. Adaptive education technology does what a good teacher would do if there was enough time to give every student the personal care they deserve.

We’ve been working on adaptivity for a while now, and we wanted to share some of the opportunities, problems, and solutions we encountered!

Adaptivity and Knowledge Tracing

The primary focus of adaptivity is improving how a student experiences the flow of exercises. This is done by adjusting the pace and difficulty of the exercises students see on their screen. The first step in giving students fitting exercises is mapping their level of understanding. There are different ways of doing so, but due to the variety in student backgrounds and usages of the platform, SOWISO uses diagnostic tests. Students will be asked to complete these short tests when a new chapter is started. The algorithm can decide whether or not certain topics have to be reviewed by the student or if they are already mastered. A student can then continue to work on the topics which still need attention.

One of the issues regarding this so-called knowledge tracing that came up in conversations with mathematics professors already using the SOWISO platform is that students shouldn’t be able to skip over certain subjects. It’s a valid point; mathematics isn’t always just about the correct answer. So what if the platform has students skip over some content, only for them to be unprepared on the test because they didn’t review the necessary solving process? For this reason, teachers using our software have the option to flag certain exercises or theory pages as mandatory, which means they cannot be skipped.

Adaptivity and Agency

We realized we could not remove the learning process completely from the teacher’s hands. Though adaptivity generally means that the algorithm decides the presentation of content and the path through the content, we have worked hard to give the teacher as much agency as possible. In practice, this means that on the SOWISO platform, any available parameters should have a workable default value and be editable by the teacher instead of only the content author.

When analyzing a student, we first need to know what the benchmark is. In other words, what are the requirements a students needs to meet in order to move to the next topic or difficulty level? We believe teachers should always be able to choose these requirements.



This can work in multiple ways. For example, a teacher has influence over the minimum grade a student is required to achieve. On the SOWISO platform, this grade is correlated to a difficulty setting. For example, when a teacher sets the minimum difficulty to 80%, a student should correctly answer an exercise from the top 20% hardest questions. Alternatively, a teacher can set a minimum streak, which requires a student to correctly answer a set amount of exercises in a row, without error.

Students have some control on our platform as well. Our software will therefore never block access to topics or chapters. Once students have completed a topic, they are able to revisit that topic at any moment.

Adaptivity and Progress

So what does this look like for the student? Instead of a fixed set of exercises, the adaptive platform will select the next exercise based on whether or not the previous exercise was answered correctly. The length of the set is therefore still unknown when a student starts practising.

Like our traditional solution, exercises get more difficult as the practice session goes on. With our new adaptivite algorithm, The rate at which exercises will get more difficult is higher than the rate at which exercises get easier. This allows bright students to finish a chapter more quickly. Students for which the pace is too high can take a small step back without having to go back to the start.

Adaptivity: regular breadcrumbs

As the amount of exercises is no longer fixed with this new way of presenting content, a different kind of progress bar was needed. The breadcrumb-type progress shown on the left of the screen shows how many exercises are in a specific set, and how many you have completed. You can also choose to redo these exercises by clicking on them again. But our new adaptive system asks for a progress bar which indicates the current difficulty, relative to the minimum difficulty and the level required to pass the subject. We have therefore implemented a bar like the one shown below:

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In Conclusion

These are some of the ways in which we’re implementing adaptivity. It’s a very exciting road to be on, and we are sure it will help many students take an even smoother approach to mathematics learning!

Look out for our official release in March!

Let’s talk again soon,

Jeroen

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