Using artificial intelligence to help children learn maths

The problem on the screen seems simple to solve: a number line from 1 to 100, divided into intervals of ten. Only the positions 0, 10 and 100 are marked respectively with the numeral. The other divisions are not numbered – the position 50 alone is emphasized by way of a slightly longer line. In various exercises using the number line, certain positions are marked successively with a red cross. Pupils are required to indicate which number a particular position is supposed to represent.

Almost all of them arrive at the correct solution. However, the path they take to get there can differ. For instance, children that are good at maths will orient themselves on the marking in the middle or at the end and can swiftly identify the result from there. Others, in contrast, will count all of the positions individually and are not yet able to use structures such as the middle numeral.

In the process, the children are observed by way of a small webcam attached to the computer monitor. The camera captures eye movements while the various basic maths problems are being solved on screen. This webcam eye tracking, as it’s referred to, records movements in the eye and stores the recorded data. The system evaluates the data and, based on the specific tracking pattern, establishes whether pupils have applied structures when solving the problem or for instance have counted everything. The learning system interprets which basic areas of mathematical competence might require additional support and offers schoolchildren explanations, videos and individually tailored learning support sessions on the computer.  

Eye tracking with affordable webcams

Many children leave primary school without a sufficient understanding of basic operations, which makes the transition from primary to secondary education considerably more difficult. At the end of the primary education phase, around twenty percent of pupils are experiencing serious difficulties in mathematics and calculation – in terms of their knowledge, they are on the same level as pupils in year two. In the case of children going on to a non-academic secondary school (Hauptschule) or a comprehensive school (Gesamtschule), this percentage is even higher, at around 25 to 30 percent. The lack of sufficient teaching staff in schools also contributes to children performing poorly with respect to basic mathematical skills or to them not being able to overcome these difficulties. Teaching staff in inclusive schools often have too few opportunities to precisely diagnose existing skill levels at the beginning of the secondary level and thus address any lack of knowledge by providing pupils with individual support.

The KI-ALF system (KI-basierte Adaptive Lernunterstützung zur Diagnostik und Förderung der mathematischen Basiskompetenzen im inklusiven Kontext – AI-based adaptive learning support for diagnosing and promoting basic mathematical skills) is a digital diagnosis and developmental support system which recognizes the individual learning requirements of pupils by way of artificial intelligence and supports children individually in an adaptive manner, using specific guidance and exercises to acquire skills. The system is already being used in the test phase at Wulfen Comprehensive School in Dorsten. This school is the first to use the webcam-based eye-tracking technology to specifically screen fifth-year pupils for deficits in their mathematical skill set and to support them individually where needed.

KI-ALF has been developed by the Professor Dr Maike Schindler and her team at the Institute for Special Education in Mathematics in cooperation with Professor Dr Achim Lilienthal at the Technical University of Munich, who specializes in robotics and IT. The recently concluded project was funded for three years by the Federal Ministry of Education and Research (BMBF).
What is special about the learning system is that there is no need for an expensive camera to perform the eye tracking. “KI-ALF can be used in schools with comparatively low financial and technical outlay,” explains Maike Schindler. “The system uses a commercially available, affordable webcam for the eye tracking and is operated using a Windows computer.” As a rule, two monitors are connected to a computer: The pupil works on one screen and the teacher can follow them as they try to solve the mathematical problem live on a second screen and offer help where necessary.

Unique in the world

Schindler and her team have developed hundreds of mathematical exercises in which children recognize numbers and represent, add, subtract, divide and multiply them. All of the exercises serve the purpose of diagnosing basic individual mathematical skill levels. “KI-ALF is particularly suited to exercises that are present in a digital learning format and which can easily be presented in visual form,” says Schindler.

After the exercises have been performed on a computer, the system compiles a digital report for teachers, wherein the manner in which the exercise has been completed and the basic mathematical skill level determined from this are presented in the form of a detailed overview, which also records the support provided to each individual pupil and the successfulness of that support. This report represents a key tool for teaching staff and at the same time relieves the burden on them, as they no longer need to manually provide a report themselves.

“Tracking eye movements via webcam, recognizing learning approaches by analysing eye movement patterns with the help of AI, offering individualized support, and then automatically generating support reports, all of this within one single system – that’s entirely new,” says Schindler. “So far, there isn’t a digital system like this for supporting basic mathematical skills anywhere else in the world.”

One aim of the project was to find a solution for schools which is as cost-effective as possible, and this has been made possible by using a commercially available webcam. Eye tracking with a small webcam has been realised in KI-ALF by using artificial intelligence. This involved a particular challenge for Achim Lilienthal, who has contributed his know-how to the project as a cooperation partner: “There are eye trackers that work very precisely, but cost thousands of euros. Webcams don’t achieve that kind of precision,” explains the robotics specialist. “In order to compensate for the greater degree of inaccuracy in the webcams, we automatically adjust the eye tracking afterwards.” The researchers use artificial intelligence to help the system learn to deal with the imprecision.

One third of pupils require support

AI is also used to interpret the recorded eye movements when the children are working on the exercise. “Depending on the problem they have to solve, certain eye movements occur, which are stored digitally. These patterns are interpreted using artificial intelligence,” Lilienthal says. For the current system, the developers have already fed hundreds of sets of eye-tracking data into the software that have been gathered during its use.  

At Wulfen Comprehensive School, a standardized maths test involving 180 pupils at the beginning of year 5 showed that around a third of them had difficulties with calculation. “We’re pleased that we can now use the AI-based learning system to help considerably more children than before in developing their basic mathematical skills,” says school principal Hermann Twittenhoff. “This means that we’ll be able to help more pupils improve their mathematical performance than we could until now with the lack of teaching staff.”

While the KI-ALF system is already in use at Wulfen Comprehensive School, the research team will be continuing to work on it. “We now have a system that is up and running in practice in the school environment and can be independently used by the teaching staff. Now we want to develop it further. And here technological developments and developments in terms of content go hand in hand,” says Schindler. Lilienthal adds, “The constantly unfolding new possibilities of AI and other technical aspects allow us to make the system even more precise and stable – which is a great advantage for the large-scale use of KI-ALF.”