Doing division with digital chocolate

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A chocolate bar with eight pieces, one of which is missing – this image helps some children understand the fraction 7/8 better. For this reason, Professor Sarah Hofer incorporates it into digital learning environments. “Specifically children whose visual-spatial skills are less well developed seem to benefit from illustrations such as divided chocolate, pizza, or cake,” explains the learning specialist. “Other children, by contrast, don’t need them and even find them distracting.” One learning concept does not fit all.

Since April 2022, Sarah Hofer has been Professor of Teaching and Learning Research at LMU. Hailing from the Chiemgau area of Upper Bavaria, Hofer studied psychology at LMU and obtained her doctorate at ETH Zurich with a dissertation titled The interplay between gender, underachievement, and conceptual instruction in physics. As a postdoctoral researcher, she worked at ETH initially and subsequently at the Technical University of Munich, where she did research in mathematics education, among other areas, and was a member of the PISA research team.

Virtual molecules

Sarah Hofer had already held an interim professorship at LMU from 2019 before moving to the Universität der Bundeswehr München in 2020, where she took a keener interest in digital technologies in mathematics and physics learning environments. In 2021, she took up a position at ETH as an assistant professor for learning and technology. “There was a lot of change over a short period,” says Hofer looking back. “But working in the very different research groups taught me a great deal.”

Hofer’s main research interest concerns the question of how to structure teaching and learning in more effective and individual ways, particularly in schools and for STEM subjects. Using experiments and intervention studies, she investigates how intelligence, prior knowledge, gender, family background, motivation, and other individual characteristics are related to teaching and learning processes.

She has studied the influence of gender on teachers’ grading processes, for example, and – based on data from the PISA study – the influence of socioeconomic status on reading ability. “This research field is experiencing something of a resurgence at the moment – partly because digital technologies are opening up many new possibilities.” Intelligent tutoring systems help students to learn math or to practice vocabulary in foreign languages. “And with virtual or augmented reality, a lot of concepts can be presented in a more tangible form – the structure of a molecule, for example, or the Lorentz force in physics,” says Sarah Hofer.

“One advantage of digital support is that it makes diagnosing problems easier. In digital learning environments, teachers can track the progress of children from moment to moment and identify weaknesses.” Another advantage is that suitable feedback can be conveyed – individual tips or details in the learning environment that are helpful to a specific group of learners.

No substitution for teachers

In a project about fractions at junior high schools and academic high schools, Hofer’s team developed a digital learning environment that is activated and interacted with using tablet computers. “The children are supported with various instructional methods that help them understand fractions.” Hofer explains that the jump from natural to rational numbers is one that many children struggle with. By means of adaptive algorithms, the difficulty level of the exercises is adjusted based on students’ past results. In addition, the system gives individual feedback to students. “This can be a prompt like: Think again whether it’s the numerator or the denominator you have to watch out for here.” Another aid to understanding is the animation illustrating the fraction, which can be activated when needed. “In that case, the children see the fraction as a kind of chocolate bar subdivided into several pieces and then converted into a number line,” says Hofer.

Nevertheless, good teaching does not necessarily have to be backed up with digital technology: “What’s really important is for teachers to be aware that not every teaching concept optimally suits every learner in every situation.” The digital media are just tools here and no substitute for teachers. It is the teachers who decide how and when to use the tools and who usually interpret the data obtained.

“Neither do I think that equipping all schools with virtual reality headsets and digital whiteboards is the key to success,” explains Sarah Hofer. It would make more sense, she continues, to jointly develop concepts with schools, identifying when the use of various tools would be beneficial. “As such, we go directly into classrooms with our digitally assisted teaching-and-learning units to test new approaches and learn from the children and teachers what works and what doesn’t.” The team is currently developing a flexible platform that allows digital lessons to be compiled, applied, and evaluated for a variety of contents – based on the input of practicing teachers.