Experiencing Algebra with All Senses

| 16.11.2016

Scientists at the University of Bremen are developing interactive objects to help students understand abstract mathematical concepts intuitively

Algebraic concepts were first recorded almost 2000 years ago, but for today’s students they still present considerable challenges. Conveying the abstract subject matter is also difficult for teachers. A joint research project lead-managed by the University of Bremen’s Center for Computing and Communication Technologies (TZI) aims to help students by allowing them to experience and grasp concepts with various senses. To achieve this, the project “Learning Algebra Multimodally” (MAL) uses new findings from research in math education and combines it with technology developed by the TZI. Scientists from the University of Bremen’s Competence Center for Clinical Trials and from the ifib Institute for Information Management Bremen – a research institute also belonging to the university – are participating in the project as well. The Federal Ministry of Education and Research provides funding of 1.4 million euros; the project’s total volume is 1.8 million euros.   

The researchers chose to focus on Algebra because it plays a crucial role in education. “Everything that is taught from eighth grade onward is based on Algebra,” explains Prof. Dr. Angelika Bikner-Ahsbahs from the research group Didactics in Mathematics at the University of Bremen. A thorough understanding of these concepts is not only important for studying science at a university level, but also for vocational training. However, many students at all levels of the education system are having difficulties when they are asked to comprehend and apply abstract algebraic concepts such as equations and variables.

Learning with the entire body


MAL’s goal therefore is to develop an interactive Algebra learning system that conveys these concepts by making it possible to experience them with a variety of senses. That way the process of learning not only happens in the mind, but in the entire body – by seeing, hearing and touching objects. The scientists are developing physical “learning elements” that are equipped with information technology and represent – for example – numbers or variables. Students can arrange the objects to find solutions to problems.

In addition to these “smart objects”, which are developed by Prof. Dr. Rainer Malaka’s research group Digital Media at the University of Bremen, students can work with displays on interactive tables or tablet PCs. They can use gestures to interact with the system, receiving feedback on their progress in the form of sounds or light signals. “The goal is not to produce conventional e-learning solutions, but to support the learning process by enabling the involvement of as many senses as possible,” says TZI’s managing director Dr. Gerald Volkmann.

Individual learning requires less direct supervision


Teachers are also expected to benefit from the project. Due to time constraints they are often unable to provide everyone with the best-possible support – particularly when there are huge gaps between students’ skill levels. The MAL system will be able to detect its users’ proficiency automatically by measuring the time it takes them to find solutions and by analyzing their approaches to the problems. To increase the students’ motivation, exercises can be presented in game formats.

However, the required technologies have yet to be developed. This activity is closely intertwined with didactics research in order to make sure that the system will in fact be of practical use in the classroom when it is finished. Prof. Bikner-Ahsbahs and her team constantly analyze the effects that the new methods have on learning outcomes, and they determine which approaches seem particularly promising. In cooperation with the biometrics department at the Center for Clinical Trials they are developing a concept for the evaluation of these processes. A comparatively recent field of study is the effect of gestures on learning: “Research in didactics increasingly shows how important gestures can be for comprehension in mathematics,” explains the scientist. An example of a simple exercise is the signaling of percentages by changing the distance between one’s hands. “With our gestures we sometimes understand concepts that our minds aren’t yet aware of,” says Bikner-Ahsbahs.

Publishing house Westermann develops educational content


The publishing house Westermann’s editorial staff for math/sciences at secondary schools – lead by Dr. Dirk Wenderoth – participates in the project in order to transfer the results into classrooms. The editors develop educational content, adapt it for existing teaching materials, and make it accessible for schools. Also involved is the consulting firm xCon Partners, which supplies its know-how in the area of smart glasses and other wearables (interactive technologies that can be worn on the body).

Meanwhile, the Institute for Information Management Bremen focusses on the ethical, legal and social facets of using the new technologies in schools. The goal is to ensure that all requirements regarding these factors are already considered during the development process – and not afterward, when it is too late to make changes. At the end of the project, the Competence Center for Clinical Trials will evaluate the effectiveness of the MAL system.

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