Finding out about and promoting mathematical talents

Prof. Dr. Ralf Benölken researches support measures for teaching mathematics for all students

"Today, the teaching of mathematics places a lot of emphasis on understanding, Ralf Benölken says, professor in the Didactics and History of Mathematics group at the University of Wuppertal. "I believe that the teaching of mathematics, especially at primary schools but also at secondary schools, has changed a lot in terms of what mathematics didactics considers good teaching." Benölken has been a teacher himself and knows about the challenges teachers face when they have to conceptualize lessons. Science always draws an ideal line to which, in the best case, teachers orient themselves, according to their student potential. According to the researcher, this includes active discovery, different approaches as well as conjectures that are then compared and discussed. Children should understand why mathematics works the way it does. In various projects, Benölken is researching the promotion of mathematical talent, which he does not limit to the highly talented.

The passion for the subject of mathematics

Benölken explains with regard to a mathematical talent, , "we have a very broad and holistic understanding", meaning that his team does not deal with intellectual giftedness across all areas. This is usually measured by intelligence quotient tests: Most people have an "IQ" score of about 100, but those who achieve a particularly high test score of usually 130 or more are considered "highly talented". Rather, the researchers are concerned with the child's prerequisites that are important for mathematical understanding. "We look at which characteristics are actually interesting for doing mathematics, for being mathematically active," he explains, "these include, for example, abilities in structuring or memory skills for mathematical facts." A special feeling or sensitivity for numbers and number relationships is also important. "For us, a part of it is that, for example, one is particularly willing to make an effort when doing mathematics, that one feels a special passion for the subject." Precise observations of the children's individual development processes and an understanding of their thought processes are important. That is why the conventional testing procedures in relation to mathematics did not apply. "For example, we would never describe a child as mathematically not talented if, according to our diagnostic instruments, the talented characteristics, such as the abilities in structuring, etc., are pronounced at a mediocre level, but they enjoy mathematics immensely."
However, the subject didactician, who both trains students and works with children interested in mathematics, sees his own strengths primarily in the reconstruction of thought processes. "I do not know whether this can be considered a kind of pedagogical-didactic talent, because at least this kind of thing is not described in talent models in the relevant literature. But my strengths actually lie more in, for example with regard to mathematical talents, really subtly reconstructing what people think. I think I can do that quite well."

The implementation of epistemological approaches

Currently, Benölken's working group, which is called 'Didactics and History of Mathematics', includes three university lecturers from other academic chairs who cover a broad spectrum of different school levels and topics. A special focus, for which Wuppertal is also internationally known, is the history of mathematics, the scientist says and explains: "Among other things, it is the genesis of things that can be applied from the history of the development of mathematics and the teaching of mathematics, and is being further developed in today's teaching of mathematics, a kind of historical communication". Likewise, he said, there is so-called material didactic work, in which questions about the problem-oriented preparation of mathematics courses are examined, as well as a lot of research that deals with the implementation of epistemological approaches in teaching. "I myself deal with mathematical talent," he continues, which has occupied him for 15 years now. In the meantime, associated topics have also moved into his focus. "Especially more recently, it is been inclusive education," he says, "the idea of broadening special talent education as the promotion of special talents and interests and asking, 'how can I use concepts from this specific area to really promote all children'?"
The planning of inclusive education, in which all pupils are supported within the framework of their possibilities and can participate in the teaching process, presents teachers with a great challenge. At the same time, the question arises as to the feasibility of such teaching in times of teacher shortages and a lack of additional staff. Benölken sees the problem in too little investment on the one hand, and a lack of training for students in inclusion, even though there have been increasing improvements in this area. "I see the great challenge for the teachers, some of whom are trained in a completely different way, to now have to implement the idea of consistent inclusive education. This already demands a lot from the teachers." Firstly, a positive attitude is a feasible way out of this misery. "Of course inclusion can succeed," the academic appeals, "because it is ethically and morally the right thing to do! You do not exclude anyone. We have to understand that we all belong together as a society, no matter what background someone brings with them. Attitude is a very important primacy for me here." Of course, this also requires adequate room and teaching equipment, reasonable equipment for multi-professional teamwork and, with regard to mathematics lessons, reasonable digital equipment.

Projects can help improve teaching

Among other things, Ralf Benölken is involved in the project "Leistung macht Schule" (LemaS), which aims to provide even more targeted support for high-achieving children and young people. "This is really a very large project. In principle, it is also a phenomenon because the Federal Government has joined forces for a joint project on educational issues. The perspective is to transform schools as a whole, i.e. to create a system for the further development of schools. To this end, they are attempting to further develop the teaching design from the perspective of supporting high-achieving pupils in particular to include all fellow pupils, and they are therefore are using various modules. "In mathematics, this is my field of research together with my colleague and some colleagues from Münster, we have a wide range of offers within this project. Together with a total of 20 cooperating schools nationwide, we are developing special mathematical task areas and creating concepts for so-called enrichment groups (enrichment is a pedagogical model for promoting gifted, interested and committed pupils, editor's note) and for revolving door models. Again, these are complementary measures which children can use in addition to mathematics lessons." The project also develops concepts for further training for teachers. In selecting the participating schools, Benölken works with institutions from NRW in Bonn, Iserlohn, Düsseldorf, Duisburg and Schwerte, but not with a teaching institution from the Bergisch Land, which the didactician regrets a little. But Benölken is a networker and says: "We, that is my team and I, have a project called "Think" (Treffen matHematisch INteressierter Kinder). Outside of the pandemic, children come to the university every to weeks to work with scientists and students. This project is also an infrastructure for us to test our materials from the LemaS project. And, of course, in this special project, we only work with schools from Wuppertal, Remscheid and Solingen." In general, the educator puts importance to emphasising that the cooperation with Bergisch schools has been going well for years. "We have already worked with most of the schools in Wuppertal and several schools in the surrounding area in recent years. These were locally based projects, but I would not separate them from this big initiative, even if they do not formally belong to it."

With digitalisation measures through the lockdown

The pandemic has stopped, delayed or even ended the work of many researchers and their projects, which are designed to take place in presence. Not so with Benölken. "In principle, the pandemic was an opportunity for us to develop all of us, and also these projects. Of course, about a year ago we were afraid that all this would suddenly no longer be possible because we visit many schools," he says. But this has dissolved into nothing. Many cooperating schools have used the material developed by the working group in the much-described homeschooling. A much broader trial level has been reached as a result, he says, and the new culture of communication with the schools has become even more intensive via the digital possibilities. "Let me give you an example. We have a cooperation school on Lake Constance, the Bodnegg education centre. Of course, it is difficult for us to travel there every week from Wuppertal. We try to have a continuous exchange, but this example shows quite well that these new virtual possibilities open up completely different paths for us to exchange ideas. The long journey back and forth suddenly no longer plays a role, even if the personal encounter naturally remains the most valuable."

Teaching-learning labs as a preliminary stage to the teacher training

Teaching-learning labs are meeting places where pupils, students and academics meet at eye level and learn from each other. Pupils are encouraged to learn independently and students, in their function as future teachers, can combine theory with practical experience even before their traineeship. In addition to the aforementioned 'Think' project, Benölken's team also offers the teaching-learning laboratory project MaThletics (Moving Learning in Primary School Mathematics) and is preparing a third offer, which will complement other already existing offers throughout the university. "We are in the process of making these teaching-learning labs a site-defining feature for subject didactics and teacher training in Wuppertal," because teacher training is still very theory-heavy. The intention is by no means to anticipate teacher training, but it is a matter of giving students primary experience in advance. "The laboratories fulfil a very important function in teacher training programmes. Competences in diagnosing and supporting, be it intellectual giftedness or other contexts, can be developed in a much more sustainable way in students. And it also creates bonds between the children and the students." The fact that many student teachers take several teaching-learning labs at once is evidence of enormous commitment and confirms Benölken in the expansion of this format. "I can prove that students receive it as very profitable to participate in the labs. Mostly in such a way that they say, 'Here, I have learned something about diagnosing and promoting intellectual giftedness, and that helps me a lot for my future career. I have developed a kind of diagnostic glasses that do not only refer to intellectual giftedness. I can now see more of what is important in children with learning difficulties and can analyse thought processes better." And this closes the circle again, because the teaching-learning labs promote one thing above all: understanding. And that is the prerequisite for good teaching.

Uwe Blass (Interview on March 3, 2021)

Ralf Benölken is Professor of Mathematics Didactics with a focus on issues relevant to special needs education at the University of Wuppertal.