The purpose of feedback is not grading, but supporting development. Technology cannot replace the role of the teacher

Participants of the FAME2 Conference exchanged experiences on renewing mathematics education in one of the buildings of the Hungarian Academy of Sciences. Chair of the local committee was Rényi's dr. Csaba Csapodi. 

Mathematical literacy is an individual capacity to reason mathematically and to formulate, employ, and interpret mathematics to solve problems in a variety of real-world contexts. It includes concepts, procedures, facts and tools to describe, explain and predict phenomena. It assists individuals to know the role that mathematics plays in the world and to make the well-founded judgements and decisions needed by constructive, engaged and reflective 21st century citizens. In mathematics, students learn that by using logical reasoning and assumptions, they can arrive at conclusions they can rely on in various everyday situations. 

The definition above comes from an OECD report published in 2018, and it was no coincidence that it was projected at the very beginning of the conference, immediately after the official opening. It perfectly illustrates the mission of the FAME2 Conference with regard to the renewal of mathematics education.

The professional exchange, organized by the Alfréd Rényi Institute of Mathematics and the MTA–Rényi–ELTE Research Group on Mathematics Education, brought together approx. 80 researchers from across Europe in Budapest. Participants contributed 40 papers and 8 posters to the conference program. 

“We have put Budapest on the map in the field of mathematics education methodology as well,” says dr. Csaba Csapodi, an economist, mathematics teacher, university lecturer, and researcher at the Alfréd Rényi Institute of Mathematics who led the Hungarian organizing team, in response to a question from renyi.hu. Dr. Csapodi completed his PhD research on the mathematics component of Hungary's high school graduation examination. He highlights the pivotal role of prof. László Lovász, former president of the Hungarian Academy of Sciences  who launched a funding program in 2016 to support academic research in subject-specific teaching methodologies across various disciplines. “One of the challenges of subject-specific pedagogy is that it belongs neither entirely to educational science nor fully to the discipline itself – in our case, mathematics. As a result, it can easily fall between the cracks. This is by no means a uniquely Hungarian phenomenon; it can be seen, for example, in the way research funding calls are often structured. The Hungarian Academy of Sciences’ program in subject-specific pedagogy fills this gap. The initiative is currently in its third funding cycle, and it extends far beyond mathematics education alone,” adds dr. Csapodi, who has been involved in the mathematics strand of the program from the very beginning, gaining first-hand insight into both its strengths and its potential challenges. Since the third funding cycle, he has also served as the leader of the mathematics projects; the first two cycles were coordinated by Ödön Vancsó, a member of the MTA–Rényi–ELTE Research Group on Mathematics Education. “Our goal is to support decision-makers with evidence-based scientific results,” explained prof. Lovász when introducing the Academy’s research program. Through this initiative, funded researchers provide research-based answers to key methodological questions in education.

“Contrary to popular belief, assessment in education is only partly about assigning grades,” emphasizes Csaba Csapodi. “Feedback plays a far more important role in teaching than grades themselves. What truly matters is how feedback and assessment help us achieve our educational goals. This involves both psychological and pedagogical dimensions, as reflected in the work of the speakers at FAME2.” According to dr. Csapodi, even the way we approach assessment deserves reconsideration.

“One of the most important prerequisites for learning is that teachers understand how their students think. Formative assessment supports this process: it is not merely a technique, but a pedagogical approach that places learning and development at its centre. Within this framework, mistakes are not failures but valuable sources of information. They reveal where students are in their learning journey, what misconceptions they may have, and what support they still need. For this reason, good questions are often more important than quick answers, because they encourage students to think. Mathematical discussion, i.e. the shared process of reasoning, explaining ideas is a particularly powerful learning tool. Through such interactions, students can become active participants in their own assessment process. Productive struggle, experimentation, and learning from mistakes lead to deeper understanding. The purpose of feedback is not to judge students, but to support their development. Technology can be a valuable aid in this process, but it cannot replace the role of the teacher. Ultimately, the goal of formative assessment is to help learners become more independent, conscious, and reflective.”

The agenda of the Budapest FAME2 Conference also included discussions on large-scale international assessments, including the Programme for International Student Assessment (PISA), as these have a significant impact on educational systems. Some countries, including Germany and Poland, have introduced substantial reforms in response to their PISA results. According to dr. Csapodi, it is important to follow the research conducted by experts in these countries and, where appropriate, incorporate their experiences into educational policymaking. “I find myself in an interesting position, because I now have to look at these issues from a policy perspective as well. As a result, I am paying even closer attention than before,”he says, referring to his recently assumed role as a Ministerial Commissioner.

“Many people, including education professionals, still do not fully recognize the profound impact the quality of feedback has on students, particularly in shaping their relationship with a subject. In mathematics, that influence can last a lifetime,” emphasized Paola Iannone, Professor of Mathematics Education at the Institute of Mathematics of the University of Edinburgh and Chair of the FAME2 Conference. “Conferences like this make a significant contribution to the sharing of experiences related to different educational approaches. Without such opportunities, everyone would be working, researching, and experimenting within their own bubbles. We hear about new ideas, and then participants return home and apply them in their own contexts as evidence-based educational practices. A substantial body of research has been devoted to the effective use of feedback in teaching. In mathematics, feedback is not about telling teachers to go back to their classrooms and teach calculus in one particular way that will magically make students happy. There are no universal solutions of that kind. Every approach must be adapted to its specific context. What can be said with confidence is that assessment and feedback are becoming increasingly important both in research and in educational practice. International exchanges of experience are essential, and it is equally important that the practical findings of our research reach classroom teachers. One way of achieving this is by working closely with those involved in teacher education, and we are fortunate to have such participants at this conference. Although the content of teacher education programmes is defined by government policies, we continuously strive to ensure that research findings in mathematics education reach decision-makers. I should add that higher education itself has undergone fundamental changes. There is now a much stronger demand for interactivity and practical relevance than there was in the past, particularly among younger academics. The scope for change may be limited, but opportunities certainly exist. At the University of Edinburgh, for example, we are currently modernising the curriculum for our upper-level mathematics students.We need to work actively to improve conditions for both teachers and students, and to make the transfer of knowledge in schools more effective.”

Education is like a vast vessel: it cannot be steered with sudden movements. At the same time, allowing it simply to drift can be equally disastrous,” reflects dr. Csaba Csapodi. “That is why it is such a great responsibility to identify the direction in which this vessel should gradually be turned. I know and completely understand that there is considerable impatience as well as high expectations in our society. For this reason, we are approaching change from two directions. On the one hand, there will be short-term measures designed to provide immediate relief and support. On the other hand, we must begin thinking in the long term, and eventually align everything else with that vision.” According to dr. Csapodi, primary beneficiaries of this long-term effort may be children who will only begin school several years from now. By the time they enter the classroom, they could encounter a school system shaped by a different philosophy and way of operating. He is convinced, however, that achieving such transformation requires engaging society as a whole, especially parents, while also strengthening and shaping the professional community of teachers. At the same time, it is necessary to rethink the very nature of schooling and consider what it should become in the future.

“It is not enough to simply say that certain topics should be taught in a certain way in mathematics. That alone will not lead to meaningful improvement. What is needed is a far more comprehensive approach. Of course, some quick steps can be taken. For example, minor revisions can be made to the current National Core Curriculum to correct its most obvious shortcomings. However, developing a new National Core Curriculum is a process that takes approximately three to four years. We are working for the future while the world is changing at an extraordinary pace.Therefore, it is virtually impossible to predict what knowledge and skills will be needed years or even decades from now.”

He notes that mathematics is in a more fortunate position than many other school subjects, as it possesses enduring qualities that develop reasoning skills and shape the way people think. The Pythagorean Theorem, for example, will remain just as valid thirty years from now as it is today. “What is far less obvious, however, is what exactly we should teach in areas such as statistics, especially when we can clearly see that data has become the new gold and that data literacy is now an indispensable skill,” he explains, illustrating the complexity of the challenge.
 

“My most important goal is to develop a long-term strategy for public education in Hungary, one that places children and teachers at its centre.” This was the first statement by Csaba Csapodi following his appointment, cited on social media. Expanding on this idea, dr. Csapodi explains that he sees his role as a Ministerial Commissioner primarily as one of coordination and consensus-building. “I am responsible not only for mathematics but for all school subjects. However, I do not intend to build this work around my own personal vision. Instead, I want it to be based on collaboration. I listen to different professional perspectives and seek to integrate them into a common direction that will, hopefully, serve the interests of the entire country. At present, we do not have a clearly articulated vision or educational strategy that defines what we want to achieve and where we want to go. I would like to begin by establishing that foundation. It does not need to be long or complicated. Once the goals are clear, we can identify the appropriate tools to achieve them, whether those tools are entirely new and unconventional, or existing approaches that can be modernized and adapted to contemporary needs.”

What might be considered modern and forward-looking today in mathematics education,and in education more broadly? One example, according to dr. Csapodi, is creating stronger connections between mathematics and other school subjects. He also believes there are sound professional reasons for distinguishing between the mathematics knowledge that all students should acquire and the more advanced material required for university admission. “We received a great deal of criticism,” he recalls, “particularly from mathematics teachers, when, during the previous round of the National Core Curriculum development (led by the above mentioned prof. Valéria Csépe, ed.), we reduced the amount of mathematics content that every student was expected to learn. Mathematics is a particularly striking example of a subject in which we are still teaching much of the same content that was taught a hundred years ago. A century ago, howecer, only 4–5 percent of the population completed the graduation examination. Today, that figure is around 60 percent, yet the curriculum has not adapted sufficiently to this change. The separation between standard-level and advanced-level mathematics examinations was already an important first step. In 2020, we and our fellow experts felt that the curriculum should retain those topics whose level of difficulty and abstraction we genuinely believe are useful for everyone. At the same time, mathematics lessons should help students develop ways of thinking, such as logical reasoning, that will remain valuable throughout their adult lives. This is, however, an extremely difficult issue, because it is impossible to develop competencies without content. The real question is: how much content is enough, without becoming too much? In mathematics, this challenge is particularly acute because students’ mathematical abilities vary enormously. Some students can glance at a problem and solve it immediately, while others may struggle with the same task for a long time, simply because they possess different skills, talents, and strengths. Bridging this gap is a major challenge. All in all, I have taken responsibility for developing a comprehensive curriculum that applies to all students,” he concludes, adding:

“What I learned during the development of the previous National Core Curriculum was that what we teach is, in many ways, secondary. Much more important is how we teach and what tools we use in the process. Developing students’ thinking skills is far more important than requiring them to master a body of factual knowledge. At the same time, the two cannot be completely separated from one another.”

A modern national curriculum makes it possible to tailor learning to individual students, their abilities, needs, and capacity to absorb knowledge, while still defining a common minimum standard for everyone. In principle, the tools of artificial intelligence may help make this level of personalization achievable. According to dr. Csaba Csapodi, the future of education, including mathematics education, is inseparable from the use of AI. “We can already see that artificial intelligence is transforming our lives, the world of schools, and the way we teach. It may become a powerful tool for enabling us to practice truly personalized learning. At the same time, there is a serious concern that using AI tools does not strengthen thinking, but they weaken it. In this respect, the situation resembles what happened when calculators first entered the classroom. As mathematics teachers, we welcomed calculators because they accelerated calculation. Students could solve ten times as many problems in the same amount of time. Yet, in the process, we lost something important: thinking associated with mental and written calculation. Many students can no longer perform written multiplication or division. That is not necessarily a problem in itself, but it means they lose contact with the structure of our numeral system. They no longer think naturally in terms of place value because they do not carry out written calculations as the machine simply provides them with the answer. Artificial intelligence poses a similar risk. Instead of thinking, they ask a question, receive an answer, and move on. It creates the illusion that the goal is simply to obtain the solution. In reality, the goal is to encourage students to think. In the long run, personalization is the objective, and artificial intelligence will be an indispensable tool for achieving it. However, we still need to determine how to use it effectively, so that while benefiting from its capabilities, children also develop the ability to think for themselves – a skill that remains absolutely essential.”