NICHOLAS PEATFIELD, SCHOOL OF EDUCATION, BATH SPA UNIVERSITY, UK
For students to learn mathematics in a way that makes it useful to them in their lives beyond the classroom, they need to go beyond learning the algorithms necessary to answer standard GCSE questions. It is clear that they must at least learn in a way that avoids instilling widespread anxiety around mathematics, as current models tend to (Ashcraft, 2002; Boaler, 2015; Lee C et al., 2018), and also lets them construct some meaning around their mathematics.
The late work of Vygotsky on the lived experience of learners, via his concept of perezhivanie, stemmed from his knowledge of the ‘system’ of acting developed by his contemporary Stanislavski (Veresov, 2016). The main idea behind this ‘system’ – a pre-cursor to method acting – is that actors must attempt to put themselves in the position of the roles that they are playing to really feel the emotions that those roles require. This idea, of the necessity of understanding the lived experience (or perezhivanie) of our pupils, allows us to highlight the importance of teachers understanding the widespread anxiety produced by current models of mathematics education so that they can analyse their own inability to reduce it. Ideas from enactivism (a theoretical framework that views learning as potential change in future behaviour – see, for example, Maturana and Varela, 1987) help to explain how mathematics anxiety is reproduced by schools operating in most current education systems, with the perezhivanie of teachers of mathematics playing a significant role.
In this perspective piece, we explore the idea of perezhivanie from a viewpoint based on social constructivism and enactivism, and consider the teacher actions necessary to take both their learners and their own perezhivanie into account in their practice. This process aims to enable creative meaning-making, with a particular focus on the mathematics classroom.Â
The concept of perezhivanie, rooted in Vygotsky’s social constructivist theory, offers a compelling framework for combining our understanding of the emotional and cognitive dimensions of learning. Vygotsky described perezhivanie as the unity of personal experience and environmental influence – a prism through which the social situation of development is refracted (Veresov, 2016). This idea has roots in the work of Stanislavski (see, for example, Pelfrey et al., 2024), whose psycho-physiological approach to acting emphasised the transformative power of emotional truth and lived experience. It is interesting that the link between mind and body (the ‘psycho-physiological’) made by Stanislavski closely mirrors ideas from the enactivist framework, which is again closely linked with ideas around embodied cognition. In any case, students of drama are likely to recognise Stanislavski’s work. Vygotsky’s engagement with Stanislavski’s methods informed his understanding of how emotion mediates development and learning.
The definition of perezhivanie is debated, with some feeling that it should just be replaced by the word ‘experience’. For Vygotsky, however, it had a deeper meaning. For example, if two friends from the same school go to see the same movie, one might say that they both have the same experience. It is precisely the ideas summed up in the word perezhivanie that tell us that it is impossible that they experience the same things while watching the movie, as each will have brought different experiences with them, which will shape how they experience what they see, including noticing different details or interpreting facial expressions differently. Therefore, we would say that the two friends’ different perezhivanie changes their new experience.
A good example of where the concept of perezhivanie can be useful is in the proper interpretation of the famous ‘marshmallow’ experiments, conducted by Mischel et al. (1972). In these experiments children were offered a marshmallow to eat immediately, but told that they could wait, with the single marshmallow in front of them, and if they did not eat it, they would get two marshmallows later. The standard way in which the results of these experiments are interpreted is to ‘prove’ that developing willpower is good. But this is essentially a misinterpretation (Kohn, 2014) and an example of the ‘fundamental attribution error’ of the ‘intuitive psychologists’ (Ross, 1977). This error is that, generally, we are likely to attribute human behaviours to individuals’ personalities, when in fact behaviour is far more influenced simply by the situation in which an individual finds themselves, with similar situations resulting in similar behaviours, regardless of personality. What Mischel et al. (1972) actually demonstrated was that children who had previously been let down by adults were far more likely to take the first marshmallow, following the logical idea that ‘a bird in the hand is better than two in the bush’, based on their prior experience. In other words, their perezhivanie led them to the logical conclusion that eating the initial marshmallow was a good idea.
In mathematics education, Lee et al. (2018) have extended Vygotskian principles by foregrounding the role of emotion in mathematical learning. Their work on mathematical resilience integrates perezhivanie to explain how learners’ emotional responses to mathematical challenges shape their engagement and identity. Lee et al. (2018) argue that recognising and supporting learners’ emotional experiences is essential to overcoming mathematics anxiety and fostering positive mathematical identities. This is pretty clear once we take into account the fear, shame and stress that many learners experience from just entering a mathematics classroom. By acknowledging the interplay of affect and cognition – in fact, the inseparability of the domains once we consider a learner’s perezhivanie – their framework offers a pragmatic structure for educators to cultivate safe learning environments and empower students to persevere through difficulty. In doing so, Lee et al. continue the legacy of Vygotsky and Stanislavski, demonstrating how emotional experience is not peripheral but is central to meaningful learning – even in mathematics.
There is, in fact, a strong argument, which I outline below, to suggest that many national education systems’ reliance on high-stakes testing emerges as a critical mechanism for reproducing mathematical anxiety. This process can be understood through the two sub-processes of emotional amplification and recursive anxiety generation. Emotional amplification operates when tests transform mathematical performance into high-pressure evaluative events. Recursive anxiety generation describes the process whereby performance anxiety leads to reduced performance, thus leading to further anxiety, and reinforcing systemic narratives of mathematical difficulty. Therefore, we can view mathematics anxiety not merely as an individual psychological state but as a systemic phenomenon, where high-stakes testing serves as a key reproductive mechanism for anxiety within educational systems. The negative feedback loop that this situation sets up results in many learners feeling that they ‘do not have a maths brain’ (a falsehood exposed by Boaler, 2015) and avoiding mathematics as much as they possibly can.
In any case, what we measure in mathematics examinations is only a proxy for measuring real mathematical expertise and skill. Using mathematics in real life, or indeed engaging in any mathematical problem-solving, is clearly only possible if one does not have an extreme adverse emotional reaction to the idea, and if one has developed certain heuristic mathematical behaviours that kick in at the appropriate time. These include defining the problem clearly, collecting data methodically, looking for patterns and making conjectures and testing them. See Mason et al. (1982) for more on mathematical thinking and some of the emotional states that even experienced mathematicians have to deal with in order to be successful.
These ideas are of upmost importance for mathematics teaching and teacher education, where most potential secondary mathematics teachers differ from the majority of the population, in that their perezhivanie around mathematics does not involve the levels of anxiety that the majority face. This means that mathematics teachers too fall prey to the fundamental attribution error, often labelling learners as ‘weak’ when they do not perform well and missing the point that these learners most likely carry a different (and overwhelmingly negative) perezhivanie around mathematics (based on their experience with high-stakes examinations), and it is this, rather than the learners’ individual ‘strength’, that prevents them from performing.
Ideas on how to build intrinsic motivation include ensuring that the learners experience some success at first, after often having experienced repeated failure, and shame as a result. Teachers can also motivate pupils by ensuring that the mathematics that their learners need has some meaning to them, even if this is in an abstract ‘game-like’ context. Allowing learners time to ‘play’ in mathematical situations is also important in this respect, although learners who are very used to being ‘told how to think’ (or just told exactly what to do at all times) may find this challenging at first – thus the importance of developing an ethos where mistakes are valued. Many of these concrete ideas for teaching mathematics to avoid anxiety are echoed – although reached from a very different starting point – by Beilock and Willingham (2014). If teachers can be given the time and space in which to do this, learners will perform more successfully in high-stakes examinations, as well as developing into confident users of mathematical reasoning.
Therefore, mathematics teachers must constantly strive to put themselves in the position – to imagine the perezhivanie – of learners who have experienced repeated failure in the mathematics classroom, and who carry shame and experience fear and anxiety on entering those classrooms. Then they can work to establish and maintain a positive ethos of true mathematical inquiry in their classrooms, where learners experience and can then start (re)building intrinsic motivation, valuing mistakes and discussion as learning opportunities, and really learning what it is to behave mathematically.
