Conference Agenda

Educational institutions sometimes emphatically declare that they are working on particular tasks with a lot of effort and energy. A closer look, however, shows sometimes that in reality the opposite happens. The presenters discuss the question of how this phenomenon can be understood.

In doing so, they refer to an example of a school that initially welcomes unaccompanied young refugees. Subsequently, however, the school does not succeed in fulfilling its educational tasks.

The discussion of a teacher’s reports lead to the assumption that the school failed in dealing with two dimensions of diversity: (a) the diversity among the pupils and the other children and (b) the diversity the school situation has been experienced within a broad spectrum between proclaimed intentions and conscious as well as unconscious anxieties. This assumption is developed with reference to psychoanalytic theories, especially with reference to the psychoanalytic theory of human relations and theories about the unconcious dynamics in organisations. Subsequently, the assumption is presented that - and in which way - institutionalised defence dynamics are significantly involved in the emergence of such processes. Finally implications for education and training as well as for the administration (leadership) of educational institutions are outlined.

The long paper focuses on diversity issues encountered in the context of research in education made during the 3rd lockdown – April 3 to May 19, 2021–, when COVID-19 infection was increasing.

The pandemic crisis led many researchers used to conduct clinical interviews for purpose of research in a face-to-face situation to continue their research in a new way by using online interviews through communications platforms. That unusual situation brought some interrogations on the methodical level as well as it sometimes brought uncertainty or anxiety about the process of the clinical interviews and the effects that an experience never made before could have on the research results, on the analysis produced.

First, we will define what a clinical interview is in our research, how we usually organise the ‘apparatus’ of our interviews and what is our positioning as researcher.

In a second time, we will come back to an experience of online clinical interviews with music teachers and, more specifically, the experience made with one of them. From this, we will evoke some new questions emerging in that unusual context.

The research concerned by this presentation has been built on clinical interviews made with music teachers in training in a higher education institution in the field of artistic practices in the performing arts.

At the request of the director of the institution, who wish to enrich the courses delivered with contributions of research in Education Sciences, a team of five researchers has been organised, each of the researcher having to conduct some clinical interviews with the music teachers in training. Trying ‘to do the best of a bad job’ (Bion, 1979), the first movement of the researchers has been to try to stay as close as possible from a so-called classic situation by making the choice of analysing only the audio recordings without taking into account what had been seen on the screen during the interviews.

Therefore, the working document on which the analysis was supposed to be produced was the transcription of what the interviewee had said during the clinical interview. That point in itself questions the positioning of the researchers more than the nature of the collected data. In the aftermath of the research, it has conducted researchers to realise there was a necessity to think more carefully about what they tried to keep from their previous experiences of clinical interviews or what kind of mechanism of defence could have been at stake with such a choice.

In the paper we come back more specifically to one of the interviews, made with a music teacher in training called here Myriam who surprised the interviewer by the way she introduced her very young baby in the situation of the interview. The interview framework allowed her to do so since nothing had been said before about the possibility or not to continue the interview while breastfeeding a child… The baby’s presence was then perceived through non-verbal elements.

While in a more usual context, researcher and interviewee are living in what J. Puget called ‘fragments of the world’ (Puget and Wender, 2021), quite isolated from each other. It seems that during this pandemic, the irruption of ‘data and problems that belonged to the external reality of the moment’ brought the two in presence closer from each other in ‘overlapping worlds’ (Ibid.). In this paper, we’ll examine the parts of fantasies possibly at stake around the question of ‘feeding’ for someone who is both a mother and a successful music teacher in training.

Today, psychoanalysis looks back on a long-lasting tradition of impacting educational theory and practice. In fact, from its very inception psychoanalytic thinking has been applied to educational settings (e.g., Freud, 1914; Freud, 1960). However, despite a long and very rich tradition, psychoanalysis in education remains a niche area in educational research and practice in Europe (Taubman, 2011). In academia, it has been almost entirely pushed out of the mainstream of educational research, with the exception of special needs education.

In this presentation, we argue that today there is an opportunity opening up for psychoanalytic thinking to (re-)emerge from the margins of educational research and practice. In the course of the past two decades, there has been a growing acknowledgment that social-emotional learning and development is a crucial part of a modern educational experience (CASEL, 2023), and an essential precondition for more effective academic/cognitive learning, and the advancement of meta-cognitive skills (Pianta, 2012). At the same time, meta-analyses of social-emotional learning/development program evaluations, based on theories and methods of the educational sciences’ mainstream, show only small effects (Corcoran et al., 2018). From a psychoanalytic perspective this is hardly surprising, because most of these programs resort to behavioral condition strategies that ignore latent/unconscious factors impacting human development. Hence, an opportunity is opening up for psychoanalysis in education to show that it can deliver better results.

However, in order to be successful, psychoanalysis in education needs to accept the methods and quality standards, which currently dominate the mainstream of educational sciences, despite their obvious limitations. Specifically, psychoanalysis in education needs to work with and show appreciation for the methods and contributions of quantitative empiricism with its focus on social ecological factors impacting development, and integrate them – which is not the same as giving up its traditional focus on qualitative and in-depth analyses of the unconscious. Initial successful and encouraging steps in this direction have been made in clinical psychoanalysis (Fonagy & Bateman, 2013).

This presentation focuses on our first attempts to bridge the gap between psychoanalysis in education and quantitative empiricism in educational research and practice. From our point of view, group analysis (Foulkes, 1983; Bion, 1991), which combines psychoanalytic and social-ecological/sociological theory and thinking, is the best-suited practice and methods framework for this endeavor. In early 2022, we began working as group analytic coaches in schools. Specifically, we have provided group analytic supervision sessions in two schools in the greater Berlin metropolitan area. In the course of this work, we have also developed a new student survey instrument, which has been theoretically derived from psychoanalytic and group analytic theory (e.g., Hirblinger, 2017; Naumann, 2014). The purpose of this instrument is to support teachers' self-reflective practices in the context of group analytic school coaching and professional development training.

This paper deals with the problem of the so-called "school phobia" and school failure. Based on my research so far, I have been able to show that the desire for knowledge of school dropouts is often blocked by psychological challenges, existential questions and anxiety. In this paper I would like to illustrate this with a clinical case of phobia.

It is about a young university student from France who decided to work through his suffering. I have been accompanying him for about two years at the rate of one session per week.

The student complains of numerous situations of social phobia, bullying, exam anxiety, fears during train or car rides, or fear of speaking in front of others in class.

His school phobia begins in kindergarten. The separation from his mother is very difficult. Especially since the teacher grumbles a lot with him, he is afraid of being penetrated by the teacher's gaze and words.

In the first school year he playfully enjoys doing the math work in advance. The teacher, however, insinuates that he has copied from his schoolmate and calls him a "freeloader". The student reacts to this misunderstanding and disregard with "laziness, doing nothing"at school : "je m'en fou". He adheres less and less to limits and rules. He is diagnosed as hyperactive and is prescribed Ritalin. In some subjects, however, he shows his excellent knowledge. Several teachers predict that he will get nowhere.

He is teased, tracked down in his hiding places, chased around the schoolyard and is even seriously injured once. He does not succeed in his school career the way he wants; whether it is through poor grades in math or obscure institutional rules.

Nevertheless, he retains the desire to learn what he likes. In some subjects, he aims for perfection. Despite completing an apprenticeship, he is unable to find a job, probably because of his shyness. After a two-year absence, he returns to school and manages to get a certificate for university entrance.

I will show how the analytical process has worked so far. Working through signifiers, situations of fear and dreams, the occupation of " finding a secured place for himself" shows up. His phobic phantasm is characterized by mistrust. Because of the "gaze" and the course introduction of some professors he is "already sure" that he will not pass the exam. Here it becomes apparent that the imaginary has the upper hand and is not sufficiently dialectized with the real.

Similar to "little Hans", the student is concerned with a "more" of enjoyment. (Freud, 1909) However, when the analysand encounters someone who seems too intrusive, panic attacks occur. They are not an expression of castration anxiety ( Lacan 1994), but precisely of the lack of separation by a third party and thus of the fragile symbolic network. When the mediation of the symbolic law of impossibility works, a transformation from enjoyment to desire occurs and the protagonist can better manage the panic moments.

Meanwhile, the analysand can develop strategies to prepare for exams in a more organized way and be less driven by anxiety. He can set limits to his rampant drive for knowledge. Education occurs through a loss of enjoyment, writes Lacan (2001, 364). In parallel, the analysand presents numerous dreams, thanks to which he cautiously - without losing too much control - approaches the truth of his own desire. In this way, he makes contact with his own strangeness, the real and thus also with his split as a subject. Only the future will show whether he can also drop his gaze as an object (little) a.

This paper is based on a research conducted in France in isolated rural elementary school in the Ardèche department where a co-teaching arrangement has been set up. In these one-classroom schools, two teachers are thus brought to teach in the same class during a school year. Co-teaching is defined by Tremblay (2012) as "joint pedagogical work, in the same group and at the same time, by two or more teachers sharing educational responsibilities to achieve specific objectives. ». Situations where co-teaching occurs have been studied in other research (Tremblay and Toullec-Therry, 2020), particularly from a didactic perspective (Prevel and Buznic-Bourgeac, 2020) or in connection with inclusive education (Tremblay, 2011).

After presenting the context of the research, this paper proposes to grasp, in a psychoanalytically oriented clinical approach (Blanchard-Laville et al., 2005), some of the psychic issues wich may be specific to co-teaching situations. In such a situation, each teacher is required to teach in the presence of another. This other is sufficiently close (he or she is also a teacher) but also sufficiently distant in terms of his or her teaching style, background and pedagogical references. In some situations, this other, constituted by the second teacher, could be the mirror of an otherness present in oneself, and a vector of the « uncanny » (Freud, 1919). Consequently, teaching "under the gaze of another" can constitute a test for the teacher that leads to certain psychological reorganizations, for example, defensiveness.

Moreover, teaching in the presence of another person is a situation that can call into question the links that the teacher forges with his or her students, but also the way in which he or she updates his or her own relationship to knowledge during the teaching sequence. These two dimensions of the link to the pupil and the link to the knowledge taught shape the psychic space of the classroom and constitute what Claudine Blanchard-Laville calls the teacher's didactic transfer (Blanchard-Laville, 1997). Thus, is it possible to extend the notion of didactic transfer, initially thought by its author in "classic" teaching situations, to situations where two teachers teach together? What modalities of didactic transfer of each teacher find expression within the class which constitutes a single psychic space?

Furthermore, I have proposed the notion of internal psychic parenthood (Guignard, 2017) to try to capture a modality of how didactic transfer unfolds in the classroom. In a co-teaching situation, in the ordeal that teaching with another can constitute, how is this internal psychic parentality reorganized? being two teachers could thus strongly refer each of them to psychic arrangements specific to the couple and to parenthood. In such a situation, wouldn't the paternal and maternal functions that are articulated during a lesson tend to be split up and taken in charge separately by each of the two teachers?

An essential form for understanding world-building through teaching is the figure of thought of the so-called "didactic triangle" (the learning triangle) by Heimann (1947), which is based on Herbart's "educational theory" ("Erziehungslehre"; 1814). According to Heimann (1947), the didactic triangle creates the pedagogical situation, which is shaped in particular by the "interpersonal encounter". This phenomenon can be described as a "primal phenomenon" as well as a phenomenon of interaction and communication and whereby learning is fundamentally based on the "interpersonal relationship". Herbart's (1814) approach, however, is theoretically more profound and also highly relevant to practice: "I require of the educator above all that he orients himself most carefully in this distinction, and practise relating all teaching and learning to it. Whoever does not do this may be an excellent empiricist, but in my eyes he is not a theoretician".

The objective of this presentation is therefore to theoretically ground the didactic triangle through different theories of sign theory in order to be able to point out new insights that result from the triadic structure. This presentation therefore attempts to open up broad range of theoretical perspectives, hence the paper combines the didactic triangle in particular with the sign theory of Bühler (1918, 1926, 1934), Cassirer (1923, 1925, 1929) and Peirce (1873, 1903, 1988) in order to open up new, different insights into pedagogy, and in particular to look at the relevance of relationship and attachment (Bowlby, 1969, 1973, 1980).

Different emphases and colourings of learning and being-in-relationship can thus be shown, enabling a broad spectrum and diversity of practices. The didactic triangle experiences a new depth of diversity through the phenomenological foundation. This variety of possibilities of learning can be connected with theories and models of communication and interaction (Wiesner, 2023b), with attachment theory (Gebauer & Wiesner, 2022; Wiesner & Gebauer, 2022, 2023) also with traditional learning theories, based on different forms of sign theory.

The research questions are based on what the didactic triangle provides and brings to pedagogy, but also how this triadic structure changes by incorporating new, different foundations and how the pedagogical relevance can thus be increased and deepened. At the same time, many connections with psychoanalytic, integrative and psychodynamic pedagogy and psychotherapy can be shown (Wiesner, 2023a). This also creates links to the concepts of being a guiding role model, being a directive role model or being an ideal role model (Bittner, 1964).

The theoretical framework thus draws on the theoretical differentiation of the didactic triangle by Herbart (1814), Heimann (1947), Gruschka (2002), Zierer (2022) and substantiates the triadic structures structurally-phenomenologically through various sign-theoretical foundations by Bühler, Cassirer and Peirce. The Vienna School of Gestalt Perception by Bühler (1912, 1926, 1934), Brunswik (1929, 1934, 1947) and Popper (1928) is also an important source for making the results and findings clearly visible in the sense of Arnheim's visual thinking (1969).

In institutional contexts, the emphasis on diversity is increasingly seen as a way of encompassing issues of gender and sexuality, and of encouraging politics of visibility and representation that celebrate the multiplicity of identities, and the joy of both embodying them and living with them (Ahmed, 2012). This tendency, if it produces preventive effects on LGBTQI-phobic violence and is part of a certain interpretation of "pride", is sometimes denounced by the workers concerned, as well as by activists, as an imperative, an order that would demand a pantomime of happiness and gratitude (ibid.) : "oh, what a joy to be seen and included !", is what people involved are sometimes supposed to express.
However, this sense of diversity also questions the effects it can have on those who are supposed to embody this diversity, and loudly claim it, especially by being "out" (Sedgwick, 1990) in sometimes reactionary or hostile institutions. What about those who are asked to hold a standard of being the safe-diversity-poster person, of being reassuring, or even, similar to certain pupils and patients (Bourlez, 2018; Horvitz, 2011). The question then arises of the tension between this sense of diversity, and the possible encounter that can occur between teachers and students, or therapists and queer patients, believing they recognize each other, or expected to. What room then is left for alterity, and what temporing to the framework might the shift from complicity to connivance imply?

The diversity of theoretical references is constitutive of the field of education and training sciences. In this discipline, a sociological conception of education has long prevailed, targeting an individual who is conscious and determined by his habitus, by dispositions characteristic of his social and cultural origin. Inequalities from birth are said to be reproduced by educational institutions, in particular by the school. Didactics, for its part, has developed a fairly abstract vision of the learner as an epistemic subject, centred on his cognitive functioning. It was not until relatively recently that the subject was granted agentivity, a capacity to act, to be a social actor from a very young age. Or to see him attributed, under the influence of psychology, emotions, self-esteem, even an affective life.
When we mobilise psychoanalysis as a central reference, combined with a clinical approach that weaves together subjectivity and the social-historical moment, we distance ourselves from these dominant conceptions. The encounter between psychoanalysis and education is indeed a troublemaker, especially when thought of in its time. Our approach aims to account for the encounter between adult and child, between professional and learner, and the influence of the peer group, in a configuration that is always singular; it aims to account for subjectivity, for the experience of the Subject. In the same movement of knowledge, it is a question of taking into account the involvement, the counter-transference of a researcher subject in his research object. Several authors have already developed this point and, among the most recent, let us quote a contribution by Claudine Blanchard-Laville (2019) to which we fully subscribe.
For all that, psychoanalysis in the field of education and training does not constitute a homogeneous reading, a new theoretical ecumenism, proceeding in a cumulative way or by compilation. It should be even less a doxa. The interpretations of contemporary educational phenomena are diverse, multiple, as is the understanding of what would be the cause or origin of them. A single example from our work is the question of the 'crisis of education', perceived as the failure of educational institutions (Lebrun), blamed on a 'crisis of authority' equivalent for some Lacanians to a foreclosure of the 'Name-of-the-Father' (Melman, Winter, etc.). The idea of decline is flourishing, referring to an idealised past and to well-identified educational and parental functions in a patriarchal system. However, there is every reason to believe, with Arendt, but also with a transgenerational and not exclusively Oedipal psychoanalytical reading, that education is in crisis as a transmission and link between generations, between old and newcomers (Gavarini, 2023). These interpretations and readings bear witness to the diversity of positions and currents of thought, of the ruptures, which have marked the history of the encounter between psychoanalysis and education, and between psychoanalysis and society. It is hardly possible today to speak of the place of psychoanalysis and erase the rough edges of this diversity. We have inherited a turbulent history and our intellectual work consists in bearing witness to it, just as the psychic work of the cure bears witness to the conflicts and misunderstandings to which we have been exposed or of which we have been the subjects.
This observation of a great diversity of psychoanalytical readings leads us to understand how we ourselves use psychoanalysis: what uses, what precautions, what ethics? These questions also lead us to reflect on the conditions necessary to think / theorise from the singularity of situations apprehended by the clinic.

If one takes a look at the german discourse on professionalization in teaching, it is noticeable that the concepts of reflection and reflexivity are gaining more and more importance (Kratz 2022, Dlugosch & Kratz 2022). This is especially true for its biography-oriented strand, which is currently experiencing an enormous upswing.
Teachers as "reflective practitioners" (Hauser, Wyss 2021), have become an inseparable part of professionalization discourses related to teaching (Dlugosch Kratz 2022). Similar ideas also emerge in anglophone discourse, drawing on diverse theoretical frameworks (Brookfield, 2009). This paradigm is closely associated - largely across school systems - with the ability to adopt "professional agency" (Kuorelathi et al. 2015) and to engage in building relationships with students who are perceived as challenging (Rae et al., 2017).
Mostly detached from each other, new theoretical reflections and didactic formats appear in this discourse, which are supposed to be theoretically justified and practically produced by trainee teachers as reflective practitioners (Paseka, Schneider & Compe 2018). This again reveals considerable theoretical openness (Hascher & Hagenauer, 2016). This close succession, and with it the vagueness of its theoretical anchoring, is now itself negotiated as an unreflective tradition (Hauser, Wyss 2021: 8).
In our contribution, we align ourselves with this skeptical view and combine it with the observation that, contrary to the diversity of theoretical concepts and higher education didactic offerings, "reflective practitioners" continue to elude empirical visibility in the field (Helsper 2011, 163).
In detail, we show that the central categories of the discourse "reflection" and "reflexivity" suffer from a theoretical deficit, which is particularly noticeable due to the exclusion of psychoanalytic knowledge. In our opinion, the categories are not (yet) suitable as a "Vanishing point of teacher education" (Dlugosch, Kratz 2022). Although Datler & Wininger (2016), for example, plead for a psychoanalytically guided understanding of emotion as the core of a university education, its structural anchoring and praxeology remain unclear.
To systemize this working hypothesis, we focus on a metaphor which is used repeatedly in connection with the concepts of reflection and reflexivity in the discourse of professionalization related to teaching. In our estimation, with the aim of overcoming the lack of theory.
Here, one can read about "experimental spaces" (Völter 2018) and "fantasy spaces" (Helsper 2018, p. 73) as well as "spaces for biographical and memory work" (ibid.) in which reflection is supposed to be made possible. This metaphor of space is thereby, contrary to its metaphorical range of meaning, very concrete and curricularly conceived in the texts and fails to negotiate space as something social that itself emerges from sociality.
With references to selected psychoanalytic metaphors of space, especially those of Alfred Lorenzer (1973), Donald Winnicott (Winnicott 1965/2006) and Wilfred Bion (1992), we broaden the view and offer new perspectives for the discourse on professionalization in teaching. In doing so, we negotiate that spaces of reflection as social entities can emerge or be prevented in institutional and organizational contexts.
 

In the scope of this paper, the main focus is set on the question, how alterity can be considered in research, namely, regarding a primary intervention programme for socially and economically disadvantaged parents and their toddlers: a psychoanalytical parent-toddler-group (PTG), established at the Child Guidance Clinic in Vienna in January 2021. In cooperation with the working unit Psychoanalysis and Education in Vienna, the research project "The Impact of Parent-Toddler-Groups on the Development of Children in the Context of Family Relations" was initiated with the support of Inge Pretorius (London, former Anna Freud Centre). Within the framework of the research project, the questions of what specific experiences children and their parents have while attending a PTG and what changes on the part of the children, the parents, and the parent-child relationship can be identified over time within the PTG, and also in everyday family life, are in focus.

The overarching aim of the PTG, based on the concept of the "parent-toddler-groups" of the Anna Freud Centre in London, is to promote toddler development, to strengthen the attachment between parents and toddlers, to strengthen their relationship, to enhance separation and individuation, so that toddlers can gain independence (Zaphiriou Woods, 2012). In order to achieve these goals, two psychotherapists lead the therapeutical PTG in Vienna, all the while referring to psychoanalytical theories on early child development. In the context of this analytically orientated group setting, the questions arise of what distinguishes the work with and the working relationship with the parents in this alternative psychoanalytic group setting from therapeutic one-to-one-setting, how the therapists’ work with the parents is shaped, and what kind of working alliances are possible within this alternative psychoanalytically group setting. These questions are all the more significant since some parents are obliged to attend the group on condition of the Youth Welfare Office and, especially at the beginning of the group, several parents dropped out of the group.

Although a review of various psychoanalytic publications suggests that since the works of Freud (1912), Sterba (1934), Zetzel (1956), Greenson (1986) as well as Sandler, Dare and Holder (1973) the psychoanalytic concept of working alliances has been widely discussed and elaborated (not only) in psychoanalytic discourses (Horvath, Luborsky 1993), these discussions are mainly related to psychoanalytical one-to-one settings. Looking for reflections on working alliances in psychoanalytic alternative group therapy services, however, reveals hardly anything with focus on psychoanalytically oriented groups. Therapists who further developed the concept of PTG of the Anna Freud Centre refer in their articles to the (at times difficult) formation of groups, but these considerations do not represent an established research focus (Zaphiriou Woods, Pretorius 2011). Eder-Steiner and Freilinger (2016) note that more than one third of the families frequenting the Child Guidance Clinic are committed to psychotherapy by the youth welfare authorities. In this context, they refer to the question under which conditions it is possible to develop a therapeutic motivation and a stable working alliance with demotivated patients. According to Fraiberg (1980), some developmental potential and processes only occur when external support is provided to the parents. In this regard, she refers primarily to parents who are unable to recognize their children's suffering and distress and thus cannot provide sufficient developmental support for their children. But following these remarks, what kind of working alliances can be developed in psychoanalytical PTG when, in addition, some of the parents are also required to participate, which may have an impact on their level of motivation, and on experiencing doubts and uncertainties? Are early terminations of the group possibly an indication of alteration, repression, negation, splitting or disavowal (Green 1986)?

This proposal is an answer to the NW 21 Special Call. It focusses on internal diversity of future nurses. In this paper I will present a part of my PhD research results about nurses’training in France. First, I will present the specificities of this training course, compared to other national approaches of this training in Europe (United Kingdom, Germany and Italy). In this research, I propose to consider the moment of the nurses’training as a time of ‘professional adolescence’. Louis-Marie Bossard, a French reseacher, proposed to transpose the adolescent psychic processes, to the transition from the student situation to the professional situation : it is called ‘professional adolescence’ (Bossard 2000, 2001, 2004). My research is situated in the field of ‘Education and Psychoanalysis’ and more specifically in a ‘clinical approach psychoanalytically orientated in Education and training’ (Blanchard-Laville, Chaussecourte, Hatchuel & Pechberty, 2005).

In this paper I propose to question the link to children of a nursing student I have decided to call Alice. Her professional plan is to work in paediatrics departement in a hospital. I met her twice, for two clinical interviews for research at the end of her first year of training (June 2021) and at the end of her second year of training (June 2022).

During the first interview, Alice was very smiling and cheerful. However, I have been very troubled during this meeting without being able to clarify the reason for this feeling. Later, on when listening again to that interview to analyse it, I have been surprised by the dissonance between her joyful attitude and the tone of her talk. Her words were full of anxiety linked with approaching patient’s death. She contrasted geriatric care, she feels linked to death, to paediatric care. This disturbance in me came to the surface in a third phase, when I made a slip of the tongue (lapsus linguae) while presenting the analysis of this interview during a conference a few months after the interview had occurred : orally I have exchanged the word ‘geriatrics’ to ‘paediatrics’ to refer to the death of patients as Alice perceives it, while I had written the opposite in my paper. This event led me to link my own disorder to the « disturbance » described by Georges Devereux (1967) about the researcher's counter-transference as a research tool (Chaussecourte, 2017).

I wondered about the negative part carried by the affects expressed by Alice and on what was played negatively in the expression of my disorder regarding the death of the children.

In this proposal, I would like to draw on André Green’s research on ‘the work of the negative’ (Green, 2011), to analyse this situation by considering the two forms of life and death narcissism, the foundation of a form of internal alterity expressing in the negative by a mortifying desire for the children.

On another way, if we consider, as Bernard Golse does, that adolescence is a period of reactivation in the deferred action of the enigma of the secret of origins (Golse, 2014), we could link ‘the baby that the adolescent thinks he was, that he would like to have been, or that he fears to have been’ (Biot, Golse, 2017), and Alice's desire to work with children, as many other nursing students, while they begin training sometimes even before the age of eighteen. Then, during the nursing training, how are adolescence and professional adolescence knitted together ? In this internal diversity, how are formed the links between ‘the baby in the adolescent’ (Golse, 2014) and the ‘adolescent in the adult ’ (Green, 1992) ?

This paper presents the research-address of “Laboratorio di Studi Lacaniani” founded in 2012 by Prof. Mimmo Pesare at University of Salento, Dept. of Human and Social Sciences, with the aim of wide-spreading the network of researchers in both Education and Theoretical Psychoanalysis fields. Here a part of my Ph.D. research contribution is presented, that is the one that connects a Lacan-oriented Philosophy of Education – which is systematically dedicated the first part of my research – and the attention to youth subcultures as a context of expression and informal education through a case study on punk subculture in Slovenia before its independence. The “Underground” scene in Ljubljana during the '80s is the background of both the punks were born (the Socialist Republic lead by Tito), but also the Grund of Ljubljana School of Psychoanalysis research, that nowadays is well-known through Slavoj Žižek world-wide philosophical activity. “Underground” is the keyword to connect the two sides of the enquiry: on one hand, it is the psychopedagogical look on the Unconscious, with the attention to the latent structures that work in each subjectivation and self-formation (Massa 1997); on the other hand, it represents the storytelling of a fellowship, the one between the intellectuals (Ljubljana School) and youth subcultures (Slovene punks and avant-gardes), that is here presented in order to enlighten a ‘minor’ context, that enriches a “Psychopedagogical and Lacan-oriented Theory of Subjectivation”. The youth subcultures are shown as “sublime objects” of the research, that welcomes the contemporary reception of Jacques Lacan theoretical and clinical interpretation by a transdisciplinary approach.

In the general theoretical context, it is specified that Subjectivation is a lemma that comes from philosophical thought, mainly from the XIX Century and, in other respects, from that of psychoanalysis. For both (philosophy and psychoanalysis), the net of the uses and research methodologies within which the notion of subjectivation appears, it is possible to isolate a transdisciplinary red thread that characterizes its semantics. Whether it is philosophy, psychoanalysis or other fields of knowledge that have borrowed the notion from them – some sociological orientations, some anthropology, the history and hermeneutics of systems of thought – we can agree on the fact that in the social sciences it is associated with the transversal concept of the construction of one’s own subjectivity.

The unconscious, as the primary vector of subjectivation – as the bearer of this transformative and relational dimension – is then, above all, thinkable as a form of social discourse, as the singular and irreducible decode that the human being makes of the structure–cultural, linguistic, educational, anthropological–that pre-exists it, re-elaborating itself in a personal way. In these terms, shifting from the clinical language to the philosophical-educational one, the subjectivation would, therefore, represent a device that catalyzes the social discourse (the Lacanian Big Other, the Foucaldian structure) in the singular assumption of the personal and formative history of an individual.

By saying that “punk is a symptom” (Žižek 1981), the Slovene philosopher starts a new consideration of punk subcultures that are related to the critique of ideology and the “symbolic” social discourse functioning. According to its theory, Žižek warns that punk irrupts into the normal functioning of the Big Other (the Socialist discourse) by representing a removed dimension. The Ljubljana School, in fact, defended punk and avant-guards by a theoretical support on the Journal of Theoretical Psychoanalysis “Problemi”, siding against censorship and repression of youth movements, that with their “symptomatic” expression were showing that “the king was naked”. That is, exactly, the inconsistency of the Big Other in the form of a crystalized ideology.

For drawings or story-telling, Jung (1959) emphasized the importance of “over time” rather than just analyzing one or two pictures or stories during the therapeutic sessions. Allan (1988) indicated that “the time-place variables act as a sanctuary space, a time out of ordinary time, which, together with a positive therapeutic alliance, fosters psychological growth and transformation” (p.21). Thus, from a Jungian perspective, the present study explored the serial stories produced or expressed from clay creation in the process of expressive art therapy for novice school teachers in Taiwan. Data were collected using semi-structured in-depth interviews with a group of six participants who were novice school teachers and met troubled by their emotional disorders. Facing a future career, they felt a high level of anxiety and uncertainty. A Jungian approach to expressive art therapy program was made up of six sessions (2 hours per session). During the process of clay creation, each participant chose one of the four elements of the universe, earth, water, wind, and fire as the basis of active imagination to create their own stories. Then, the participants in pairs co-created new serial stories and expanded the symbols of their inner worlds. The study found that there were five aspects. First, the process of clay creation facilitated the emergence of the inner world and allowed the imagination to express itself freely through art creation without being restricted by self-criticism. Second, the visualization of three-dimensional creation helped participants to recognize the feelings and thoughts which have long been hidden and neglected, and they had further opportunity to engage in self-dialogues, their inner voices then being honored by telling their own stories. Third, Taiwanese family culture expects "making ancestors proud", which leads to participants' high anxiety about their future and self-doubts about whether they can achieve it. Fourth, Taiwanese culture places great emphasis on "filial piety", which brings about the dilemma—of whether to obey the family's expectations or to go independently toward their own goals. Fifth, the serial story co-created by the participants combine different thoughts, together they transform difficulties into opportunities, and finally overcome one’s inner contradictions, anxieties, and conflicts. The present study highlights that ”symbol formation” is the natural language of inner expression, and with the help of expressive art therapy, we can further understand symbols through “Active Imagination”.

Verbal communication is one aspect of language education in German elementary curriculums. Elementary students are supposed to learn linguistic practices that ultimately allow them to participate in all communicative areas of society. Therefore, language teaching in school builds on the communicative practices that students experience at home and outside of school (Becker-Mrotzek, 2009).

Due to ongoing migration, there is a growing language diversity among elementary school students in Germany and dealing with this is a key challenge for language teachers (McElvany et al., 2013). Teachers’ are supposed to create inclusive language-learning environments that appreciate this language diversity, are adapted to students’ individual needs and allow all students to achieve desired language learning goals. Teachers create such an inclusive environment mainly through their speech and dialogue with the students. They provide tasks and activities that allow all students to participate and offer instructional and emotional support when it seems necessary and appropriate to help students overcome certain learning barriers (Naugk et al., 2016).

During such language lessons, teachers and students frequently make verbal errors. Such errors are an important diagnostic indicator for the assessment of the students' linguistic competence and for the selection of individual language teaching strategies (Schiefele et al., 2019). According to Kleppin (1997), a linguistic error refers to a violation of formal grammatical rules, informal rules or specific social norms. The definition of an error is always very much dependent on the situation and is usually subject to the judgment of the teacher. Verbal errors also provide individual learning opportunities for the students. To help students learn from their errors, teachers’ should give students an immediate corrective feedback (Lüdtke & Stitzinger, 2017). However, corrective feedback can also expose students’ failure and impair their sense of belonging and the inclusive climate in the classroom. Therefore, the timing and wording of the corrective feedback and the corresponding interpretation of the respective student is critical for the maintenance of inclusive language learning environments.

The teacher’s corrective feedback can have an explicit and often an implicit meaning, which can trigger different emotions. From a psychoanalytical perspective (Hierdeis, 2016), the implicit or unconscious meaning of a teacher’s corrective feedback refers to unspoken expectations, wishes, desires and motivations towards the students and the lesson. At the same time, a student’s interpretation of the corrective feedback is affected by previous experiences with the teacher and relational dynamics between the student and his parents. Students also project parental desires and wishes onto the teachers and possibly respond to criticism in the same ways as they respond to deprivation of parental affection. Therefore, the unconscious meaning and meaning making of a corrective feedback is of special importance with regard to the learning outcomes of the corrective feedback and the students’ experience of the inclusive classroom community.

However, little is known about possible implicit meanings of a corrective feedback and students’ emotional responses to it. In the light of this research gap, the presented study explored the corrective feedbacks of a teacher in a diverse elementary German language classroom and the corresponding emotional student responses, with a specific focus on unconscious meanings and dynamics. The results highlight, that even minor connotations of a corrective feedback can trigger certain unconscious relational dynamics that result in very negative emotional student responses and potentially exclude minority students from the classroom community. Further implications for the implementation of corrective feedbacks and possible teacher training measures are discussed.

Teachers have to take into account the diversity of their students, and this requires recognition of the uniqueness of each individual. This reality seems to be even stronger for foreign language teachers who organise exchanges between students and offer them to open up to alterity through the teaching of the language-culture.

In a group interview with secondary school students, I was able to observe the extent to which cultural representations of the foreign other and the « linguistic imaginary » (Houdebine, 1997) are still very active for the students considering European languages. German, English and Spanish bear for them the traces of European socio-historical experiences (wars, migrations, etc.) transmitted through the generations in silences and stories and in the presence of these languages and cultural objects in their immediate environment (Pujol Berché & Díaz, 2018). Similarly, travelling from France to Spain is central to the discourse of students for whom the world of their border neighbour becomes an idealised elsewhere.

So, we can ask how foreign language teachers manage to involve students in this opening up to cultural diversity. Is it their didactic proposals based on European works or cultural events related to the language taught that make this easier ? Is it the intercultural work that takes into account the cultural diversity of their students with a migrant background that makes this possible? Or is it essentially the teacher's ability to welcome the alterity of each student that contributes to this opening?

Within the framework of a "research with" (Dubois & Kattar, 2017) inspired by the monographic writing devices proposed in Institutional Pedagogy (Vazquez & Oury, 1971), Spanish teachers were able to work on their ability to open a space between themselves and the individual students and to accept their powerlessness in the face of the radical alterity within the group entity. This position implies respect for the student's desire, which can be expressed through his or her involvement or lack of desire to learn. Also, in an ambivalent movement that oscillates between "individuation" and "indifferentiation" for the group, foreign language teachers must work to "deal with" the forces of unbinding and partially "alphabetize" the active instinct (Bion, 1962) in the groups.

In one of the texts produced in this group elaboration device, one of the teachers describes her experience of the post-lockdown back-to-school in September 2021 in a text entitled "Rentrée masquée". This title introduces us to the context of Covid-19 and its consequences on the teachers' professional practice, but at the same time it leaves us with the idea of a hidden face, a covered identity, a carnival or a masked ball... Faced with the emotions that arise in class, the teacher expresses the desire to "de-clutter" the student from what "comes from outside", which could perhaps refer to a desire to remove the transference, to smooth out the exchanges and to avoid conflict beyond the desire to free up psychic space for the group that she asserts. This could correspond to a desire to make the negative disappear, but as Eugène Enriquez writes, "the negative has two faces: that of destruction, a sign of hatred for the living form, and that of the destruction of unity-identity, a sign of love for variety" (Enriquez, 1987, p. 94). This acceptance of 'variety' would thus be based on the ability to renounce fusion, to move away from identifications and to analyse transference, in order to accept the alterity of the other at the same time as one's own subjectivity.

In this paper I will refer to my personal and academic experience of writing collaboratively with colleagues across different disciplines, countries and institutional affiliations acroos Europe and beyond. I will think-with authors located within Posthumanism (Braidotti, 2011, 2013, 2018), New Materialism (Bennet, 2010) and Post-qualitative theories and methodologies (Lather & St.Pierre, 2013) who challenge the traditional view and practice of academic discourses, particularly in relation to academic writing. I will refer to my personal experiences of writing some papers for academic publication with colleagues across different disciplines, opening therefore a space for dialogue and for new meanings to emerge at the crossroad of different fields of inquiry and of different national boundaries.

I will particularly think-with the work of Richardson and St.Pierre (2005) in their view of academic writing as a creative and disruptive practice that destabilizes traditional, fixed academic structures in favour of rizhomatic and multiple experiences where the poetic and the playful replaces the objective and the quantifiable. Through the work of Holman Jones et al.(2013), of Gale and Wyatt (2021), I will paly with the idea of a collaborative voice, where the individual position get lost in between a diffractive multiplicity of voices. Diffraction (Barad, 2007; Lambert, 2021) , a key concept within Posthuman theories and practices, is also a guiding principle in my writing and in my presentation, whereby diffraction is conceived as a concept borrowed from quantum physics where the multiplicity of voices and positions, like waves in their interaction with each other or with an obstacle, loose their individuality in their merging into one new entity. Diffraction is not just a reflection of each other into each other's voice, it is rather a juxtaposition and a merging of different perspectives. It is not 1+1=2, but rather 1 with1= multiplicity, where the thinking space becomes a relational and creative inquiry, highlighted through a sense of togetherness and of withness.

Collaborative writing will be proposed throughout this paper as an alternative, poetic and evocative (Kirkcpatrick et al, 2021) way to conceive and to practice academia differently (Bozalek, 2022); as a way to resist a neoliberal discourse that places productivity and quantity over quality and beauty. Collaborative writing will be proposed also a 'learning' possibility beyond the traditional conception of teacher education as a mere development of skills and as a quantifiable training through a set of frameworks. Proposing in this way an alternative view of research, possibly starting from teacher training, research that is entangled with practice, with identity, with embodied and lived experiences that matter and that we care about. A practice-research that is grounded on the value of ourselves as individuals beyond the professional domain that considers us solely as a means of production.

The paper will also draw from psychoanalytical theories, particularly in relation to object-relation theories that position relationality at the centre of identity formation in the work of M.Klein, Winnicott and W.Bion, through which collaborative writing can be seen and read as a transitional space for learning and for approaching education differently.

Professional work in the fields of psychoanalysis as well as psychoanalysis and education is based on the fundamental assumption of a dynamic unconscious in the human being (Freud 1915), so that the subject carries diverse, even contradictory parts within itself. The subject is a divided one, in this sense diversity is internal to the subject.

The planned contribution deals with the significance of theories on internal diversity of the subject and other psychoanalytic theories for practice in the field of psychoanalysis as well as psychoanalysis and education from the perspective of persons who are professionally occupied in these fields.

Even if the reference to scientific theories can sometimes grant professionals a certain degree of security, relevant publications from a psychoanalytical perspective (Zwiebel, 2013; Datler, 2016) and in accordance with literature on pedagogical professionalism (Helsper, Hörster & Kade, 2003; Rottländer & Roters, 2008) point to the conviction that it would be illusory to think that the orientation to theories or concepts could lead to the fundamental elimination of the moment of uncertainty in processes of psychosocial practice. Based on brief reflections on the theory-practice debate, the special nature of psychoanalytic theories is discussed as they take into account moments of complexity and instability or dynamics of psychosocial processes and help professionals to understand that and why the experience of uncertainty in various situations is unavoidable in different intensities and colours.

In my planned contribution, results from an ongoing research project TheoPrax of the Research Unit Psychoanalysis and Education at the University of Vienna will be presented. Within the research project, persons working in different educational and psychotherapeutic fields were interviewed with the help of a specific interview instrument. In the course of these interviews, professionals were asked to give self-selected examples of the ways in which they are guided by theories or concepts in their daily practice. In the course of the evaluation of these interviews, (a) we identify which theories or concepts are mentioned, and (b) using a rating system, we determine with what precision the interviewed persons are able to explain the practice-guiding significance of the theory or concepts they have mentioned (Strobl & Datler, 2020, p. 210).

In the context of the conference topic, of particular interest are those interviews that were conducted with people who, in their practical work, are guided by theories and concepts that assume a divided subject.

The following research question will be addressed:

With what precision the interviewees who mention psychoanalytic theories and concepts are able to explain their practice-guiding significance, by example of their daily practice?

Enrolled in “psychoanalytically orientated clinical approach in education science” (Blanchard-Laville et al., 2005; Blanchard-Laville & Chaussecourte, 2012), we have been conducting participatory research for several years: action-research (Dubost, 1987), intervention-research (Dubois & Hans, 2018), intervention in an open environment (Bordet, 2021) with education professionals (middle and high school teachers, academic trainers, special educational needs teachers…) in France, Lebanon and Morocco. For us, one of the challenges of contemporary educational research is to strengthen the link between researchers and education professionals. This link engages work “with” professionals (Lieberman, 1986) but also work “on” the discourse of the participants involved in the research (Dubois & Kattar, 2017).

However, what we call “participatory research” should be understood more as appellation grouping together a diversity of nominations and practices, rather than a methodology per se. Yves Bonny’s work (Bonny, 2017) highlights this diversity. Indeed, for this author, participatory research can be distinguished from one another according to the place of the scientific frame of reference and the participation of professionals within. Without going back over the history and debates concerning “participatory research” which have marked the different fields of the human and social sciences for more than sixty years, this diversity of doing research “with” refers to epistemological issues which make up the richness, diversity and conflict of the scientific field. Moreover, diversity is also to be understood from a second angle, that of the actors with whom the work is done and pushes us to think about the commitment and the unconscious framework of these actors, their practices as well as the contexts in our research.

For this paper, we will rely on participatory research projet (2019-2021) conducted with eight academic trainers (A.T.) of the academy of Amiens (France) in which we sought to understand how the set of values, social norms and cultural and educational models that support the accompaniment, is experienced by the academic trainers; to study how their representation of the accompaniment that they provide is developed.

Starting from the diversity of participatory research, we will show what characterised our research by analysing the work “with” the A.T. in the aftermath. More specifically, we will discuss the impact of the research process on these professionals involved as the research stages unfolded. In other words, in what way did the collaborative work that was instituted between practitioner and researcher allow for collective elaborations based on experiences that opened up a balance to be achieved between their expectations as academic trainers, the researcher's request and the expectations of the institutional order? In the aftermath, we will analyse the researcher's commitment on the one hand, and on the other, the A.T.'s position, caught between the will to transform elements of their professional practice and the intention to search in a comprehensive way. Moreover, as the A.T. constitute “an instituted collective”, their links “are in a way already there” (Dubois & Hans, 2018), inscribed in an institutional history. Our paper will therefore be an opportunity to return to the “containing function” (Bion, 1962; Winnicott, 1960; Ciccone, 2001; James, 2016) experienced in this group space (A.T. and researcher) where a singular phantasmatic is actualised and in which unconscious anxieties emerge and unfold, including those of fragmentation. Indeed, this unconscious anxiety of fragmentation is present in training and research groups and each member is, more or less, inhabited by the fear of losing “his unity” (Anzieu, 1999) when confronted with alterity.

Algebra includes the relationships between quantities, the use of symbols, the modeling of phenomena, and the mathematical expression of change (Carraher, Martinez & Schliemann, 2008). In order to learn algebra by understanding its content, it is necessary to have algebraic thinking skills, which is one of the types of mathematical reasoning. Driscoll (1999, 2001) interpreted algebraic thinking as thinking about quantitative situations that support clarifying relationships between variables, based on Cuoco, Goldenberg, and Mark (1996)'s useful ways of thinking about mathematical content which they defined as habits of mind. Driscoll (1999) put forward a theoretical framework for the habits that students should acquire in order to develop algebraic thinking skills, by claiming that when the student learns symbols, they will take an important step in expressing generalizations, revealing algebraic structures, forming relationships, and formulating mathematical situations. Driscoll (1999) conceptualized habit of algebraic thought as Building Rules to Represent Functions and Abstracting from Computation as habits of mind, which are taken place the umbrella term of the Doing-Undoing.

Doing-Undoing: This algebraic habit of mind is an umbrella term for the other two habits. Students should be able to both conclude an operation related to algebra and reach the starting point by working backwards from the result of an operation which they found the result. Thanks to this mental habit, students not only focus on reaching the result, but also think about the process.

Building Rules to Represent Functions: This mental habit includes recognizing and analyzing patterns; investigating and representing relationships; making generalizations beyond specific examples; analyzing how processes or relationships have changed; and looking for evidence of how and why rules and procedures work (Magiera, van den Kieboom & Moyer, 2013). The sub-themes of this habit are; organizing information, predicting patterns, chucking the information, different representations, describing a rule, describing change, justifying a rule.

Abstracting from Computation: It is the capacity to think about calculations regardless of the numbers used. Abstraction is important for this habit of mind. Abstraction is the process of extracting mathematical objects and relations based on generalization (Lew, 2004). The sub-themes of this habit are; computational shortcuts, calculating without computing, generalizing beyond examples, equivalent expressions, symbolic expressions, justifying shortcuts.

Magiera et. al. (2013) investigated algebraic habits of mind 18 elementary school pre-service teacher with problems. Magiera et. al. (2017) examined pre-service teachers' habits of building rules to represent functions in the scope of the algebra problem. Strand & Mills (2017) stated that the studies in the literature examined pre-service teachers' algebraic thoughts within the scope of problem solving. Therefore, in the studies in the literature, it is seen that problems are used as a tool to examine the pre-service teachers' algebraic thoughts. Also, Kieran et al. (2016) mentioned the importance of problems in developing algebraic thinking. In this context, unlike other studies, this study will examine how pre-service teachers' algebraic habits of mind differ in well-structured and ill-structured problems. Simon (1973) stated that students' solutions to ill-structured problems differ from their solutions to well-structured problems. In addition, Webb & Mastergeorge (2003) examined the differences in the solution strategies of student groups solving ill-structured problems and well-structured problems. Kim & Cho (2016) examined how pre-service teachers' motivations affect their problem solving processes in ill-structured problems. In this study, it is aimed to compare the algebraic thinking styles used by pre-service elementary mathematics teachers in the process of solving a well-structured and ill-structured algebra problem. For this purpose, "What is the difference between the algebraic habits of mind that teacher candidates use in solving a well-structured and ill-structured algebra problem?" an answer to the research question was sought.

Given the ongoing advancement of technology across many areas, the use of technology has become not only a significant tool, but an inevitable component of education. National Council of Teachers of Mathematics (NCTM, 2000) underlines the importance of technology in mathematics education as follows: “technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning” (p. 11). Although there is an increasing access to technology in classrooms, mathematics teachers have difficulty in integrating it into their teaching practices (Erduran & Ince, 2018). Teachers’ knowledge determines how effectively technology is used during instruction (Guerrero, 2010). Therefore, mathematics teachers should be equipped with the necessary knowledge and the positive stance to arrange an effective utilization of technology in supporting students’ learning.

What teachers’ knowledge should encompass has been the subject of many studies. Shulman (1987) proposed that approaching to content and pedagogy as separate entities in education is inadequate, and instead, integration and balance between the two must be achieved. Thus, Shulman (1987) offered pedagogical content knowledge (PCK). Subsequent studies, building upon Shulman’s conceptualization of PCK, have associated technology with the discussion of teacher knowledge. For example, Niess (2005) abbreviated technology-enhanced PCK as TPCK. Similarly, Koehler and Mishra (2005) used TPCK to refer to the term “technological pedagogical content knowledge” which presents how teachers’ understanding of technologies and pedagogical content knowledge interact with one another to produce effective teaching with technology. Then, in 2007, TPCK was changed to TPACK, to make it a more easily pronounced and remembered term (Angeli &Valanides, 2015).

If a teacher is competent in using technology but lacks the ability to transfer this knowledge effectively during teaching or to integrate technology with the content, there is an issue related to TPACK (Hew & Brush, 2007; Mishra & Koehler, 2006). From the perspective of mathematics, teachers should have necessary TPACK in all areas of mathematics, such as numbers and geometry. According to Mathematics Education in Europe report (2011), numbers, algebra, data and chance, and geometry are the areas of mathematics which are widely presented in the curricula of European countries. Compared to these areas, probability is stated as a less frequent one. Similarly, NCTM (2000) stated that number and operations, algebra, geometry, measurement, and data analysis and probability are the main contents of mathematics. In this respect, mathematics teachers should not see technology as “a way to keep kids busy” (Hew & Brush, 2007, p. 229), but have high self-efficacy related to their TPACK in different areas of mathematics. Since self-efficacy is a domain-specific construct (Pajares, 1996), the purpose of this study is to investigate whether mathematics teachers’ self-efficacy beliefs toward TPACK differ across the areas of mathematics.

According to Bandura (1997), self-efficacy, which is a central aspect of social cognitive theory, is a concept related to perceived capability. In more detail, self-efficacy is defined as “beliefs in one’s capabilities to organize and execute the courses of action required to produce given attainments” (Bandura, 1997, p.3). Self-efficacy covers some distinctive features. One of the features is that self-efficacy includes judgments of capabilities to perform activities rather than personal characteristics. Another feature is that self-efficacy measures are not only domain-specific but also context-specific. For example, a student may have lower self-efficacy about learning in a competitive classroom than in a cooperative classroom. In addition, self-efficacy beliefs are multidimensional so that they vary across specific tasks within a particular domain (Zimmerman & Cleary, 2006).

By considering these points, the research question is given below.

Do self-efficacy beliefs of mathematics teachers regarding their technological pedagogical content knowledge (TPACK) vary across the areas of mathematics?

Problem-solving has been a part of school mathematics for a long time (Stanic & Kilpatrick, 1988), but problem-posing research (Cai & Hwang, 2002; Kilpatrick, 1987; Silver, 1994; Silver & Cai, 2005) is fairly new. Since educational research is done to help students learn better, research on problem-posing is no different. Researchers and curricula have mentioned how important it is for elementary school students to be able to pose mathematical problems. Researchers have suggested that problem-posing activities are good for students' creativity (Silver, 1997) and help them get better at solving problems (Brown & Walter, 2005).

On the other hand, reading comprehension research has a longer history than problem-posing research. Reading comprehension research has shown that getting students to pose problems can help them understand their reading much better. Rosenshine, Meister, and Chapman (1996) found gains in students’ reading comprehension when the students were engaged in problem-posing, with a 0.36 effect size measured by standardized tests and 0.86 when using researcher-designed tests. Yu (2011) mentioned that posing problems could be a good way to get students to do higher-order thinking instead of just trying to memorize and understand the learning content. This could help students figure out what the key ideas are while they are learning. Other researchers have also mentioned that when teachers help students with problem-solving activities, it can strengthen their understanding of the course material, improve their learning outcomes, and improve their ability to understand what they are reading (Sung, Hwang, and Chang, 2013). Studies have shown that those who are very good at reading comprehension point out that they are the most effective readers in constant contact with the text (Duke and Pearson, 2002; Cartwright, 2009; Brassell and Rasinski, 2008). Despite this interest in integrating mathematical problem-posing into classroom practice, little is known about the cognitive processes involved when students generate their problems and how problem-posing relates to other cognitive processes in students, like their reading ability.

Even though the research is limited, these quantitative results show that problem-posing should be used in math classrooms because it helps students understand what they are reading and solve problems. Even though it makes sense, in theory, to give students problem-solving tasks to help them understand and improve their learning, more research is needed to show the link between these two ideas. The research in reading comprehension can be used as a model for a systematic study of how mathematical exploration and problem-posing activities affect how well students learn math. This study addresses some of these questions by investigating students' problem-solving abilities and reading comprehension skills. Therefore, this study aimed to examine the relationship between problem-posing and reading comprehension skills.

All networks hold a meeting during ECER. All interested are welcome.

This paper tells an overarching story emerging from an inquiry into the affordances and constraints of using global citizenship (GC) themes in secondary mathematics classrooms in Scotland. I argue that not only does mathematics, as a human tool for measuring modelling and making sense of the world, have something distinctive to offer GC education but also that GC opens spaces to rethink and potentially rewild mathematics education. The project has roots in ‘global citizenship education otherwise’ (Andreotti 2021) and critical mathematics education for social justice (Skovsmose 2014, Weist et al 2007, Stinson et al 2012). It is pragmatically connected to the current requirements of the Scottish ‘Curriculum for Excellence’ (Scottish executive 2004) where Global citizenship education is an entitlement for all learners and the responsibility of all teachers.

The secondary mathematics teachers in this project have chosen to attend subject specific professional learning courses offered by a development education centre. They engaged with GC themes and classroom materials that contextualise mathematics tasks in complex and sometimes controversial topics. Some of the teachers were able to then use these materials in their classrooms.

Two sub plots identified in the research project are drawn on here. The first describes the power and tenacity of what I have called ‘business as usual mathematics education’ where the overriding purpose is to meet performance targets in the achievement of tradeable qualifications. The second describes teachers finding and giving space, both of which require professional and pedagogic courage, in which they teach about, through and for GC.

I privilege possibility over probability to suggest that global citizenship education can help to rewild the damaged and denuded site that is the typical mathematics classroom (Ernest 2020) where mathematics is the “handmaiden of capital” (Darder 2018 pviii). GC materials (see e.g. Scotdec 2021) which echo the “spiritual turn” (Gutierrez) and the “socio-ecological ecological” turn (Coles 2022) that have been called for in mathematics education, require dispositions and pedagogies that may be unfamiliar to, but also welcomed by mathematics teachers.

Following their meta review of typologies of GCE Pashby et al (2020 p.158) “identify three different layers of analysis and intervention … methodological (the level of doing), epistemological (the level of thinking) and ontological the level of being.” Each of these maps to this story and I add a fourth axiological the level of valuing. When the teachers adapt their pedagogy to give choice or enable collaboration they are engaging methodologically. When the teachers reimagine the curriculum to embrace wider purposes that better match the use and beauty of mathematics they are engaging epistemologically. When the teachers carve out spaces within which pedagogy and curriculum can be enacted differently, they are engaging ontologically. When the teachers respect young people as more than Homus O Economicus (Valero 2018) in the making, care about their foregrounds (Skovsmose 2012) and mind about our shared world (Griffiths & Murray 2017) they are engaging axiologically.

A recovered ecosystem is not a virgin one and it is important to manage our expectations of the mathematics classroom. The social environment of individual competitive capitalism, austerity policies and powerful social media places pressure to adapt on teachers and young people. The education policy environment in Scotland seems to be very encouraging for the teacher who is committed to social justice and yet in practice the requirement to raise attainment always dominates the requirement to embed learning for Sustainability (Scottish Government 1012). This project has given some glimpses that suggest that GC in mathematics can have the strength of a plant growing up through concrete and making a crack in what seemed to be impenetrable.  

India’s National Curriculum Framework 2005 (NCERT, 2006a) posited an epistemic change towards learning. Learning was seen through a constructivist lens with the learner being focused on in the policy discourse (Sarangapani, 2007; Saxena, 2006). The Position Paper in Teaching of Mathematics proposed the guideline of ‘Math for all’ (NCERT, 2006b, p. 12). Curriculum was proposed to be coherent, ambitious and having depth rather than being tall and spindly (NCERT, 2006b, p. 7). It was recommended that mathematics learning should cater to the minority of learners who have the potential to do well in mathematics as well as include the majority of learners who usually find mathematics challenging (NCERT, 2006b, p. 12). The proposed shift raised an expectation on teachers’ role in classrooms. They were expected to make the classroom space more inclusive in order to make mathematics learning equitable. The teachers were assumed to have a role of implementing these envisioned changes in their practice by implementing reform-based curriculum and textbooks (Chowdhuri, 2020). NCF 2005 and earlier policies as well as curricular frameworks have been criticised to follow the route of top-down approach in bringing any change (Anand & Lall, 2022; Ball & Cohen, 1996; Batra, 2005; Choppin, 2009; Remillard, 2005).

It has been well researched that teachers negotiate with reform-based textbooks and curriculum in varying ways (Remillard, 2005). Teachers’ negotiations with any proposed reform are a product of their identity and beliefs (Heyd-Metzuyanim, 2019, Thompson, 1984). The proposed research explores the relation between teachers’ identities, their beliefs and choices they make in their practice. For the given research, case study of seven teachers teaching mathematics in primary grades were done. These teachers were employed in a non-governmental organisation (NGO) but were teaching in state-run government primary level schools. The site of research presents a unique case of partnership of an NGO with the government. Open-ended interviews were carried ahead with each of them. Classrooms of five of these teachers were observed for a period of a week to see how their choices translate into practice.

The conclusions derived from the study discusses how teachers viewed themselves as an agent of change. Working within the protocols followed in the school and the expectations set by the NGO, they kept the learner in focus while making any decisions related to their practice. These practices encouraged both individual and collective participation of learners. Collaboration through group work was encouraged to make learners interdependent. These collaborative practices shared the onus of learning within the learners. Teachers also talked about challenges and limitations they usually faced.

This proposed research will add to the discourse of teachers’ engagement with mathematics education reforms in India. At global level, teachers’ engagement with the reforms has been researched upon from teachers’ identity, teachers’ beliefs, teachers’ agency perspectives and this research will enrich the existent discourse from the India context (Anand & Lall, 2022). It is imperative that theorization of teachers’ engagement with reforms is evolved from ground and this research will help take steps in that direction.

The following paper comes from one of the dimensions that make up the Yard4All project, built under the Erasmus+ program. To reform conventional education, escape the traditional four walls and get in touch with reality, this document exposes the importance of working mathematical concepts in concrete, bringing this curricular area closer to children's daily lives. According to Feille (2021, 2013), the schoolyard is an essential pedagogical tool in the holistic development of any child, that helps them achieve several skills.

When students are able to touch their learning, experience it in real life, their understanding seems to emerge like snap peas peeking out of the fresh dirt. Their green tips poking above the nourished and moist earth. Nurtured with care and attention, they stretch and reach for fresh air and sun. (Feill, 2013, p.1)

The theoretical component presented here is linked to a research question: What practical activities, using mathematical concepts, are necessary to promote the global development of children, while exploiting the schoolyard?

Consequently, this project essentially defines three main objectives: (i) Develop and improve, in every child, cognitive, social and emotional skills, throughout non-formal learning and teaching environments, using outdoor activities in the schoolyard, that follow the principles of permaculture, while using mathematical concepts; (ii) Develop practical and useful activities that motivate all children to have a positive attitude towards Mathematics, where the entire school community is included and can actively participate; and (iii) Create a guide for teachers and other educational actors, specifying some activities, within the scope of Mathematics, for children with special educational needs and children without impairments, between six and twelve years old.

Firstly, it is important to define permaculture, since all the activities created are based on it. Permaculture is a form of agroecology and an alternative paradigm of production, based on ecological principles such as recycling waste, minimizing energy and water use, maximizing genetic diversity, regenerating soil, and promoting other beneficial biological synergies (Hathaway, 2016). Permaculture school gardens offer particularly valuable opportunities for a sustainable education, crucial for the XXI century learner. This practice is innovative in the school context and can provide children with practical experience of sustainable production means (Yard4All, 2022). But to work in a learning environment with these principles, children need to go outdoors and get to know nature, sense the biosphere, and explore their motor, cognitive, emotional, and social abilities. In fact, while discovering the schoolyard, children find opportunities to make decisions that encourage problem solving and creative thinking (Sá, 2016). Mathematics is often seen by children as a “bogeyman”, being considered not very humane and useful for everyday life. But Mathematics is in any day-to-day circumstances, and it is possible to relate it to various topics, formally and informally. The Yard4All (2022) project focuses on one of the most appropriate ways to work with Mathematics nowadays, using it with context. Mathematics in Context aims to use mathematical concepts in significant real contexts, moving from concrete and informal situations to the formal understanding of abstract concepts (Martins, Fernandes, & Guedes, 2020). This allows children to gain confidence and feel predisposed to learn Mathematics, in a place where they are curious, safe and, at the same time, have unpredictability (Feille, 2013) – the schoolyard. As a pedagogical tool, the schoolyard allows children to participate in the development of “their social and cognitive abilities, their sense of connection with other people, with nature and their natural environment” (Tsevreni & Bentenidi, 2013, p.39), including children with special needs. The schoolyard is a place where everyone can have their sense of belonging and participate in decision-making, characteristics of an inclusive education.

England’s move to a marketised, new public management schooling model has impacted heavily on primary schools (DfE, 2010).  The ongoing changes have created a fragmented and constantly shifting school system which even a decade ago was described by Stephen Ball as “messy, patchy and diverse” (Ball, 2012). Over one third of schools have moved from local government oversight under a policy of ‘academisation’, although numbers vary between regions.  

The academisation policy (HMSO, 2010) has also altered arrangements for teacher Continuing Professional Development and Learning (CPDL). Some of the previous mechanisms for accessing CPDL provision having been lost, adapted or replaced (Greany, 2020). Subject leaders in England’s primary schools have oversight of curriculum, pedagogy and attainment, as well as subject CPDL, meaning changes to CPDL provision have impacted their work in ensuring access to high quality CPDL provision for colleagues. This paper reports on findings from a Wellcome-funded project exploring local learning landscapes for CPDL (Greany et al., 2023), focusing on the case of mathematics in primary schools, and particularly on the challenges facing mathematics subject leaders. 

CPDL for primary mathematics is almost unrecognisable from that of twenty years ago (ACME, 2016). Previously Local Authorities (LAs) were the key CPDL coordinators and providers for mathematics, often mediating national programmes at local level (e.g. National Numeracy Strategy, DfEE, 1999). The previous LA role has been replaced by a patchwork of regional Maths Hubs that implement national development priorities and have much larger footprints. In addition, the creation of legally-constituted groups of school academies (Multi-Academy Trusts or MATs) has enabled schools to pool resources, share expertise, create CPDL programmes, and appoint Trust subject leaders. MATs can use their collective buying power to secure preferred providers of CPDL (Greany & Higham, 2018) and might mandate particular schemes/textbooks. Where education businesses and in-house CPDL once supplemented the core LA offer, these have increased significantly as part of a self-improving, school-led system.   

The fragmentation and diversification of the CPDL nexus has created a professional learning landscape that is complex to access, understand and navigate. With growing numbers of increasingly strong MATs, weakened LAs, national patchworks of curriculum hubs, expanding edu-business and the continued option for in-house CPDL, mathematics leaders in primary schools no longer have access to the entire CPDL offer in their locality. They are often isolated (if not part of a MAT) and there is no longer any well-established map of that local CPDL offer. 

Drawing on interview data from 19 primary schools in three localities in England, we demonstrate how the role of the mathematics lead has fundamentally changed and is now significantly more variable between schools. These key staff are typically responsible for orchestrating much of the CPDL in their schools, yet the evidence points to widely differing levels of autonomy and training. Support for subject leaders is patchy; some are accessing professional networks of mathematics leaders, but many are not. Given the ongoing prioritisation of improvements in mathematics teaching and impact of CPDL on pupil attainment (Cordingley et al., 2015), greater support is needed for these mathematics leads. This should include consistent access to leader networks, knowledge exchange and sources of innovation. Evidence suggests that establishing more aligned, simplified, coordinated and collaborative local CPDL offers would increase coherence (Burns & Koster, 2016), reducing the workload burden on mathematics leads to provide so much of the CPDL themselves. It would also enable greater balance within a system where the knowledge of the subject leader is in danger of becoming a single point of failure for schools. This would in turn increase the quality and equity of mathematics CPDL across England’s primary schools. 

International concern has long focussed on the lack of girls and women engaged in STEM, including mathematics. Yet, it is predominantly women who provide academic support when their children are engaged in mathematics in the home in the form of homework. One reason for the prevailing gender disparity in mathematics participation more widely (a disparity not evident in outcomes or achievement levels) is the gendered nature of the discipline itself (Mendick 2005). The idea of mathematics as a masculine discipline is well established, with Bench et al. (2015, p.537) highlighting how STEM disciplines, including mathematics, have a “set of masculinized norms and expectations that limit approaches to scientific inquiry”. It is these norms and expectations that create an discursive environment in which those who do not either see their gender reflected or who perceive risk in engaging in particular gendered performances may not feel comfortable and/or valued within the discipline area. Mendick (2005) cautions that this does not mean the academic challenges of mathematics are different for girls, but instead highlights the differences regarding the social expectations and experiences they function within. While people who inhabit feminine subjectivities can, unsurprisingly, engage in masculine performances, they do so under different social expectations than boys and men and hence such activities (i.e. a masculine dominated subject like mathematics) can be less appealing to girls/women (Cheryan et al., 2009; Mendick 2005) or imbued with risk. For example, Mendick (2003) describes boys as engaging in masculine performances when they choose to study mathematics as a means of proving their intelligence. Yet, girls who also engage in masculine performances in relation to mathematics do so with a degree of risk to their feminine identities in the process. Simply put, masculine dominated environments – in terms of stereotypes, social norms and expectations – create an additional barrier for women and girls as they may struggle to identify themselves as being ‘good at mathematics’.

In terms of how feminine subjectivities play a role outside of the mathematics classroom, we are interested in how female caregivers negotiate mathematics, as a masculine-coded discipline, when it comes to supporting their school-aged children with their homework. Schools often rely on the assumption that caregivers “have time to dedicate to their children’s education, contributing to the functioning of the school in ways that are seldom recognized as work” (Griffith & Smith, 2005, 24). The reality of this is that schools rely on mothers to bridge the gap between school and home life, as it is well established that it is mothers who assume the greatest responsibility in children’s education at school and at home (Griffith & Smith, 2005; Lareau, 2000; Reay, 1998; 2004, Vincent, 2017). As a result, mothers place responsibility on themselves for children’s educational performance as well as being held responsible for this by others (Griffith & Smith, 2005; Lightfoot, 2004; Reay, 1998).

Mathematics homework, although taking place in the home, is a practice of school mathematics and as such is shaped by the structures and norms of both the practices and relationships relevant to the classroom context (Kemmis & Grootenboer, 2008). Therefore, the masculine characteristics of mathematics are identified as present within school mathematics contexts. In this paper we share the experiences of mothers with mathematics homework and discuss how their view of themselves as caregivers shapes the ways in which they engage with mathematics as a mothering (feminine) activity rather than mathematical (masculine) one.

This paper presents results from a part project on early assessment in mathematics, from a special educational perspective: Sustainable national assessment in mathematics - equity and quality in focus now and in the future. The focus is implementation of support for assessment in preschool-class and the teachers experience of this. Earlier results in this project indicates that some of the concepts used in the governing documents are not in harmony with the teaching culture in the early school years and that there is a risk of narrowing down the curricula and of “schoolification” (Bagger, Vennberg & Björklund, 2019). Bagger & Vennberg, 2019; Bagger & Vennberg, 2021). Policy work argues for early identification and support by a need to raise goal achievement, quality of teaching and to secure teachers assessment practices and support for learning so that it is distributed more equal (Regeringen, 2017). Hence, early detection and well-designed teaching for students is a target (Swedish Government, 2017). Research supports this as, early interventions and identification of students in need of support has been proven to make a difference (see eg Dweck, 2015; Holmes & Dowker, 2013; Cohen Kadosh et al., 2013; Kallberg, 2018; Mononen et al., 2014; Sterner, 2015; Vennberg, 2020).

Mandatory support for assessment in mathematics has been implemented in preschool-class, (six-year-olds) since 2020 and with a tryout 2019. Preschool-class is a first school year situated in both the curricula of the preschool and of the compulsory school, it is mandatory and has a curriculum of its own. These students, and often their teachers, had not before this first year of tryout experienced assessment in this form and the teaching culture is imprinted by both care and learning. Furthermore, the group of students starting preschool-class have very varied prerequisites. Some of the students might never even have been to preschool before their year in preschool-class. For all the children, this is a first experience of going to school and part of learning how to be a student. The purpose of the assessment material in preschool-class, called Find the Mathematics, is to impact the teachers' understanding, teaching, and the students' learning and consists of several parts. The intention is that the assessment will lead to early and systematic teaching in mathematics, which also has been proven to be positive for students' development of knowledge and positive identities in mathematics. It is supposed to be carried trough as a group exercise, in which students talk with each other and answers questions, are active and show their thinking in mathematics.

Assessment has had a way of taking over in classrooms, and sometimes learning is rather for assessment, than the opposite. Following from this, an expected challenge when implementing the material is to keep the care discourse that is an important part of teaching in preschool-class and at the same time provide high quality teaching. Watson (2021) has explored care of, for, and through mathematics teaching and then refers to “…care for mathematics in its fullest sense; care for students including knowledge of community; and these two are connected by care for their learning of mathematics’ (p. 91). Watson then shows that care for students learning mathematics, and the care for mathematics is interdependent. Without caring about mathematics and at the same time meeting high expectations and to be challenged, it is not possible to reach deep learning. The purpose of this paper is to explore opportunities and obstacles for the care of mathematics learning, in teachers experiences from preparing and working with the material, Find the Mathematics.

Numerous curricula aim to develop students’ mathematical reasoning, which is an essential aspect of their education. Students can develop reasoning skills through various tasks that go beyond the formal curriculum (McFeetors & Palfy, 2018). However, appropriate tasks are essential to support students’ mathematical reasoning in the classroom (Brodie, 2010; Jeannotte & Kieran, 2017). Mathematical reasoning can be developed and elicited through meaningful and challenging learning experiences (Stein et al., 1996). Moreover, it has been suggested that tasks should encourage students to make conjectures and generalisations, search for similarities and differences between objects, and use their prior knowledge and other generalisations with which they are already familiar (Jeannotte & Kieran, 2017). Games play an essential role in these educational tasks because they provide students with an appropriate environment for presenting and defending their arguments (Mousoulides & Sriraman, 2014). Furthermore, strategic games have a large number of potential strategies that include a number of different components. Therefore, while playing these games, students use various reasoning skills without realising it (McFeetors & Palfy, 2018).

The role of mathematical games in the teaching and learning of mathematics has been recognised for decades (Dienes, 1963; Brousseau & Gibel, 2005). According to Ernest (1986), games have the potential to positively influence the development of students’ conceptual reasoning, higher-order thinking, and motivation to learn mathematics. Moreover, carefully designed mathematical games can help students develop problem-solving skills (Pintér, 2010) and effectively apply the critical actions of mathematical reasoning (McFeetors & Palfy, 2018). Although reasoning is a significant component of student achievement in mathematics, few studies have reported how students demonstrate reasoning skills while playing games. Our research aims to examine the reasoning process of fifth-grade students while they play a strategy game.

The ability to reason is essential to understanding mathematics (The Programme for International Student Assessment [PISA], 2022). Lithner (2000, p. 166) defines reasoning as a way of thinking that is adopted to make claims and reach conclusions. It is critical for educators to develop students' reasoning skills to prepare them for more advanced learning (Vale et al., 2017). Many elements of reasoning are closely related to elementary school mathematics, such as forming hypotheses, sampling, comparing, recognising patterns, justifying, and generalising (Lampert, 2001). According to reSolve: Assessing Mathematical Reasoning (Australian Academy of Science [AAS] and Australian Association of Mathematics Teachers [AAMT], 2017) these actions of reasoning can be classified into three main categories: analysing, verifying, and generalising.

This paper focuses on the actions students display during the process of analysis, including the first steps of mathematical reasoning. We expect this study to provide new insights into the different types of reasoning students use when playing strategic games and the function of these games in early grades.

Mathematics is typically conceived of as being a core discipline in curricula at all levels of education. For this reason, mathematics achievement is crucial to student placement, selection, and admission across most educational systems around the world. This information is also highly relevant in view of the fact that testing is a common practice in contemporary society, which is widely used to make important decisions about an individual’s status across primary, secondary, and higher education (Zeidner, 1998). Test anxiety, however, is a key affective variable can impede both achievement in general (Cassady & Johnson, 2002) and mathematics achievement in particular (Higbee & Thomas, 1999). It is defined as a subjective emotional state that includes a set of cognitive, physiological, and behavioral responses to concerns about possible fear of failure, experienced before or during an evaluative situation (Bodas et al., 2008). It has detrimental effects on schooling, occupational, and overall life outcomes (von der Embse et al., 2015). It is widely acknowledged that high level of test anxiety is associated with lower level of performance (Ng & Lee, 2015). Since students have to cope with constant mathematics pressure at school, it is of major interest for teachers and researchers to identify and strengthen/weaken those factors in students, which primarily influence mathematics achievement negatively. Additionally, metacognition plays an important role in mathematics achievement, as it shapes students’ conscious use and control of their own cognitive functions in educational settings (Brown, 1987). Metacognition is causally referred to as one’s awareness and regulation of own cognitive processes consisting of two components: knowledge of cognition and regulation of cognition (Flavell, 1979). Although research on metacognition has made it quite clear that highly metacognitive students perform better than their less metacognitive counterparts on most performance assessments including mathematics tests, the role of test anxiety in activating metacognitive knowledge and regulatory processes, are much less clear (Hacker et al., 1998). It has been suggested that the impact of affective factors such as test anxiety on performance is also related to metacognition (Zeidner, 1998). However, previous studies have predominantly examined the effect of each variable in isolation, and mainly in relation to general performance that place little demand on specifically mathematics achievement.

There is a vast amount of empirical evidence for the influence of test anxiety on metacognition and mathematics achievement as well as the impact of metacognition on mathematics achievement (e.g., Miesner & Maki, 2007; Sherman & Wither, 2003). Despite this, the combined importance of test anxiety and metacognition in mathematics achievement has been largely ignored, as most studies approach test anxiety in the form of math anxiety whereas others neglected metacognition. To the best of our knowledge based on a comprehensive review of literature undertaken, only two studies (Tok, 2013; Veenman et al., 2000) were conducted that in a sense harmonizes with our emphasis on the differential effects of test anxiety, metacognition, and mathematics achievement on one another.

More specifically, little is known about how these affective and cognitive factors differentially contribute to individual differences in mathematics achievement. This question added significance in light of the researchers, who suggested that “the relationship between test anxiety and metacognition may be a worthwhile field for research, while simultaneously helping to establish links between affect and cognition more generally” (e.g., Zeidner, 1998). Specifically, we hypothesized that: (a) test anxiety would significantly effect metacognition and mathematics achievement (H1); (b) metacognition would significantly effect mathematics achievement (H2); and (c) metacognition would mediate the relationship between test anxiety and mathematics achievement (H3).

Algebra is described as a “mathematical language that combines operations, variables, and numbers to express mathematical structure and relationships in succinct forms” (Blanton et al., 2011, p. 67). It is one of the crucial branches of mathematics which constitutes a gateway between arithmetic reasoning in elementary school and advanced mathematics of higher grades (Blanton & Kaput, 2005). Researchers have agreed on the importance of algebraic thinking in learning mathematics (Asquith et al., 2007; Kieran, 2004). Stephens (2008) suggested that algebra in K-12 refers to “a way of thinking instead of something we simply do (e.g., collect like terms, isolate the variable, change signs when we change sides)” (p. 35). Researchers emphasized that the focus should not be on understanding the rules to manipulate symbols and use algebraic procedures excellently but on developing algebraic thinking. Hence, identifying students’ conceptions, difficulties, and errors in algebra might be a good step in determining these standards.

In Third International Mathematics and Science Study (TIMMS), students were asked real-world problems to use algebraic models and explain the relationships. Despite Turkish eighth-grade students performed gradually increasing performance in algebra tests from year to year (MoNE, 2014; MoNE, 2016; MoNE, 2020), the scores of eight grade students in algebra items in TIMMS 2019 presented that Turkish eighth-grade students’ algebra scores were under the average mathematics score (MoNE, 2020). The difficulties students faced while learning algebra resulted in them becoming isolated from mathematics and stopping learning mathematics early in high school (Kaput, 2002). Thus, a nationwide movement, algebra for all, was called by U.S. educators and researchers to get all students to attain algebra (Moses & Cobb, 2001). In response to these concerns, the National Council of Teachers of Mathematics (NCTM) proposed instructional programs that enable learners “to understand patterns, relations, and functions,” “to represent and analyze mathematical situations and structures using algebraic symbols,” “to use mathematical models to represent and understand quantitative relationships,” and “to analyze the change in various contexts” (NCTM, 2000, p. 37). Thus, it might be beneficial to explore the algebraic thinking of Turkish eighth-grade students to improve their algebra performance. This study investigates the research questions:

1. What is the nature of eighth-grade students’ algebraic thinking around the issues of equivalence and equations, generalized arithmetic, variable, and functional thinking?
2. Which difficulties and errors do eighth-grade students have around the issues of equivalence and equations, generalized arithmetic, variable, and functional thinking?

This contribution shows an inquiry-based learning approach to mathematical modelling, and provides a first insight into its effectiveness for prospective primary teachers. There is a consensus among different authors in mathematics education that the mathematical knowledge that should be expected from a primary school teacher goes beyond the knowledge of the content to be taught (Hill et al., 2008; Carrillo et al., 2013). However, research reports the difficulties that prospective teachers have with regard to skills such as reasoning (Kaasila et al., 2010), problem-solving (Verschaffel et al., 2005) or the application of mathematics to real contexts (Sáenz, 2009). Working with mathematical modelling tasks creates opportunities to alleviate these difficulties.

Over the last decades, modelling has become a crucial area in mathematics education (Barquero, 2019). In fact, curricula in different countries have gradually incorporated modelling competencies, and modelling is generating a growing interest in teacher education, specially in prospective Primary Teachers (Guerrero-Ortiz & Borromeo-Ferri, 2022). Likewise, there has been a proliferation of international projects aimed at designing resources that can support the learning of modelling, such as LEMA, MASCIL or MERIA (2016). In this European project whose main objective was to promote the teaching of mathematics applicable to real life. It combined the principles of Realistic Mathematics Education (Van den Heuvel-Panhuizen & Drijvers, 2014), the ideas of Inquiry-Based Learning (Maaß & Doorman, 2013; Dorier & Garcı́a, 2013) and the pedagogical approach of Didactic Situations Theory (Brousseau, 1997). The key idea developed in MERIA is to implement the principles of inquiry-based learning. In this context, teaching should provide students with just the right amount of help to support mathematical learning. These ideas can be harnessed to stimulate the autonomous development of modelling activity by pre-service teachers, thus it give rise to our research question: Does the inquiry-based learning influence the models developed by prospective teachers?

Modules and scenarios for an inquiry-based learning of modelling

For the sake of providing the “right” amount of direction to inquiry, teaching approach developed in in the MERIA project were based on two key tools: Modules and scenarios. A module is the union of a scenario with all the material needed to implement this scenario in the classroom. Likewise, a scenario is a full description of a lesson in terms of the Theory of Didactical Situations (TDS, Brousseau, 1997). Under the TDS approach, students are intended to construct new knowledge when they solve a task while adapting to what is called a didactical milieu. It consists of the task, students’ previous knowledge, and the artifacts to solve the task. The role of educators is to design such milieu and to help student to adapt to it. In this process, two kind of situations appear. The first one is composed of adidactical situations, which are those where the students are engaged in the task and explore the milieu without the teacher’s interference. The second kind of situations are the didactical ones, where students and educators explicitly interact. A balanced combination between didactical and adidactical situations leads to the inquiry process and the students' construction of new knowledge. Therefore, a proper scenario should contain such combination of situations along different phases. (i) Devolution: the educator introduces the task and explains the rules to solve it (didactical situation). (ii) Action: students are engaged with solving the task and actively work on it (adidactical). (iii) Formulation: students explicitly formulate outcomes of the action phase (adidactical). (iv) Validation: students test their hypotheses and strategies against the milieu (adidactical). (v) Institutionalisation: educator declares the institutional knowledge (didactical). In this phase, teacher may put ideas together, compares viewpoints and explains optimal strategies.

Over the past few years, Asian students, especially students from Shanghai, China, always obtain extremely excellent performance in mathematics competitions (e.g., PISA, TIMSS, etc.) in comparison with their peers from other countries. A growing number of scholars hope to discover what can be learned from these high-scoring Asian education systems. In particular, the Department for Education (DfE) of the UK is adopting the Shanghai Mastery Pedagogy to improve the mathematics achievement of their students (Boylan et al., 2019).

Distinguished from the English and other mathematic education practices, Shanghai whole-class interactive teaching aims to develop conceptual understanding and procedural fluency of students. Some big ideas, such as coherence, variation, representation, and structure, are promoted by mastery specialists (NCETM, 2017). Teaching is famous for its mathematically meaningful and coherent activities with well-designed models and examples systematically using variations. Actually, the characteristics mentioned above, especially the effective use of “variation”, are also noticeably emphasized in the exploration of Chinese mathematics teaching (Gu et al., 2004). Teaching with variation has almost become a common teaching routine for many Chinese mathematics teachers (Marton et al., 2004) and has been applied either consciously or intuitively for a long time in China (Li et al., 2011).

The main research question of the study is: How do Chinese mathematics teachers make use of variation to foster student learning in their teaching? While there have been extensive studies on the effective use of variation in mathematics teaching, some gaps still exist in the following aspects. Firstly, most of the studies utilized one of the variation theories as the lens to analyze mathematics teaching in China (e.g., Qi et al., 2017; Mok, 2017; Häggström, 2008). However, insufficient attempts have been made to employ an integrated variation perspective based on several variation theories. Secondly, most of the existing studies adopted the approach of quasi-experimental or lesson study with intervention (e.g., Pang et al., 2017; Al-Murani, 2007; Kullberg, 2010). Nevertheless, very few studies adopted the naturalistic perspective to explore what actually happens in more authentic and diverse situations. Thirdly, due to the limited size of the research, some studies chose one or very few excellent public lessons or experimental lessons, even if a series of lessons were collected (e.g., Mok, 2017; Pang et al., 2016; Pang et al., 2017). The mathematics structures, relationships, and coherence within and between the sub-topics are not the major factor and draw little research attention, but they are actually the key ideas of Chinese pedagogy and the very essential platform for unfolding variation. Lastly, including the movement of the UK, most practices and studies were unfolded in a relatively primary or junior stage, while the senior-level mathematics knowledge and topics were less involved.

The basis of the theoretical framework is the Variation Theory (VT) of Ference Marton. With the help of variation and invariance, students could “discern” the “critical aspects” of an “object of learning” with certain “patterns of variation” (Marton, 2015). The “critical aspect” in VT is considered identical with a dimension of variation (Pang & Ki, 2016). Watson and Mason (2005) further developed this concept with the term “dimension of possible variation”, associated with the notion of “range of permissible change” on the extension of Marton’s originally general notion. This extension captures the qualities of variation arising in mathematics (Mason et al., 2009) and better fits the nature of mathematics. Meanwhile, their concepts of example and example space are also elaborated in a mathematical manner. In addition, the analysis is also inspired by the Chinese theory “Bianshi Jiaoxue” (teaching with variation), which is developed by Chinese mathematics expert Gu Lingyuan (Gu et al., 2004).

The errors and imprecisions in teaching mathematics are part of mathematics classrooms and might negatively influence student learning (Ball & McDiarmid, 1990; LMT, 2011). The errors and imprecision dimension is one of five in Mathematical Quality of Instruction (MQI). The other domains are the classroom work is connected to mathematics, the richness of mathematics, working with students and mathematics, and common core-aligned student practices. MQI (2014) defined the errors and imprecision dimension as "teacher errors or imprecision in language and notation, or the lack of clarity/precision in the teacher's presentation of the content" (p.19). Most studies in the literature are interested in possible errors, misconceptions, or difficulties in learning statistics (e.g., Batanero et al., 1994; Capraro et al., 2005). To illustrate, certain studies conducted on revealing possible errors or difficulties made by students during interpretations of graphs (e.g., Aydın-Güç et al., 2022 for scatterplots; Capraro et al., 2005 for bar, line, and circle graphs; Edwards et al., 2017 for boxplots). On the other hand, there are also studies showing pre-service teachers’ errors or imprecisions on graphs as well (e.g., Işık et al., 2012 for line graphs; Ulusoy & Çakıroğlu, 2013 for histogram). However, there is a lack of research on what kinds of teacher errors and imprecision are present in teaching statistics. It is essential to explore teacher errors and imprecision to learn from them for not to transfer inaccurate information teachers possess to the students (Ball & McDiarmid, 1990). By exploring teacher errors and imprecisions in teaching practices, it is possible to identify areas of improvement, leading to more effective and engaging instruction and better student outcomes. Ultimately, understanding teacher errors and imprecisions is crucial in promoting high-quality mathematics education (LMT, 2011). In light of this gap in the literature, the purpose of this case study is to explore two 7th-grade mathematics teachers' statistics teaching with regard to errors and imprecision. The central research question guiding this study is: What types of teacher errors and imprecisions are present in 7th-grade mathematics teachers' statistics teaching?