**1. Introduction**

The amount of scientific research related to teacher education is extraordinary and is focused on multiple unresolved aspects such as educational policies, quality education, or professional development, amongs<sup>t</sup> others.

This article is centered on the professional development of pre-service teachers and, more specifically, on one of its main purposes: to transform prior knowledge, experiences, and belief systems into professional competence through progressive professional development, in order to effectively exercise the teaching profession [1], taking into account sustainability principles. In this paper, we follow Mayer and Lloyd [2] who state that while professional development can be described as the planned activities teachers engage in to improve their practice, professional learning implies how their practice changes. This change can be a result of their professional development, but also of the informal learning that takes place in their everyday classroom work. According to Webster-Wright [3], a prevailing view in this regulation is that there is a stage-based progression in competence from novice to expert. There is an assumption that, through continuing professional learning, professionals will maintain their competence and develop expertise. This assumption is also implicit in current moves seeking to make professional development mandatory for most professions. However, there is an increasing awareness that competence and expertise are context dependent. There is no question that competence development occurs; whether it is stage-based and linear has been challenged by those

who acknowledge its situated nature. Professionals develop their competences and skills in diverse manners depending on contextual issues influencing their practice, and how they understand practice.

The intention of this article is to offer various keys that empower the professional competence of pre-service teachers [4] in the area of mathematics education for sustainability. From this point of view, and as happens in other highly complex professional contexts, it is assumed that teacher education cannot be rethought based on mere intuition and experience. Progress will only occur if university lecturers, responsible for training pre-service teachers, explicitly incorporate key knowledge and lessons learned provided by research in various fields linked to teacher education. In this paper, we focus on two of these fields: education for sustainability and reflective learning. The first has been endorsed by the international community as a fundamental approach to address sustainable development—one of the most important challenges of our history [5–7]—as well as to move towards a 21st century pedagogy [8]. The second is an integral component of education for sustainability and has been shown to be effective for the development of teachers' professional competences [9].

This paper analyses and describes the teaching practice of a university lecturer who has embedded education for sustainability principles and reflective learning approaches in the course "Learning Mathematics" of the Degree in Early Childhood Education of the University of Girona. The purpose of the analysis is to identify and characterize key elements that contribute to challenge pre-service teachers' prior knowledge, experiences, and belief systems into professional competence in the area of mathematics education for sustainability.

#### *1.1. Mathematics Education for Sustainability*

For the past 30 years, education has been described as the grea<sup>t</sup> hope to create a more sustainable future. Underpinning education for sustainability is a commitment to engaging people and social groups in learning to live in sustainable ways. It encompasses a new vision of education that supports learners to reflect upon preferred futures and define their vision for sustainable development [10]. Education for sustainability is focused on pedagogy as it seeks to equip learners to respond to the complexities and uncertainties of the future, and uses well established and less well-known pedagogical approaches [11], such as futures thinking, learning to change, systems thinking, stakeholder engagement, reflective learning, and participatory learning [10,12,13].

Mainstreaming sustainability in teacher education has been identified as a key priority in authoritative international documentation [5–7]. The education of pre-service teachers plays a vital role in achieving changes in teaching and learning in schools [14], as well as shaping the knowledge and skills of future generations [15]. Bourn and Hunt [16] highlight that education for sustainability amplifies questions about the purpose of teachers in society. They do not only hold the key to promote sustainable development understanding and competences, but also support social justice, equity, and environmental responsibility in our communities.

Much has been written about re-orienting teacher education for sustainability [15–23], stressing the need to rethink content and competences, but also promoting the clarification of sustainability values and the development of reflective practices [6]. There are many experiences documented regarding the embedding of sustainability principles in specific pre-service teacher education subjects such as language or science education [24–26]. However, there is a lack of literature unpacking the connections between mathematics education and sustainability. Most of the documentation consists of reports and booklets describing inquiry-based school projects that have engaged students in using mathematics to explore specific sustainability challenges. There is little research that investigates the fundamental role of mathematics education in supporting learners to design creative ways to meet sustainable development needs in efficient ways, understanding the natural world and our relationship with it, acquiring a critical understanding of progress and technological advance, or solving complex problems using systems approaches, to mention some.

In Spain, competences form the scaffolding around which university education courses are constructed. These competences usually appear as generic, specific, and transferrable skills that graduates must demonstrate over the course of their degree. The University of Girona has included sustainability as a transferrable competence, and all lecturers are expected to embed education for sustainability in their courses. The Department of Specifics Didactics of the Faculty of Education has worked in this direction for a long time, especially in the areas of science and mathematics education. Many subjects have been rethought in order to tackle the sustainability challenge and help pre-service teachers understand their personal and professional responsibilities regarding sustainable development. First, sustainability competences were embedded using the framework developed by ACES (Higher Education Environmental Curriculum Network) [27] and, later, the guidelines developed by the Conference of Rectors of Spanish Universities (CRUE) Sustainability Group [28] and the UNECE Education for Susatinable Development Competence Framework [29]. The design of the subject "Learning Mathematics" has been informed and shaped by the latter and has implied making an emphasis on holistic thinking, envisioning change, and transforming learning systems, as well as developing learning experiences focused on the pillars of learning to know, learning to do, learning to live together, and learning to be. The professional development experience of this course, therefore, is built on critical reflection and participatory and action learning pedagogical strategies, reflective learning being at the core of the learning experience and being used as a tool for values clarification and action empowerment. This article is interested in analyzing the transformative model of reflective learning in the context of mathematics education and sustainable development. We consider that critical reflective learning should be a key pillar to enhance the professional development of pre-service teachers in the area of mathematics education for sustainable development as it helps learners to clarify and challenge their prior knowledge, experiences, and systems beliefs and transform them to include sustainability criteria.

#### *1.2. Reflective Learning as a Transformative Model of Knowledge, Experiences, and Belief Systems*

Reflective learning promotes the integration of people with their experiences as students, with theoretical knowledge, and with their representations of what it is to teach and learn. This approach guides students towards inquiry-based practices within the professional context, in a way that creates new mental structures during the training process through self-regulated learning [30].

Black and Plowright [9] designed a multi-dimensional model of reflective learning for professional development that can be helpful to frame mathematics education for sustainability. In this model, they included the following dimensions: (a) the source of reflection, comprising learning experience and practice experience and known as the experiential process; (b) the target of reflection, namely reflection-on-learning and reflection-on-practice, and, also the levels of reflection in relation to the target; (c) the realization of reflection, through written and internal dialogue with oneself, which is known as the transformational process; and (d) the purpose of reflection, i.e., reflection for learning and reflection for practice, referred to as the developmental process. This model includes reflection on learning for further learning and self-development; reflection on learning for application to professional practice; reflection on professional practice for further learning and self-development; and reflection on professional practice for application to future professional practice [3] (p. 255).

In recent years, there has been an increasing number of studies focusing on analyzing the e ffects of reflective learning on teacher education and on designing tools aimed at transferring control and awareness of each activity to students, so that they can appropriate the meaning of the knowledge and use it independently through formative and authentic evaluation. A review of the literature has been carried out in relation to the main benefits and obstacles of reflexive learning [31]. The results of this body of research on reflection in teacher education indicate that the main benefits of its application are as follows: it promotes collaborative work among equals [30]; it constructively guides the process of reflection individually and in groups [32]; and it fosters self-regulation processes to promote autonomous learning [33]. Regarding sustainability, reflective learning allows us to understand our own values and abilities and provides strategies to transform our practice; also focusing attention on the process and not the results, thereby helping to better understand the complexity of future professional

practice [34] and sustainable development. Regarding the obstacles, previous studies indicate that reflective learning implies a change in the way teaching, learning, and evaluating are conducted at universities, a challenging task that not everyone is willing to adopt [35]; it requires practice as a starting point for reflection and also an awareness of knowledge, experiences, and beliefs [36]; it can provoke emotional conflicts when contrasting ideas with others and it requires the use of new tools (portfolios, narrative texts, questionnaires, etc.) that can be difficult to develop for students, and challenging for university lecturers to assess [37]. Alsina et al. [38] point out that the use of reflexive learning in the managemen<sup>t</sup> of discourse and practice during teacher education, together with the use of specific tools, promotes processes of self-regulation and confrontation in pre- service teachers that lead to the deconstruction, co-construction, and reconstruction of knowledge (Figure 1). These processes are key for pre-service teachers to challenge current unsustainable values, practices, and experiences and develop alternative ways of teaching that promote sustainability principles.

**Figure 1.** Pre-service teacher elements for the transformation of prior knowledge, experiences, and belief systems into professional competence.

"Deconstruction" is meant as a process from which students become aware of their implicit knowledge, values, and beliefs while seeking alternatives to transform them and improve their professional profile in teacher education and sustainability [39]; "co-construction" is conceived as a social and interactive process in which students share their prior knowledge, experiences, and beliefs with the mediation of an expert, to promote professional learning through collective scaffolding, that is, through collective reflection and construction [40]; and finally, "reconstruction" is a process that involves the transformation of prior knowledge, experiences, and belief systems into professional competence [41]. Loughran [42] indicates that all these processes promote socially acquired knowledge, personal opinions, and the reconstruction of social knowledge.

In particular, Alsina et al. [39] identified 12 elements, which have been called self-regulation traits [43], which facilitate the transformation of prior knowledge, experiences, and belief systems about the teaching profession into professional competence. The first five traits foster cognitive processes related to the deconstruction of: prior experiences; beliefs about oneself; beliefs about the way the class functions; implicit disciplinary knowledge; and implicit didactic knowledge. The remaining seven traits promote processes related to the co-construction and reconstruction of professional competence: interaction with context I (at the school); interaction with context II (the university); interaction with oneself; interaction with peers; interaction with experts; interaction with theory; and critical professional knowledge. According to Larrivee [44], these elements are fundamental for the training of reflective teachers who are critical and capable of learning throughout their lives. Thus, they are fundamental to promote sustainability across the schooling system.

In addition, other elements that have been defined from the results of educational research on teaching practices also intervene in this transformation process. Due to its important role, we want to highlight the element called "agentic engagement", which Reeve and Tseng [45] (p. 258) define as follows:

"Agentic engagemen<sup>t</sup> is students' constructive contribution into the flow of the instruction they receive. What this new concept captures is the process in which students intentionally and somewhat proactively try to personalize and otherwise enrich both what is to be learned and the conditions and circumstances under which it is to be learned."

The above definition includes emotional and cognitive elements. Thus, we must consider that in addition to the conflicts and contradictions indicated in Figure 1, other elements also participate in the construction of new knowledge and experiences that take into account sustainability. These are elements of an emotional and cognitive nature, such as intentionality and proactivity or, more generically, attitudes towards learning and sustainable development.
