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Educational innovations supported by digital games are proliferating in primary and secondary classrooms, generating research on their effects upon learning outcomes. This review analyzes 27 experiences in the field of life sciences education, identifying the experimental design, traits of the control group, results achieved and the role of the teacher as relevant factors to assess their effectiveness. Most research highlights the increase in student motivation; however, only a few of them show significant achievements in scientific learning. The didactic integration of digital games could promote the students’ involvement in socio-scientific topics and the inclusion of learners with different abilities, although more research with mixed designs is needed, so as to identify the role of the teacher and the most effective didactic intervention model for each context.

Aquest article presenta l’experiència de planificació i desenvolupament d’una intervenció didàctica per millorar la competència literària d’un grup d’alumnes de segon curs d’educació primària. S’analitza el paper de mediació que exerceix la mestra en activitats de diàleg al voltant de la lectura de diversos àlbums il·lustrats, centrant-se en dos aspectes: d’una banda, en la creació i utilització d’un recurs didàctic per fomentar l’expressió dels infants en clau literària i, de l’altra, en les intervencions de la docent com a participant i guia en el transcurs de les discussions.----------------------------------------------------- Este artículo presenta la experiencia de planificación y desarrollo de una intervención didáctica para mejorar la competencia literaria de un grup de alumnos de segundo curso de primaria. Se analiza el papel de mediación que ejerce la maestra en actividades de diálogo sobre la lectura de álbumes ilustrados desde dos ámbitos: en el aspecto de creación y utilización de un recurso didáctico para fomentar la expresión de los niños en clave literaria y en la vertiente de participante y guía en el transcurso de las discusiones.------------------------------------------------------This article presents the experience of the planning and development of a didactic intervention to improve the literary competence of a group of primary education second course students. The role of the mediation exerted by the teacher in dialogue activities revolving around the reading of various illustrated albums is analyzed from two different scopes: on the one hand, the creation and usage of a teaching material to promote the expression of children in a literary way and, on the other hand, the role of the teacher as a participant and a guide throughout the discussions.

Reseña de The Mind on Paper: Reading, Consciousness and Rationality, por David Olson.

Es presenta una innovació educativa consistent a introduir a estudiants d'Educació Secundària en els rudiments de la recerca científica. Inserit en un Projecte més global, en el qual participen diverses institucions educatives, es descriu aquí el procés seguit en el desenvolupament d'una recerca oferta sobre les il·lustracions dels llibres de text de ciències. Els estudiants, que la van triar lliurement, es reuneixen periòdicament amb els responsables d'aquella per conèixer els seus objectius i col·laborar en la presa de dades, la seva anàlisi i en l'elaboració de les conclusions finals. Així mateix es valora la recerca duta a terme i es proposen línies de millora en l'ús de les il·lustracions en l'ensenyament. Els resultats finals són presentats en un Congrés en el qual es mostren els de tots els projectes elaborats.

This paper describes a case of the practical application of thematic analysis to organise and interpret qualitative data on the presence of technological contents in the field of translator training in Spain. Thematic analysis allowed us to identify and interpret key ideas (themes) within the data sample obtained from a corpus of module syllabi from undergraduate degrees in Translation and Interpreting (T&I) in 2019-2020. This paper presents the study from a purely methodological perspective. It explains in detail the different phases of thematic analysis according to the model proposed by Braun and Clarke (2006), together with the decisions taken in each phase. This is part of a broader research project that aims to map the current situation of technologies in the academic field (undergraduate degrees in T&I) and in the professional market of translation in Spain, when digitisation is directly impacting the demands of the translation industry.

In addition to its widespread use in various disciplines, LL has garnered attention from researchers in education for its role in enhancing language learning and promoting linguistic diversity. However, its systematic integration into language teaching contexts, particularly in high school settings, remains limited. This paper aims to demonstrate how LL-centered activities were designed for integration into an 11th-grade English classroom in a public high school in southeastern Turkey. Over a 12-week period with 32 students, three LL-oriented tasks—Designing a job advertisement, Creating a T-shirt design, and Crafting a ‘Wanted’ sign—all aligned with the curriculum were implemented. Following the stages outlined by the pedagogical model of Linguistic Landscapes in Second Language Teaching and Learning (LLinL2TL), LL activities were systematically integrated. The objective is to provide a comprehensive illustration of the step-by-step integration of LL resources into high school English classrooms, supplemented by sample student works to offer a clear overview of the process. The study concludes by offering recommendations and implications for language education professionals.

In the light of ongoing international debate about the purpose of explicit teaching of grammar, this paper considers the relationship between metalinguistic understanding and development as a writer. Drawing on a cumulative series of studies over a period of ten years, adopting a functionally-oriented approach to grammar, the paper argues that purposeful grammar teaching occurs within the teaching of writing, not divorced from it; and that this teaching develops students’ metalinguistic understanding of how written texts are crafted and shaped. In this way, grammar is positioned as a resource for learning about writing and one which can support students in becoming increasingly autonomous and agentic decision-makers in writing. We show through practical examples how the pedagogy works in practice, and through classroom interaction data we highlight how metalinguistic talk (metatalk), which enables and encourages the verbalisation of choice. The data also shows, however, that teachers’ skill in managing metatalk about metalinguistic choices in writing is critical in framing students’ capacity to think metalinguistically about their writing and to be autonomous writerly decision-makers.

Over the course of two centuries (since 1807), the Czech lands have seen fundamental changes in the paradigm of special L1 didactics for pupils with vision impairments (hereinafter the VI). The individual didactic transformations often found theoretical backgrounds in special education approaches simultaneously designed across Europe (especially in Austria, England, former Yugoslavia, Italy, Hungary, Russia, etc.) and accentuated respect for the special teaching requirements of pupils with VI. The embrace of specific European approaches usually depended on the general (especially political and social) context of the period, which also had an impact on the aims and tasks of special language teaching. The paper defines the historically shaped aims of L1 teaching for pupils with VI and contextualizes them in order to understand the current aims.

The purpose of this paper is to explore the metacognitive practices that elementary school teachers foster in their Mathematics classes under conditions of non interference. In order to accomplish this, the paper defines an Interpretative Frame that serves as the basis for examining the cognitive and metacognitive processes that arise in the mathematics classroom. The Frame is applied in the exploratory case study of metacognitive practices promoted by two elementary school teachers in their regular Mathematics classes. Non-participating observation was chosen for data collection and our focus centered on proportional reasoning-related contents. The experience shows, inter alia, the flexibility, scope and consistency of the frame.

This study identifies visualisation processes in student primary teachers when they solve geometry problems requiring mathematical proof, in a pencil-and-paper environment. The results reveal the importance of the initial diagrams that accompany the problems, as well as subsequent modifications of these diagrams in the development of discursive and operative apprehension, constituting as they do links between mathematical reasoning processes and the visualisation of geometry-problem solving in a paper-and-pencil context. Finally, we identify the possible causes of those limitations that hinder the development of such apprehension.

In the last decades, a growing number of physicists have taken up the challenge of implementing in the learning and teaching of physics the same research discipline applied to traditional research in the field. Such commitment is largely known as «Physics Education Research» (PER). In this paper we will discuss a proposal of utilization of results of the research for classroom practice at High School and university level. This paper presents evidence from different studies to demonstrate the potential positive impact of the research on teaching and learning physics on students’ understanding of physics. Finally, we will show some practical challenges and propose some steps that could be taken to ensure PER growth and productivity.

In this paper, we addressed the concept of classroom participation and the way it is affected by a traditional teacher-centred (TC) approach and a more innovative learner-centred (LC) approach which uses the principles and strategies of active learning and cooperative learning to engage students in the learning process. The study was carried out in a public secondary school in Spain with two groups of learners of English (n=54). The analysis of the number of learners on task showed that in the LC sessions learner participation increased by 20 % as compared with TC sessions. We also detected some challenges a teacher might face while implementing learner-centred sessions including the facilitation of equal participation in group work, adequate time allocation for a task, individual and group assessment, and development of learners’ autonomy.

This paper reports on a survey which sought to identify the state of the art in the practice of telecollaboration in Europe. It was the first large scale survey carried out on the practice of telecollaboration in Europe and was carried out as part of the European Commission funded project, INTENT - Integrating Telecollaborative Networks into Foreign Language Higher Education. Also known as Online Intercultural Exchange (OIE), telecollaboration engages groups of foreign language learners in virtual intercultural interaction and exchange with partner classes in geographically distant locations. Much research has been carried out on telecollaboration, though this comprises largely of small-scale studies on single telecollaboration projects. The aim of this paper is to discuss the findings from the final report on the survey, provide recommendations for decision-makers and teachers based on these findings and present the UniCollaboration website that was developed largely on the basis of the findings. The paper ends with a brief comparison of the INTENT survey results to findings from two other OIE projects: eTwinning and the COIL Institute for Globally Networked Learning in the Humanities.

Despite the surge of Content and Language Integrated Learning (CLIL) studies in many areas, assessment practices in CLIL contexts are considered to be much unaccounted for (Poisel, 2007; Hönig, 2009, Maggi, 2012). This paper intends to become a contribution to this area and addresses the issue by approaching to the case study of a Science through English CLIL unit implemented on a state-funded secondary school in Barcelona, Spain. The paper focuses on the written test of the unit and analyzes the students’ responses and degree of satisfaction of the teacher after implementing and correcting the test, which provides valuable insights in the light of teacher development and offers a snapshot of CLIL assessment practices and their effects. The results present a close look at the teacher’s attitude towards content and language errors and points out the lights and shadows of assessment in CLIL while highlighting the need of disclosing further assessment practices in similar contexts.

Tradicionalment s’ha pensat que la traducció com a eina a l’aula de llengües estrangeres va quedar desaconsellada en el mètode directe. Així, des de llavors, molts docents han defensat la idea que la traducció és un recurs nociu per ensenyar idiomes, encara que, segons Cook (2010), no hi ha evidències que ho hagin provat científicament. Abans de continuar acceptant aquesta creença heretada del mètode directe, pensem que és necessari revaluar si la traducció va ser rebutjada per tots els seus exponents i si va ser realment possible excloure-la de les aules del moment. Per tant, l’objectiu d’aquest article és dur a terme una revisió teòrica sobre què va ser, quan i per què va sorgir el mètode directe, quin paper es reconeixia a la traducció dins d’aquest mètode, quina posició van adoptar els principals teòrics que el recolzaven i si aquests plantejaments van ser vertaderament aplicables a l’aula.

This paper aims at exploring the complexities of students’ interaction in a collaborative learning task set within a CLIL unit in the EFL classroom. By way of illustration, a sample from a 4th year classroom grade in a secondary school of Catalonia has been collected. The paper examines, through the students’ outcome, the impact of cooperative learning in a content-rich information swap task and discusses the role of content and language integrated learning in the classroom. This paper concludes with several implications for research and practice.

Mathematical modelling allows students to associate their learning with real situations. This paper analyzes an experience with engineering students when they were developing a mathematical modelling project using virtual forums, which considers the levels of interaction and depth of their messages and the influence of those forums on the modifications made to improve their work. The results mainly reflect that medium levels of interaction and low levels of depth were achieved, that the level of interaction depended on how the experience was performed, and that the highest levels of interaction and depth corresponded to the greatest improvements in the work. This opens up for future possibilities in the use of virtual forums by integrating modelling into university-level mathematics learning.

The aim of this paper is to identify the learning difficulties that children from 1st to 3rd grade of primary education have in the construction of natural numbers. Such difficulties do not come from teaching, but from mathematics themselves; in order to observe these difficulties, it is necessary to reduce the problem to the basics. Through Local Theoretical Models, as a theoretical and methodological framework, a Teaching Model has been designed by translating the formal component (J. Von Neumann Model) into a sequence of activities, with the use of manipulative material. We analyze the teaching experience and results highlight and explain the children’s difficulties in these activities.

This paper analyses the argumentative operations performed by pre-service teachers during a role play about setting down a nuclear waste deposit. The types of knowledge used for constructing their arguments when they try to reach a final agreement are also studied. The participants are undergraduate students from the degree of Pre-school and Primary Teacher Training at three different Spanish universities. Data collection includes video recordings of the role play. The findings point to the students’ ability to make statements and justify their arguments, although they find it difficult to use other argumentative elements in their speech. Moreover, social and scientific-technological knowledge are proved to be the most used types of knowledge in the participants’ search of a consensual decision about setting down the nuclear deposit.

This paper is a comparative analysis of "The Storyteller", by Saki, “Cuento de la niña condecorada” by Jorge Ibargüengoitia and "Super Dooper Jezebel" by Tony Ross: three works aimed directly or indirectly at younger readers, which share a single archetype or motif: that of the obedient, overly perfect young girl who behaves more like an adult than a child. This examination of the similarities and differences between the three versions of the good-girl story, from the perspective of reception theory, highlights the role played by the implicit reader as an intrinsic element of the work's artistic make-up. Using different resources, and from their very structure, the three works conjure up the presence of an active reader who sees events coming, sets off the ironic and humorous games, uncovers meaning, interprets and, above all, generates that magical alliance between work and reader that breathes life into the text. This paper traces the steps of a pre-determined reader in three stories that condemn a character who, in the quest for perfection, falls into the horrific trap of embodying it.

Future teachers must know, in addition to the basics of the subjects, the basis of the different methodologies that they will be able to use in the classroom. Project-based learning is a methodology which is currently used at schools so as to make a dramatic change possible in relation with the roles of teachers and students, as well as the development of skills. This paper presents a didactic research developed in the subject of Natural Sciences at the degree in Primary Education with the aim of analyzing what it means for students the use of this methodology in the development of an interdisciplinary project in the field of sustainable development. The results that come out of the analysis of the projects show a remarkable level of quality in their elaboration and students express a positive attitude towards their use.

The aim of this paper is to identify profiles of future teachers in secondary education based on their perception towards the acquisition of competences, relating them with the previous background. By means of an online questionnaire, data were collected from student teachers or recently graduated teachers in mathematics from the Master’s degree in Secondary Education Teacher-Training in different Spanish universities. The analysis has allowed to identify three profiles, which are correlated with a higher or lower perception of attaining the competences, either related to mathematical knowledge or to pedagogical content. Thus, results are in line with the theoretical model used to describe mathematics teachers’ knowledge. This study supports the need to design and implement interventions that improve the weaknesses of each profile during initial teacher training.

In this paper, we present a research work whose main objective is to reveal the opinions of active teachers about the implementation of a didactic proposal for Natural Sciences in Context, with an interdisciplinary approach, linked to a project-based methodology. The research shows the advantages and limitations indicated by teachers who did not apply the proposal with their respective students, and the opinions of those who did implement it in their classrooms. The latter showed social representations that are rooted in the educational community and would act as implicit obstacles when implementing innovative proposals.

The theory of didactic situations in mathematics postulates that learning is produced by adaptation to an antagonistic milieu, given the central role that this theory assigns to the adidactical situations (moments where the students’ autonomous production of knowledge takes place). However, the relevance of constructivist approaches is questioned by sociocultural theories, when referring to learning scientific contents. In this paper, we justify the importance of a dialogical-cooperative didactic model –in which teacher and students work together in the resolution of problems-situations– during the students’ first encounter with mathematical objects. This justification is based on the epistemological, ontological, semiotic and instructional assumptions of the onto-semiotic approach to mathematical knowledge and instruction.

In this paper we present some findings from a 3-year research project that sought to characterize epistemological representations on scientific thought competencies (STC) among elementary trainee teachers (ETTs) in three Chilean universities. In a first phase, the project delves in the representations of the ETTs as related to the notion of STC, which we analyze characterizing them as densely as possible from «antagonistic» epistemological spheres: moderate rationalism and positivist rationalism, by means of a questionnaire applied in 3 science teaching courses. The results suggest the coexistence of both epistemological representations, which has important implications in relation to the initial training process of future science pre-school teachers.

This paper presents a study based on an analysis of introductory lessons to biology and geology and to physics and chemistry in Secondary Education textbooks. The aims of this study are to characterize the view on the «nature of science» that is transmitted, to determine whether science is differentiated from pseudoscience and to detect whether certain concepts appear, by examining both the theoretical content of the textbooks and the recommended activities. The analysis reveals a lack of an introductory lesson in some books. Where such lesson is included, the text usually focuses on scientific method, paying little attention to the evolution of science, scientific models or other significant concepts. The image of science that is promoted, although it has positive aspects, is often deficient. In short, there is a lack of reflection on what science is and how it is constructed.

This paper reports a pre-service teaching experience, which combined the multiple intelligences theory with environmental education, in the context of a macro design-based research, with the mediation of a learning community through collaborative research. In this methodological framework, the teacher designed and applied a strategy about water with a group of 25 first grade students, including some children with functional diversity (Attention Deficit Disorder –ADD–, learning disabilities without diagnosis, and blindness). This was so designed to respond to the diversity of children in terms of ways of learning, and facilitate its diverse expressions, as well as to seek environmental literacy. The teacher’s achievements in the classroom are thus exposed with regards to teaching about water resources, drawing on the theory of multiple intelligences, together with the implications that collaborative research has for initial teacher preparation.

This paper presents a proposal for health literacy through the specification and definition of the competences that students must acquire during Compulsory Education. Eight areas of health were determined through a Delphi study, identifying the problems or health situations that students must know how to solve, as well as the competences to be developed and the learning contents necessary to face each of these problems. These learning contents constitute the instrument of analysis to verify to what extent those health situations are present in the official Compulsory Education curriculum. The studies carried out regarding mental and emotional health show that the prescriptive curriculum has some deficiencies that hinder the development of competences, which negatively affects health literacy.

In this paper we analyse the performance of 8th, 9th and 10th grade students (14, 15 and 16 years old respectively), attending Physics and Chemistry lessons, when assessing the design of scientific research on a precipitation problem identified in the dairy industry. Students’ performances are examined separately for each dimension involved in the design: identifying the issue to be studied, posing the hypotheses, planning the research and selecting the ending criterion. For the analysis, we collect participants’ individual proposals, which have to include the following tasks: selecting the best option, justifying their choice and modifying the alternative option so that it will be correct. The less adequate results correspond to the last two dimensions.

In this paper, we analyse how the epistemological and didactic models that a lesson study community assumes determine the way this professional development process is conducted, as well as its outcomes. To do this, we propose a reinterpretation of lesson study as a praxeology of the teaching profession, drawing on tools from the Anthropological Theory of Didactics. The analysis of three cases will evince the role that different epistemological and didactic models play in the organisation and development of the work of lesson study groups, and in the potential learning of teachers. Thus, we provide new theory-informed insights into lesson study.

This paper evaluates the past achievements and future challenges on the field of Science Education. It tries to offer a panorama of the most important consensus achieved by the research community and it synthesizes some essential elements of the paradigm emerging from science teaching in line with them (goals, theoretical foundations and curriculum prescriptions). Lastly, it analyzes the difficulties to face change and it submits proposals in order to invigorate it from a scientific perspective, as well as from an ethic and sociopolitical point of view.

This paper presents an innovative didactic proposal to treat some contents related to energy and the matter changes belonging to the physics and chemistry subject of third course of Compulsory Secondary Education. Its purpose is the approach of science to the real environment of students, through an everyday activity as is cooking. The proposal aims to encourage motivation and interest in science and the elimination of possible sexist attitudes. The proposal combines three practical activities: preparation of muffins, spherifications, and cooking of meat using different energy sources; and three ICT activities: analysis of TV spots, search of energy sources in a cooking program and presentation of an energy efficient kitchen. All activities are supported by the principles of recreational science and teamwork.

In this paper, we analyze the cognitive-linguistic skills (description, explanation, justification and argument) of 5 students in a technological course, Management of Agribusiness Production Program at the Universidad Tecnológica de Bolívar, in collaboration with Edupol. The study is set at an online course with convergent media, where students analyze industrial processes related to industrial chemistry. The methodology is qualitative with case study; the results show that the cognitive-linguistic skills of students, synchronously and asynchronously, can be enhanced by developing content and social writing through a dialogic communication, and creating a learning environment based on the principles of constructivism in online education.

A teacher’s knowledge is considered a significant factor contributing to their classroom performance and the promotion of mathematics learning in their students. This paper examines the knowledge deployed by a secondary teacher when working on the topic of similarity of triangles, focusing on the connections between subdomains within Pedagogical Content Knowledge in the model Mathematics Teachers’ Specialized Knowledge. Specifically, drawing on data from lesson observations and interviews with the teacher, it considers connections between the subdomains knowledge of mathematics teaching and knowledge of the features of learning mathematics. The results underline the relationship between research and practice, in that they bring to the fore specific connections between subdomains and their related categories and illustrate how these contribute to classroom decisions.

This paper examines the adequacy of different teaching strategies to scaffold students’ engagement in scientific practices. The participants are two secondary teachers and their respective groups of 9th grade students attending Physics and Chemistry. The task requires students to investigate the effectiveness of two toothpastes to prevent cavities. For the analysis we examine the discourse of both teachers during the implementation of the task and we code their interventions according to a framework for scaffolding strategies developed by Van de Pol, Volman and Beishuizen (2010). The results point to differences in the strategies employed by the teachers, which affect to students’ performances for planning and carrying out investigations.

This paper presents the research conducted to create a history-of-science-based resource that would introduce students to chemical formulas in secondary education in France. This elaboration is based on theoretical frameworks dealing with educational reconstruction of teaching-learning sequences and on the analysis of teaching practices. Preliminary empirical investigations conducted with students and some teachers show the need to articulate the registers of models, reality and language at the submicroscopic and macroscopic levels for learning the concepts of chemical change and chemical reaction. The first part of the resource is implemented in the classroom. The second part that allows to write the reasons justifying the chemical formulas is rejected by two teachers. This leads to a first proposal of the evolution of the resource.

En aquest article s’avaluen les Competències Ambientals (CA) del professorat en formació inicial a l’inici i a l’acabament del grau de mestre d’educació primària a una universitat espanyola. S’ha desenvolupat i validat un qüestionari amb la finalitat d’avaluar sis CA en relació amb els coneixements, actituds i comportaments ambientals dels estudiants de la mostra (n=3419. Els resultats de l’estudi revelen que al professorat en formació inicial li manquen CA que els permetin educar ambientalment a l’alumnat. A més, s’ha pogut veure que no existeixen diferències en el seu grau d’adquisició entre l’alumnat de primer i quart curs del grau de mestres d’educació primària. Com a resultat, es qüestiona el paper de la universitat i els nous programes dissenyats en el procés de convergència cap a l’Espai Europeu d’Educació Superior i s’assenyalen algunes propostes de millora.

Aquest treball aborda la reintroducció d'estratègies didàctiques en ciències experimentals al món rural de la província de València que va tenir lloc a partir dels anys 60 del segle passat. Per a això s'han analitzat documents relatius al Patronat d'Educació Rural (1958-1985), organisme depenent de la Diputació de València constituït amb l'objectiu de millorar l'educació en zones rurals de la província. La metodologia utilitzada en la recerca es fonamenta en el mètode analític descriptiu mitjançant la cerca, revisió i anàlisi de fonts històriques i iconogràfiques dipositades en l'Arxiu de la Diputació Provincial de València. La recerca pretén posar de manifest l'abast i el paper essencial que van tenir els mestres i mestres del Patronat d'Educació Rural en la modernització i europeïtzació educativa del món rural valencià.

Lexical bundles (LBs) have been described as the ‘building blocks of discourse’; in addition to being highly frequent in writing and reducing processing time for readers and writers, they also perform important functions in language. LB choice, however, can vary according to genre, discipline, and different sections of the same text, which poses a challenge for novice L2 writers. This paper explores the use of LBs in a learner corpus of bachelor dissertations written in English by Spanish L1 students in linguistics and medicine, and compares it with published research articles in the same disciplines. By focusing on the introduction and conclusion sections, we identify the most frequent 3-, 4- and 5-word bundles in the corpora, to later study their types, structures, and functions. The results show differences in the use of LBs across disciplines, genres and sections, suggesting pedagogical implications for the inclusion of LBs in the L2 writing curriculum.

Poland’s foreign language teaching and language policy have been affected by tremendous changes in the last decades. Not only bilingual sections in secondary schools have mushroomed, but also international schools with instruction in a foreign language, mainly English, within the International Baccalaureate Diploma Programme (IBDP) started their existence in 1993. This paper draws on the translanguaging pedagogy as used in the selected secondary schools with IBDP. The schools provide evidence for the stance that most students, if not all, are multilingual in such teaching environments. Therefore, they apply multiple strategies to benefit from their linguistic repertoires. In addition, the teachers perceive such practices as positively affecting the students’ performance and allowing them to more rapidly acquire the imparted content as well as further develop their linguistic proficiency. The overriding aim of this study is to identify the situations when the students translanguage and analyze their linguistic behaviour as well as explore the functions of students’ translanguaging practices.

Aquest treball es planteja estudiar el paper de la Química Verda a l'educació científica per contribuir, des d'aquest camp, a la Ciència de la Sostenibilitat i, per tant, a la transició cap a societats sostenibles. Es mostraran uns primers resultats d'una recerca duta a terme sobre l'atenció que l'ensenyament secundari i la pròpia recerca en el camp de la didàctica de les ciències estan prestant a les aportacions de la Química Verda, i la possibilitat de la seva incorporació en la formació de la ciutadania i l'adopció de mesures necessàries per contribuir a la construcció d'un futur sostenible. Es pretén així respondre a les nombroses crides perquè l'educació, tota l'educació i molt en particular l'ensenyament de les ciències, pari esment als problemes i desafiaments que afecten a la humanitat, contribuint a la cerca de solucions i a la formació d'una ciutadania responsable i preparada per a la presa de decisions.

Basats en la teoria APOE com a marc teòric i metodològic, investiguem, des d'una postura cognitiva, les estructures mentals necessàries per construir el teorema per al canvi de base de vectors (TCBV). Amb el propòsit d'analitzar la forma en què estudiants universitaris ho aprenen, es va dissenyar una descomposició genètica (DG) per al teorema. Mitjançant tres casos d'estudi es mostra com estudiants d'aquests casos construeixen el concepte de coordenades d'un vector, però tenen dificultats per utilitzar-ho en la construcció de la matriu de coordenades de vectors. Aquesta dificultat està vinculada al fet que no han coordinat els processos involucrats en termes del quantificador. Específicament, es mostren les dificultats en la construcció del TCBV com a objecte i el paper determinant que exerceix el concepte de combinacions lineals en el TCBV.