Responsive learning design: Epistemic fluency and

British Journal of Educational Technology doi:10.1111/bjet.12704

Vol 49 No 6 2018

1162–1173

Responsive learning design: Epistemic fluency and generative pedagogical practices Yishay Mor

and Rotem Abdu

Yishay Mor is the head of the Centre for Innovation and Excellence in Education. His research interests are in the design and use of technology for social and individual empowerment, through opening opportunities for participatory learning, collective action and expression. Rotem Abdu is a lecturer at Levinsky college of Education. His research interest is in designing digital dynamic mathematics environments and understanding how to empower teachers to design and enact meaningful learning experiences utilizing these environments in mathematics classrooms. Address for Correspondence: Yishay Mor, Gush Halav 2, Tel Aviv, Israel. Email: [email protected]

Abstract Several decades of research and development have produced a rich ecology of technologies designed to support active, collaborative constructionist pedagogical practices. Nevertheless, many teachers are reluctant to use these technologies in their teaching or fail to devise learning designs which leverage their qualities. We argue that this tension reflects a dissonance between the epistemic practices (manners of constructing knowledge) implicit in teachers’ pedagogical practices and the ones embodied in the technology. We demonstrate this argument in the case of Dynamic Mathematics Environments (DME) through the epistemic practice of identifying invariants, and its dynamic manifestation in the technology, and illustrate it further with examples from an online course on CSCL. For teachers to effectively design learning experiences in a technology rich environment, they need to develop their capacity to critically assess the epistemic and pedagogical practices associated with this environment, identify a set of target epistemic practices and carefully devise the pedagogical practices which will engender these. We call these “generative pedagogical practices.” To do so, teachers need to actively participate in activities that would provide them with opportunities to make that epistemic change: building, experimenting with and designing for learning in diverse environments. Sometimes, applying such an epistemic disposition, requires supressing old practices of activity design.

Introduction In their seminal paper, Morrison and Collins (1995) argue that the purpose of constructivist learning environments is to create opportunities for learners to develop epistemic fluency: “the ability to identify and use different ways of knowing, to understand their different forms of expression and evaluation, and to take the perspective of others who are operating within a different epistemic framework” (p. 40). This claim seems even more convincing today, in the age of post-truth and abundant information. It would seem to resonate with more recent calls for education to promote epistemic literacy, or as Barzilai and Chinn (2017) call it “apt epistemic performance,” except that Morrison and Collins acknowledge the diversity of ways of knowing, and their correspondence to particular cultures and communities of practice. Indeed, one could argue that a culture or community of practice is defined by the ways in which it creates and © 2018 British Educational Research Association

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Practitioner Notes What is already known about this topic • In this age of information abundance and diverse and rapidly changing cultures of knowledge, it is important to cultivate epistemic fluency – as Morrison and Collins (1995) define it: “the ability to identify and use different ways of knowing, to understand their different forms of expression and evaluation, and to take the perspective of others who are operating within a different epistemic framework.” • Several decades of research and development have produced a rich ecology of technologies designed to support active, collaborative constructionist pedagogical practices. Nevertheless, many teachers are reluctant to use these technologies in their teaching or fail to devise learning designs which leverage their qualities. What this paper adds • An alternative view on the tension between teachers’ pedagogical practices and educational technology is through the lens of the implicit target epistemic practices of learners. • Specifically, Dynamic Mathematics Environments (DME) embody an epistemic practice of identifying invariants. This is a core domain epistemic practice, but teachers are not necessarily aware of it, and in particular of its manifestation in DME • Teachers need to first experience this epistemic practice themselves, and then consciously weave it into their learning designs. Implications for practice and/or policy • Teacher education should go beyond content and highlight the core epistemic practices of a knowledge domain, and their manifestation in various technologies • When designing learning experiences, teachers need to identify target epistemic practices, and devise pedagogical practices which will catalyse their uptake by learners. We call these “generative pedagogical practices” • Specifically, in the field of mathematics education, teachers need to acknowledge the practice of identifying invariants, and its dynamic form in DMEs.

communicates knowledge. Moreover, these structures appear to be implied and implicit, in the sense that members of a community assume that their way of constructing knowledge is obvious and universal. The importance of epistemic fluency has been highlighted in the context of professional education of knowledge workers (Goodyear & Ellis, 2007; Markauskaite, & Goodyear, 2014) and teachers (Goodyear & Markauskaite, 2009). Inspired by Symour Papert, we argue that all school and university students should be considered knowledge workers, insofar as their work is to acquire knowledge. Furthermore, technology is constantly changing the ways in which we create knowledge, making it essential for learners to develop a reflective and critical view of these. Like Morrison and Collins above, Sandoval, Bell, Coleman, Enyedy, and Suthers (2000) also consider the qualities of learning environments aimed at promoting desired epistemic practices. Yet both neglect the role of the teacher in these environments. Our main argument in this paper is that the best designed learning environment will fail to engender the expected epistemic behaviour unless teachers are aware of this behaviour and design their pedagogical behaviour accordingly. We illustrate this argument through an analysis of the use of dynamic geometry environments, and a vignette from a CSCL course. © 2018 British Educational Research Association

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Morrison and Collins (Ibid) suggest three ways in which technology can contribute to people’s epistemic fluency: as communication environments, as construction kits, and as simulation environment for epistemic games (we’ll discuss epistemic games below). All three have been explored extensively in the field of mathematics education. Some technologies brought about new ways to enhance instructional delivery by the teacher or increase processing power by relieving learners from complex calculations. Other solutions, which are at the focus of this paper, were meant to provide new ways to learn mathematics with dynamic, digital representation of mathematical ideas (Hoyles & Noss, 2009; Tran, Smith, & Buschkuehl, 2017; Young, 2017). These spawned several genres of educational technologies such as the microworlds (eg, Hoyles, Noss, & Adamson, 2002; Kynigos, 2004), dynamic mathematics environments (eg, Hadas, Hershkowitz & Schwarz, 2006; Leung, 2003; 2011) and recently also technologies for embodied interaction (eg, Abrahamson & Howison, 2010; Jackiw & Sinclair, 2017). Specifically, dynamic mathematics environments (DME) offer diverse ways to design environments for learners to explore mathematical concepts, by direct manipulation of dynamic visual representations of these concepts (Hoyles & Noss, 2009). In contrast with solutions that are meant to provide the student with processing and calculating power (eg, Wolfram-Alpha; www.wolframalpha.com), DME provide students with objects to think with (see Papert, 1980). The dynamic attribute changes how mathematical ideas can be perceived: not prototypical static examples drawn with pen and paper, but infinite manifestations of a single mathematical concept. One particular DME, GeoGebra (www.geogebra.org) seems to dominate its category in the last years and will be the focus of the examples in this paper. GeoGebra is an open-source DME that affords the creation of a wide range of mathematical objects within the context of a single learning environment (Hohenwarter, Hohenwarter, & Lavicza, 2009; Tomaschko, Kocadere, & Hohenwarter, 2018). DME, such as GeoGebra, Cabri Math and the Geometer’s Sketchpad, carry a promise to bring a significant change in the way mathematics is being taught at school (Clark-Wilson, Robutti, & Sinclair, 2014). Yet, as a recent ed-tech survey demonstrates (http://goo.gl/tR7yr2, see also, Budinski, 2013), despite acknowledging them as powerful technologies for learning mathematical ideas, mathematics teachers rarely use them in their classrooms. A second-order meta-analysis performed by Young (2017) suggests that, compared to technologies that enhance instructional delivery by the teacher or increase processing power, the actual effect of DME on mathematics education is still very modest. Young suggests two explanations for this finding. First, DME are considered “young” in comparison with other genres, with insufficient empirical evidence for such a second-order meta-analysis. Second, that the use of DME is considered more complex for learning and instruction, since DMEs do not simplify learning and instruction but require the student and the teacher to engage in unfamiliar practices (Sinclair & Yurita, 2008). Other factors contribute to the underuse of DME in classrooms such as fear from technological failure, and limited professional development (Anthony & Clark, 2011; Litlle, 2009; Trouche, Drijvers, Gueudet, & Sacristán, 2012) and lack of control over “what was learned” that leads to exacerbation of misconceptions (Abdu, 2015). Teachers are also not always convinced that using DME would help them achieve curricular goals – a critical requirement for mathematics teachers (Anthony & Clark, 2011). This echoes back to the magnificent failure of early attempts to foster learning mathematics with LOGO programming: while teachers were able to see educational value in such activities for learning mathematics, it was perceived as incommensurable with curricular goals and ultimately scarcely used in mathematics classrooms (Litlle, 2009; Trouche, Drijvers, Gueudet, & Sacristán, 2012). © 2018 British Educational Research Association

Responsive Learning Design    1165 We propose here a somewhat nuanced reading of the evidence. Our claim is that every pedagogical practice (i.e., manner of teaching) reflects the teacher’s perception of a corresponding epistemic practice, a manner of knowledge construction. Similarly, the implicit functionality of educational technology reflects the designer’s epistemology. When the teacher’s epistemic model is misaligned with that of the technology designers, she will not be able to utilize the technology in her design of learning experiences for her students. To illuminate this argument, we inspect a specific epistemic practice – identifying invariants – and consider its role in trainee teachers’ learning designs. Epistemic and pedagogical practices A practice is a recognizable pattern of actions used by individuals in a given context to achieve specified aims. Since this context often includes other individuals, practices tend to be socially interdependent; i.e., both individual and social. There are various ways in which one masters a practice: participation, imitation, interaction and exploration. In particular, epistemic practices are the “socially organized and interactionally accomplished ways that members of a group propose, communicate, assess, and legitimize knowledge claims” (Kelly & Licona, 2018, p. 140). Sandoval et al. (2000) draw a distinction between epistemic understanding – learners knowledge about constructing knowledge, and epistemic practices – the cognitive and discursive activities that lead to epistemic understanding. Collins and Ferguson (1993) introduce the constructs of epistemic forms and epistemic games. Sherry and Trigg (1996) offer these definitions: An epistemic form is a target structure that guides the inquiry process. It shows how knowledge is organized or concepts are classified, as well as illustrating the relationships among the different facts and concepts being learned. The completion or creation of the structure is the object of the epistemic game. An epistemic game is a set of moves, entry conditions, constraints and strategies that guide the building of the epistemic form. The rules may be complex or simple, implicit or explicit. (p. 39)

The notion of epistemic games is akin to the concept of epistmic practice, which we prefer. A discussion of the nuanced distinction between the two is beyond the scope of this paper. Suffice to say that whereas the objective of a game is intrinsic (the completion of an epistemic form), the objective of a practice is either intrinsic or extrinsic (establishing knowledge, as a basis for future action). Arguably, the overarching objective of education in any domain is not just to deliver knowledge, but to enable learners to acknowledge, adopt and ultimately master the epistemic practices of the domain (Laurillard, 2002). This can be done by utilizing generative pedagogical practices: engaging students in practices designed so that by imitating or interacting with them students will participate in and adopt the desired epistemic practices. A teacher can either display an epistemic practice for the students to copy, prompt and correct the students’ actions, or set a task for exploration where the target practice will yield the expected results. In effect, this is what teachers do, albeit in a tacit manner: when a teacher talks to her students for 90 straight minutes, she assumes that they will construct knowledge by passively absorbing her thought process. When a teacher solves an exercise on the board, she assumes that her students will construct their knowledge by copying and memorizing her solution. Yet neither are practices by which scientists and mathematicians construct their knowledge. Sandoval et al. (2000) propose five epistemic practices for scientific inquiry and identify corresponding design principles for learning environments. To these, we add our suggested examples of related pedagogical practices (Table 1):

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Provide epistemic forms for students’ expression of their thinking Give distinct forms of knowledge distinct representations Design representations that can be coordinated and linked Representations should prompt and support epistemic (not just conceptual) practices Communicate evaluation criteria and connect them to representations

Explicit articulation and evaluation of one’s knowledge Coordinate theory and evidence

Hold claims accountable to evidence and criteria

Develop representational fluency

Make sense of patterns of data

Design principle

Epistemic practice

Prompt students to share and discuss their thought processes. Ask students to formulate theories and seek evidence to support them. Demonstrate a worked example using linked representations to make sense of patterns of data Provide explanations utilizing multiple representations and ask students to connect them. Use the agreed evaluation criteria in classroom discussions of student claims.

Pedagogical practice

Table 1:  Mapping pedagogical practices to Sandoval et al (2000)’s epistemic practices and design principles

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Responsive Learning Design    1167 Invariance Freudenthal (1991) proposes the idea of re-invention of mathematical ideas. Ideally, claimed Freudenthal, students should engage in activities in which they deal with problems earlier encountered by mathematicians, and try to solve them with the means they have. With this in mind, the activities and resources we offer our students should embody the mathematical epistemic practices we wish to engender. Consequently, the objects we include in these activities should allow students to actively inquire, re-invent and articulate mathematical ideas compatible with curricular goals (Leung, 2011; Leung, Baccaglini-Frank, & Mariotti, 2013). One of the most fundamental epistemic practices of mathematicians is identifying invariants. This is also a prime example of an epistemic practice modulated by technology. In the following sections, we “zoom in” on this theme, do demonstrate the importance and complexity of aligning pedagogical practices with epistemic practices of a given knowledge domain. Invariance is a property of a class of objects that remains stable under a class of transformations: they represent the properties of a mathematical concept. Identifying invariants and utilizing them in argumentation and action is a key epistemic practice in Mathematics. As Vergnaud (1982) notes, one of the greatest challenges of mathematics education is creating the conditions for learning about invariants as theorems-in-action: modes of action that are de facto conditioned on intuitive recognition of an invariant. Learners then need to articulate the underlying invariants, to make these theorems-in-action part of their mathematical discourse. Invariance is central to the idea of learning with dynamic objects. In DME, an invariant is a property of a dynamic object that does not change as a result of dragging (Leung, 2003). Learning an idea when interacting with a dynamic object is bounded by the ability to identify the “things” that remain intact (i.e., invariants) when other ‘things’ change (i.e., variants). We argue that in order to align the use of DME with curricular needs, teachers need to acknowledge and utilize this manifestation of invariance. Take for example the case of a right triangle that is defined by two perpendicular segments in GeoGebra (Figure 1, up-left). The ends of these segments are free but dependent: one can move points A or C, but the whole object (ABC) will change accordingly to maintain perpendicularity between segments AB and BC. Building a third segment, AC, creates

Figure 1:  Up - Building (left to right) a right-triangle based on perpendicular segments, AB and BC. Down – Dragging vertex C and extending segment BC (left); then dragging vertex A (right) [Colour figure can be viewed at wileyonlinelibrary.com]

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a dynamic right triangle ∆ABC. Dragging any of its vertices is possible; but since the whole figure was constructed upon a predefined pair of perpendicular segments, then any dragging of the vertices will not change the invariant perpendicularity between segments AB and BC (Figure 1). This model also has the potential to simulate any right triangle in the Cartesian space. This is a product of the degrees of freedom that are allowed: the object’s segments can be stretched and the object as a whole can be rotated. The invariant – perpendicularity between segments AB and BC – is a property of a right triangle. Creating a dynamic mathematical model in a DME can also elicit acknowledgements of the sufficient conditions that define a mathematical idea. In the case illustrated in Figure 1, for example, the two perpendicular segments are sufficient conditions that define a right triangle. Note, however, that for some mathematical ideas such as the square and the linear line there may be more than one set of satisfactory conditions – thus, there are several ways to build these objects with a DME. When a teacher builds a mathematical object with a DME to simulate mathematical ideas, he needs to decide what should be the invariants she builds with, and what other invariants might emerge later on. The object created should allow manipulation in as many degrees of freedom as possible, while keeping the properties of the objects in a way that aligns with the target mathematical concept. Constructing mathematical concepts by identifying and manipulating invariants with a DME is an active learning process, in line with Piagetian constructivism (eg, Piaget, 1968; Piaget & Inhelder, 1969), as further elaborated in the Constructionist approach (Hoyles & Noss, 2009; Papert, 1980) and Freudenthal’s “re-invention” (Freudenthal, 1991). Similarly, research in mathematics education highlights the importance of learning design that affords active inquiry (eg, Geiger, 2017; Leung, 2017; Schoenfeld, 2007). However, teachers find it challenging to orchestrate such learning experiences, and are concerned about compatibility with curricular goals (Anthony & Clark, 2011; Lester, 1994; Schoenfeld, 2007). As a result, teachers often tend to refrain from applying inquiry learning within classes, thereby neglecting the constructivist approach for mathematical thinking (Schoenfeld, 2007; Trouche, Drijvers, Gueudet, & Sacristán, 2012). Incorporating DME in the classroom requires a change, in curricular goals or in the mapping of pedagogical practices to existing curricular goals. In this paper, we focus on the latter. Epistemic practices: from static to dynamic Teachers’ ability to design learning experiences that properly utilize DME requires a shift from static to dynamic perception of invariance. Teachers’ construction and use of dynamic objects in DME should be guided by pedagogical practices that encourage students to discern invariant properties of mathematical objects. This may yield an enrichment of mathematical activities, yet, as we will show below, depends on deep understanding of the invariance principle. To illustrate our claim, In Appendix I we present three case studies, in which teachers designed geometric models with GeoGebra. In the first case, in-service teachers that were presented (but did not interact) with various dynamic GeoGebra simulations during their studies were asked to construct geometric models on their own. In their construction they created mere static objects, without attention to the invariance principle of these objects. In the second case, a lesson was planned by a pre-service teacher who participated in constructing several dynamic GeoGebra models. Analysis of that lesson design shows that the invariance principle was applied by the teacher, but still constrained by what seems like remnants of traditional epistemic practices. The third case study will focus on a pre-service teacher who participated in a course for building lesson designs with GeoGebra. She created a lesson design that utilized the invariance principle in © 2018 British Educational Research Association

Responsive Learning Design    1169 a way that is conducive to constructivist learning the properties of a parallelogram. Each one of these cases displays a different pedagogical practice, suggesting an implicit assumed epistemic practice (Table 2). A vignette: harnessing the epistemic affordances of prevalent technology DME are a prominent class of meticulously designed learning technology. It is easy to acknowledge the epistemic qualities of such technology and prescribe appropriate pedagogical practices. However, when a similar phenomenon concerns prevalent technology, designed with no educational objectives in mind, it might unfortunately elude us. To make effective use of technology Table 2:  Pedagogical practices and corresponding implicit epistemic practices from the three cases in Appendix I Case 1 Pedagogical Practice 1. Ask a student to construct a mathematical object on the board. 2. Discuss the results with the class 3. Repeat until a student produces the desired outcome. Implicit Epistemic Practice Learners can re-discover mathematical concepts by constructing mathematical objects with minimal guidance (“Naïve” constructionism). Notes Given the long history of critique of such naïve approaches, from John Dewey to Paul Kirschner, it is no surprise that it fails. Yet again and again enthusiastic and unexperienced teachers fall into this trap. Case 2 Pedagogical Practice (deduced from the model the teacher built) 1. Present students with a representation of the mathematical concept in multiple modes. 2. Allow the students to interact with the representation in a constrained model. 3. Discuss their insights. Implicit Epistemic Practice Learners construct a socio-cognitive model of mathematical concepts by interacting with structured models that link different representations of these concepts. Notes The learning design presented by the teacher in this case suggests a pedagogical practice founded on a healthy intuitive understanding of the target epistemic practice. However, it replicated a traditional design, thus failing to acknowledge the nuances (and epistemic affordances) of dynamic representations. Case 3 Pedagogical Practice 1. Guide students in the construction of a dynamic model of a mathematical object. 2. Ask students to explore the model freely in groups. 3. Convene a plenary discussion, where students propose conjectures about the model and these are evaluated by the class. Implicit Epistemic Practice Learners construct a socio-cognitive model of mathematical concepts by interacting with structured dynamic models that reify these concepts and are congruent with their key features. This knowledge is consolidated through conversation adhering to scientific norms of discourse. Notes The learning design in this case extends and adapts the guided constructionist pedagogy of case two to account for the dynamic manifestation of the invariance principle. © 2018 British Educational Research Association

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in our learning design, we must be aware of – and critical of – the ways in which technology constantly changes our epistemic practices. Consider the use of videos and social media on mobile phones. A recent NY times paper tells the story of racial riots in Sri Lanka spurred by videos showing false evidence of conspiracy theories. This is an extreme and undesired example of a global phenomenon: we all construct knowledge through sharing videos (and other constructs) on social media. Lotan, Graeff, Ananny, Gaffney, and Pearce (2011) demonstrate this through analysis of information flow and political action in the Arab spring. As educators, we need to acknowledge this epistemic practice, and help learners develop a more robust and critical version of it. Dabbagh and Kitsantas (2012) consider the epistemic practices of self-regulated learning associated with PLEs (personal learning environments) built on social media, and propose a set of corresponding pedagogical practices – albeit without using the epistemic / pedagogical practice terminology, or going into the operational details of these practices. Such considerations were at the background of a learning design implemented by one of the authors in two recent courses on CSCL for pre-service teachers. CSCL is concerned with providing learners with digital technologies that foster group learning in face-to-face and online (synchronous/asynchronous) settings (Stahl, Koschmann, & Suthers, 2006). CSCL epistemic practices are tightly connected to dialogism (Bakhtin, 1993) and dialogic thinking (Wegerif, 2015) by means of providing learners with the opportunities to develop their own voices in the process of group learning. Dialogic education in CSCL contexts gained even more leverage with the presentation of web 2.0 – where knowledge is not only broadcasted from a central hub but distributed between many agents, or, voices (Wegerif, 2015). By contrast, dominant forms of online courses (eg, xMOOCs and common VLEs) are inherently monologic, where the teacher uses the digital medium to broadcast information and assign students individual learning tasks. In an attempt to bridge this divide, the author projected CSCL learning and teaching theories onto the now common epistemic practice of sharing “how-to” videos on YouTube. In one task, each pair of students was asked to identify one software tool they find conductive for learning, create a 7-8 minutes YouTube video tutorial for this tool and analyse the type of learning it may support. The result was 32 YouTube videos about 22 different digital tools, 5 of which were unfamiliar to the lecturer. In a second task, students read papers about group learning or CSCL, and were asked to choose a concept out of a list provided them by the lecturer and create an explanatory movie that deepens and widens – by choosing other resources of their will – the explanation of their chosen concept. All videos were collated in a YouTube channel which served as a platform for dialogue: the contributions of students in early assignments were used as resources by other students in latter assignments. For example, students were asked to choose a digital tool they were not familiar with and two group learning behaviours out of their friend’s movies and create a lesson plan that utilizes them. As all contributed to and were contributed by this shared repository; voices may remain alive until the end of these courses, at least, and wishfully beyond them. This design adopts an emergent epistemic practice, modulates it by reference to a relevant learning theory, and devises a generative pedagogical practice for it. Conclusions Our overarching claim in this paper is that in order for teachers to design effective technology-enhanced learning experiences, they need to be minded to the core epistemic practices of the knowledge domain and tune their pedagogical practices accordingly. Furthermore, teachers need to be critically minded of the ways in which technology is driving the evolution of epistemic practices and devise pedagogical practices which respond to these in a proactive manner. © 2018 British Educational Research Association

Responsive Learning Design    1171 To illustrate this claim, we provided three cases in which pre/in-service teachers have built GeoGebra models, and a vignette from two CSCL courses taught by one of the authors. The first two cases exemplify epistemic gaps by teachers, manifested as misuse of the invariance principle. The third case provides an outlook on (a potential genre of) activities designed in a course for pre-service teachers, which utilize the “good-old” principle of invariance in order to design learning with DME, compatible with curricular goals. The three cases stress the need for teacher training programmes that address this gap in epistemic practices – even among teachers that are supposedly familiar with DME. For that matter, we maintain that teachers need to participate in activities that would provide them with opportunities to make an epistemic shift: they should be engaged in building such models in addition to observing other (i.e., lecturers, teacher trainers) who do so. Thus, applying constructivist pedagogical practices, in which invariants are being reinvented by teachers, in professional programmes for mathematics teachers. Lecturing with DME, without teachers’ (or students’) hands-on experience and building of objects, has the potential to limit learning in terms of achieving mathematical thinking that is dynamic (see also, Leung, 2011; Little, 2009). This observation also carries a nesting effect: if a teacher is not familiar with the invariance principle, there are good chances that her students too will not assume such an epistemic practice. The change of pedagogical practices towards what we call “the pedagogy of invariance” was exemplified in the third example, which we consider to be fruitful for active learning. In case 3 above, pre-service teachers were given opportunities to participate in activities that utilize epistemic practices compatible with the pedagogy of invariance. Particularly, they were engaged in building GeoGebra models as well as observing others who do so, rather than receiving complete models or merely observing their lecturer. As a result, students learned how to design a lesson relevant to curricular needs which exploit the invariance principle. Finally, the vignette from the CSCL courses highlights how the evolution of epistemic practices is ubiquitous and elusive. As technological developments open up new possibilities for us to interact with the world, other people and ourselves, they inevitably facilitate new ways of creating knowledge. Some productive, some less so. When designing a learning experience in a technology-rich environment, teachers need to be critically aware of the emergent epistemic and pedagogical practices associated with this environment, acknowledge underlying theories of learning and teaching, identify a set of target epistemic practices and carefully devise the pedagogical practices – and the technological configuration to support them – which will engender these. Consequently, teachers need to be trained to identify new epistemic practices and implement learning designs that make them explicit and open them to critical debate. Acknowledgements We would like to thank Mr. Dvir for letting us use his lesson design, and the anonymous teachers who agreed that we share their works in this paper.

Statements on ethics, open data and conflict of interest The data used in this paper were obtained from the field notes of one of the authors and his colleagues, with the informed consent of the individuals participating in the described activities. In compliance with the institute’s ethical policy, the data were not analysed until the subjects had completed their courses, in order to avoid any conflict of interests. All names have been changed and all identifying details have been removed to illuminate any risk to subjects’ privacy.

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