Introduction and aim

The last decade has witnessed several concerted movements towards an integrated science, technology, engineering, and mathematics (STEM) education philosophy (e.g. Peterman, Daugherty, Custer, & Ross, 2017). Integrated STEM is typically invoked when discussing education policy, curricula and economic competitiveness, but the acronym has also become a cornerstone of education for so-called twenty-first-century skills. STEM as an educational enterprise has grown in importance during the past 10 years, particularly in the USA, UK, and other Anglo-Saxon countries (Banks & Barlex, 2014; Barlex, 2011). Albeit so, criticism against STEM approaches has also been put forward and includes, for example, that it may lead to a conflation of science and technology, or that the “T” and the “E” often tend to be downplayed in favour of the “S” and the “M” (e.g. Bers, Seddighin, & Sullivan, 2013; Sanders, 2009). Arguments have consequently also been put forward for a completely discipline-based STEM education (Henderson et al., 2017). There is therefore a certain vagueness around the actual concepts of STEM, and Pitt (2009) notes that:

Some people define any activity that involves any of science, technology, engineering or mathematics as a STEM activity; others argue that intrinsic to the concept is some linking of two or more of the component areas of learning, and that real STEM must be more than the sum of its parts (p. 41).

The root of this ambiguity arises from the fact that science, technology, engineering and mathematics as disciplines are not necessarily connected in neither content nor pedagogy (e.g. Tang & Williams, 2018). Therefore, a great challenge for teachers in STEM subjects is to design classroom activities that integrate two or more of the subjects in their teaching in both a meaningful and relevant way (Bell, 2016; de Vries, 2017; Kertil & Gurel, 2016; Margot & Kettler, 2019; Radloff & Guzey, 2016). In short, STEM teaching needs to be authentic (cf. Williams, 2017), and, in Pitt’s words, “more than the sum of its parts”.

In recent years, models and modelling has been argued as a means to increase relevance and authenticity in the STEM disciplines (e.g. Banks & Barlex, 2014; France, 2018; Gilbert, 2004; Herrington, Reeves, & Oliver, 2010; Justi & Gilbert, 2002; Kertil & Gurel, 2016; Rau, 2017; Turnbull, 2002). This is not only because modelling is central to the disciplines themselves as authentic practice in laboratories and workshops (Roth, 1995), but also since modelling is considered a fundamental aspect of STEM instruction. Two decades ago, Gilbert, Boulter, and Elmer (2000) flagged the importance of modelling and models in pursuing an authentic science and technology education, in lucidly stating that:

‘Authentic’ educations in science and technology must reflect the natures of the parent disciplines as far as is practicable. Modelling and models are common to both, thus providing a potential bridge between science education and technology education. […] The purpose of modelling in both fields is to facilitate communication through a visualisation of the relation between the intention and the outcome of the activity (p. 3, 17).

As part of the same cogent line of thinking, Davies and Gilbert (2003) also argued that models and modelling could forge natural links between STEM disciplines such as science and design and technology, due to certain similarities in modelling practices. For example, in chemistry and physics, both teachers and students utilize various atomic models, and in technology and engineering, conceptual and physical models are used to represent and test various designs. Through processes of modelling in STEM education, the disciplines become bound by a synergistic relationship, often requiring a learner to transit between the learning areas while engaging scientific, mathematical and technological activities, which often render these processes interdependent (Gilbert et al., 2000).

We are aware of the accepted importance of models and modelling in STEM education literature, but at the same time assert that there is limited prior research on the nature of modelling as a bridge between STEM disciplines. Therefore, this commentary expands upon the position that models and modelling can be used as a basis to foster an integrated and authentic STEM education and STEM literacy. In reinforcing this argument, the aim is to synthesize key publications that document relationships between authenticity, models and modelling, and STEM education. We conclude by providing implications of the presented contributions for STEM education, across all the four disciplines.

Authentic learning as a key component of STEM education and STEM literacy

Science, technology, engineering, and mathematics as practices have been dependent on one another for centuries, which could account for the common conflation of them in public discourse. The evolution of modern science from the 16th and 17th centuries onward was largely dependent on the parallel development of instruments and laboratory equipment (Ihde, 1993). Galilei’s telescope is one explicit example of what we could term, together with Ropohl (1997), science as “applied technics” (p. 66), while Newton’s laws were penned in the “language” of mathematics. Conversely, modern technological development is equally unthinkable without its connection to science, for example, in industrial laboratories and in modern genetic engineering and nanotechnology (de Vries, 2001; Feenberg, 2006). However, from an epistemological point of view, these disciplines constitute different fields of knowledge, because a scientist studies nature to uncover its laws, whereas the technologist and engineer solve problems with workable technological solutions. Mathematicians, in turn, aid both scientists and technologists with the analytical tool of mathematics. The previously mentioned equivocalness between the subject-specific and the interdisciplinary aspects of STEM may in part emanate from the fact that although science, technology, engineering and mathematics are separate epistemological fields, they are closely related in scientific and engineering practice, not only historically, but particularly today (cf. Pitt, 2009).

With reference to an Australian national curriculum document, Williams (2017) points to another built-in ambiguity of STEM literacy. STEM literacy should relate both to goals of national economic growth and the development of the individual student in terms of acquiring knowledge, attitudes and skills to identify real-world problems through an understanding of the characteristic features of the STEM subjects. In other words, the concept has both vocational and general educational connotations (Williams, 2017). We argue that in terms of educational settings, STEM literacy aims for general educational goals, but that these goals need to address authentic issues by incorporating two or more of the STEM disciplines (Sanders, 2009). Incorporation should not be understood as creating mere mergers between science, technology, engineering and mathematics but rather as an interdisciplinary cooperation on equal terms, which considers the central epistemological concerns of each discipline as well as the rich historical heritage and common concepts and practices.

Designing authentic learning scenarios is therefore one of the key challenges in education interventions that aim for STEM literacy (Ciolan & Ciolan, 2014). Although the concept of authenticity is ubiquitous, it is also contested (Anker-Hansen & Andreé, 2019). In this commentary article, we adhere to a socio-cultural conception of authenticity where it is defined as students’ participation in practices and activities of professional scientists and technologists, or activities appropriate for, or corresponding closely to these (see Murphy, Lunn, & Jones, 2006). According to Herrington and Parker (2013), the key elements of authenticity comprise an authentic context, an authentic task, the presence of expert performances, multiple perspectives, collaboration, reflection, articulation, metacognitive support and authentic assessment. Previous research on authentic learning in science and technology education has focused on several of these elements, such as the importance of creating an authentic context for performing authentic assessment, and the relevance of modelling for authentic technology education (e.g. Bulte, Westbroek, de Jong, & Pilot, 2006; Fox-Turnbull, 2006; Svärd, Schönborn, & Hallström, 2017). Thus, authentic learning often concerns the central concepts, principles, and practices in a discipline, or across several cooperating disciplines.

Models and modelling for authentic STEM education and STEM literacy

As pointed out by Gilbert and colleagues (e.g. Gilbert et al., 2000; Justi & Gilbert, 2002), models and modelling play a central role in science and technology education. In a recent commentary on a conceptual framework for integrated STEM education in this journal, Kelley and Knowles (2016) unpack a comparison of science and engineering practices from the National Research Council (NRC) in the USA. Herein, models feature as a salient aspect of both practices and include using models to “develop explanations about natural phenomena” in science, while using models to “analyse existing solutions” in engineering. Furthermore, the same essay also identifies mathematical models and modelling thinking as central to developing design solutions before prototyping stages in engineering practice. It follows, that discussing the notion of an authentic STEM education relies heavily on considering the pivotal functions of models and modelling. Models and modelling are important tools for problem solving, prediction, decision making, and communication and have been studied and analysed in the history, philosophy, and sociology of science and technology, and in the engineering sciences (e.g. Müller, 2009; Vincenti, 1990). Moreover, the important relationship between mathematical modelling and authenticity as a social construct has been pointed out by Vos (2011). Models simplify aspects of reality and range from simple conceptual sketches and rough prototypes to advanced mathematical models. Models in engineering are largely defined in functional terms. For example, where friction or gravity can often be ignored in the modelling of multiple phenomena in the natural sciences, this is not the case in real engineering settings (Hansson, 2007, 2013).

Their application in prediction is the major quality of engineering models, as they are used to predict whether future innovations, processes or systems shall be able to perform intended functions. Prediction requires correlation, but not necessarily a causal connection. This means that the demands on models for prediction are lower than on scientific models that strive to be useful for explanation of natural phenomena (cf. Scriven, 1988). Engineering models are also used to facilitate communication and to illustrate problems and principles. One of the core communication capabilities of the engineering community is to use graphical representations of objects and processes in the form of sketches, drawings, diagrams and charts (Ferguson, 1992; Mitcham, 1994). Therefore, the ability to create, use/apply, evaluate and revise models are necessary skills for acquiring an in-depth understanding of both technological development processes and scientific practice and are a core component for pursuing authentic learning in technology, mathematics and science classrooms (Schwarz et al., 2009).

Whereas models and modelling are an integral and well-researched aspect of science, mathematics, and to a certain extent engineering education (Justi & Gilbert, 2002; Lesh, English, Sevis, & Riggs, 2013; Vos, 2011; Zawojewski, Hjalmarson, Bowman, & Lesh, 2008), only a few technology education research studies and writings have focused on the explicit role of models and the modelling process. Examples of work include that by Gilbert et al. (2000), France, Compton, and Gilbert (2011), Haglund and Strömdahl (2012), and Nia and de Vries (2017). Gilbert (2004) distinguishes between five different representational modes of models: the concrete or material; the verbal; the symbolic; the visual; and the gestural. This diversity of representational modes must be taken into consideration when developing authentic STEM education interventions, although each of these modes possesses relative “representational power” as well as limitations. There is a high potential application of symbolic, visual as well as physical models in technology education. Discerning and interrogating a model’s strengths and weaknesses are conducive to solving real-world authentic tasks.

The main argument underpinning this commentary is that a successful integration of two or more STEM disciplines is dependent on authentic concepts or practices as a bridge. We hereby reinforce the role of models and modelling as such an authentic bridge across STEM education, also strongly motivated by earlier workers such as Gilbert (2004) who argued that “a central role for models and modelling would greatly increase the authenticity of the science curriculum” (Gilbert, 2004, p. 115). At the same time, if the means for teaching modelling processes is to be authentic, then this must be founded on conceptual frameworks that reflect the practice of science itself (Justi & Gilbert, 2002). If we extrapolate this argument to the STEM disciplines, it follows that integration of science, technology, engineering and mathematics could be greatly enhanced by operationalising the influence, functions and implications of models and modelling.

Modelling in the form of visual representations is one way of operationalising because it is both authentic and serves a crucial role in supporting learning in science, technology, engineering and mathematics (Rau, 2017). Such representations are often in the form of externalised visual models, where the interpretation and use of models is common and often a central practice in STEM domains. Indeed, instruction relies heavily on modelling concepts and processes in science, technology, engineering and mathematics. For example, in a science domain such as chemistry, in order to understand how atoms bond to form molecules, it is necessary for students to interpret and interrogate models that represent how individual atoms participate in bonding (e.g. Lewis structure models), consequent bond angles in 3D space (e.g. ball-and-stick models), as well the associated molecular volume (e.g. space-filling models). In a technology education domain, models related to the drawing or visuospatial manipulation and representation of an artefact or design process are often engaged. For example, if secondary students design a house in technology class, they might begin with producing a 3D model in CAD (computer-aided design) software, continue with utilizing mathematical models for calculating dimensions of load-bearing structures, and, finally, build a physical prototype. Furthermore, in a mathematics domain, various models are used to highlight different conceptual interpretations of fractions, for example. According to Rau (2017), such models include “area models that help students understand equipartitioning and parts-of-a-whole concepts (e.g., pie chart, rectangles), linear models that highlight measurement concepts (e.g., fraction strips, number lines), and discrete models that emphasize ratio interpretations (e.g., sets, counters)” (Rau, 2017, p. 746; cf. Lesh, 1981; Lesh, Post, & Behr, 1987). Tang and Williams (2018) view visual modelling as a common literacy skill in STEM, although they also caution that visual representations may be specific to a particular field.

According to Rau (2017), it follows that from a socio-cultural point-of-view, learning of representational and associated modelling competencies:

[…] first manifest in social interactions, which then become internalized [...] Through social interactions with a more knowledgeable person (e.g., teacher, another student, parent), students learn how to use visual representations in authentic tasks. During this process, students often start by observing experts and may then use visual representations themselves with the support of the more knowledgeable person. With increasing experience, this support is faded out and students take on increasing responsibility for solving authentic tasks themselves. Thus, participation in community practices is a critical socially mediated mechanism through which students acquire representational competencies (Rau, 2017, p. 724).

Rau (2017) thus points to the importance of operationalising a modelling pedagogy for the STEM disciplines, although few attempts have been made to do so. As motivated above, all the STEM disciplines engage with modelling and yet struggle with authenticity. To the authors’ knowledge, no synthesis of the literature has yet been conducted on the nature and role of models and modelling across the STEM disciplines as a whole. In response, Table 1 presents fifteen key STEM education contributions, related to the role of models and modelling as a means of bridging STEM disciplines in pursuit of authentic STEM education.

Table 1 Roles, functions, strategies and recommendations for using models and modelling in pursuit of authentic STEM education and literacy
Full size table

A number of different model uses and modelling processes and skills are proposed by the contributions referred to in this commentary, but we focus on those related to authentic practices and skills for an integrative STEM education. Based on the overview presented in Table 1, we offer the following three assertions about the role and functions of models and modelling for pursuing authentic STEM education:

Firstly, our STEM community requires a definition and classification of the nature of model types and model uses and components of the modelling processes. Although models and modelling differ slightly between the STEM disciplines, there are some clear similarities, for example, concerning visual models and representations (e.g. Tang & Williams, 2018). Exploring these similarities and bridging differences could strengthen STEM education and STEM literacy. In this regard, Nia and de Vries (2017) have proposed a framework for the “dual nature” (cf. de Vries & Meijers, 2013) of models, which could in principle be applied across the STEM disciplines. They describe the “intrinsic” nature of models as concerning the material structure and form of models, whereas the “intentional” nature of models concerns their functions, that is, whether they are used for exploration, design or communication. In line with Nia and de Vries (2017), Table 1 infers that modelling is often about representing simplified versions of reality that take on concrete/physical, conceptual, verbal, gestural or symbolic/mathematical forms (Gilbert, 2004). Models are therefore simplified representations of phenomena that often include concrete entities that can be smaller or larger than the represented phenomenon. Models could also be abstractions such as force depictions or graphs or equations (Lesh et al., 1987). Models are therefore representations of ideas, objects, systems, events, or processes which are central in science, technology, engineering and/or mathematics. At a conceptual level, models are even systems of description in themselves, for explaining, constructing, modifying, manipulating and/or predicting a complex series of experiences. Models thereby help to organize relevant information so as to generate or (re)interpret hypotheses about given situations, events, designs or processes, or explain how information is related.

Secondly, the STEM community requires a classification of central functions of modelling processes and skills associated with models and modelling. Central functions of models are to support development of theories and artefacts through manipulation (e.g. concrete models) or mental exploration (e.g. conceptual models, sketches) (de Vries, 2013), and, in the latter case, modelling ideas in the mind for communicating with oneself and modelling ideas in the world for communicating with others (Davies & Gilbert, 2003). Some of the primary skills associated with modelling include understanding what a model is and how to use it; carefully defining the context of the modelling process (i.e. is it a real-life or an educational context?); mentally visualizing a model outcome; deciding what mode of representation (e.g. physical, visual, verbal or symbolic/mathematical) to express the model in; and understanding how a model can be constructed, interpreted, tested/evaluated, revised and (re-)used. A crucial skill is also being able to evaluate the scope and limitations of a certain model. Nia and de Vries (2017, p. 647) further claim that students should learn about the relationship between the intrinsic and intentional/functional nature of models by taking both users’ and designers’ viewpoints into account:

  • Users’ view: Associated with understanding how a specific property of the model at hand makes it suitable for serving certain action(s). This understanding can occur in diverse ways such as direct learning about, reflecting upon, or testing ready-made models.

  • Designers’ view: Associated with how designers learn to produce useful models that realize their intended functions. To achieve such learning, students can be faced with various predefined functions regarding a model and be asked to develop their own, what they consider to be, relevant models. One may point in this regard to the example of asking students to conceptualize, construct, and/or discuss their graphical simulations of the design of a comfortable driver, passenger or baby car seat.

In such authentic design situations students will also “design” scientific and mathematical formulae and models to optimise their designs; new knowledge is developed about the design process itself but also about science and engineering, wherein students are required to apply existing knowledge previously learnt in science, technology and/or mathematics (Ammon, 2017; de Vries, 2018; Kertil & Gurel, 2016).

Lastly, common to all four STEM disciplines is the fact that a model can exist in different modes of representation. The ability of students to switch and transit between various representational modes increases their potential for learning, not only of modelling itself but also about the central concepts and practices of the STEM discipline in question. Furthermore, knowledge about mode of representation also increases the potential of using the same model but in different contexts, which also augments the opportunity for interdisciplinary cooperation between the STEM disciplines.

Conclusions and implications for STEM education

Modelling is an authentic practice in science, technology, engineering and mathematics education (see e.g., Banks & Barlex, 2014; Gilbert, 2004; Herrington et al., 2010; Turnbull, 2002) and therefore must be seen as a fundamental component of STEM literacy (cf. Williams, 2017). Even though this premise, in itself, is not a novel stance, recent studies have shown that STEM students possess more advanced “meta-modelling knowledge” than students of other, single disciplines at tertiary level (Krell & Krüger, 2017), so there are evident advantages beyond strictly discipline-based for teaching and learning modelling as an aspect of an integrated STEM literacy. Thus, although models and modelling can thereby be construed as one of the core tools or “languages” of an integrative STEM literacy, more urgent educational research is needed on how modelling can be developed to meaningfully link the STEM disciplines.

We argued at the outset that the STEM disciplines are not necessarily related in either content or pedagogy. However, as described in this commentary, science, technology, engineering and mathematics become closely intertwined during authentic practice (e.g. de Vries, 2018; Hallström & Ankiewicz, 2019; Kelley & Knowles, 2016). There can be active linking and educational cooperation on an equal footing through modelling, although it is still crucial to distinguish between models for educational purposes and models as part of authentic practices. We suggest that Gilbert and colleagues’ earlier initiated vision from 2000 not only applies to science and technology education but to the whole STEM education spectrum:

The nature of authentic education in science and (design and) technology has suggested that modelling and models should be taught across both fields as a way of linking them (Gilbert et al., 2000, p. 17).

The implications drawn from the synthesis presented in this commentary for STEM education are as follows:

  • Authenticity must be viewed as a cornerstone of STEM literacy (e.g. Roth, 1995).

  • Models and modelling processes can bridge the gap between STEM disciplines through authentic practices (e.g. France, 2018; Gilbert et al., 2000).

  • Models and modelling should be used as a means to promote STEM literacy and the transfer of knowledge and skills between contexts, both in and out of the STEM disciplines (e.g. Niss, 2012).

  • Modelling activities can serve as a meaningful route toward authentic STEM education (e.g. Davies & Gilbert, 2003; Gilbert, 2004).

  • Teaching authentic modelling processes must be rooted in explicit and tested frameworks that are based on the practice of the STEM disciplines (e.g. Justi & Gilbert, 2002), such as the approach provided by Nia and de Vries (2017).

  • Authentic STEM education should be driven by developing interaction between STEM subjects in parallel with maintaining the integrity of each subject (Williams, 2011).

  • Integrating science, technology, engineering and mathematics remains a complex challenge that calls for “a new generation of STEM experts” (Kelley & Knowles, 2016).

  • Authentic STEM education should focus on decreasing the vocational—and often politicised—notion of STEM as a way to increase economic competitiveness in favour of promoting STEM as an interdisciplinary way of learning authentic science, technology, engineering and mathematics (Pitt, 2009; Williams, 2011, 2017).

In conclusion, this commentary has reinforced the importance and implications of models and modelling in the promotion of an authentic STEM education. If this vision is to be realised, it is crucial that implementing any model-based authentic educational activities are underpinned by meaningful and evidence-based frameworks and recommendations for teaching practice (e.g. Kertil & Gurel, 2016; Tang & Williams, 2018). The contributions described in this commentary are central to each of the STEM disciplines and could be used to further operationalise potential recommendations for a broader STEM education mandate. It is also imperative that intended model-based pedagogies for STEM education classrooms are further researched and tested in real educational settings, in order to contribute to an integrated STEM literacy.