Authentic STEM education through modelling: an international Delphi study

Abstract

Background

The literature asserts that science, technology, engineering, and mathematics (STEM) education needs to be authentic. Although models and modelling provide a basis from which to increase authenticity by bridging the STEM disciplines, the idea of authentic STEM education remains challenging to define. In response, the aim of this study is to identify consensus on significant elements of authentic STEM education through models and modelling. Views were gathered anonymously over three rounds of questions with an expert panel. Responses were subjected to a multimethod analysis that pursued identification, consensus, and stability in the panel’s revealed propositions and themes around authentic STEM education through modelling.

Results

The panel reached high consensus concerning the potential of STEM education to support learning across traditional subject borders through authentic problem solving. The panel also consented that modelling is indispensable for achieving real-world relevance in STEM education, and that model-based integrated STEM education approaches provide opportunities for authentic problem solving. Furthermore, results showed that integrating individual STEM subjects during teaching, in terms of including disciplinary knowledge and skills, requires specialised competence. Here, technology and engineering subjects tended to implicitly underpin communicated teaching activities aimed at STEM integration.

Conclusions and implications

The panellists stress that STEM disciplines should be taught collaboratively at the same time as they are not in favour of STEM as a subject of its own but rather as a cooperation that maintains the integrity of each individual subject. Many respondents mentioned integrated STEM projects that included modelling and engineering design, although they were not specifically labelled as engineering projects. Thus, real-world STEM education scenarios are often viewed as being primarily technology and engineering based. The panel responses also implicate a need for multiple definitions of authenticity for different educational levels because a great deal of uncertainty surrounding authenticity seems to originate from the concept implying different meanings for different STEM audiences. These international Delphi findings can potentially inform integrated STEM classroom interventions, teacher education development, educational resource and curriculum design.

Introduction and aim

Science, technology, engineering, and mathematics (STEM) education is often discussed in relation to education policy and economic competitiveness, but the acronym has also become associated with classroom teaching and learning to promote skills such as creativity and problem-solving capability. STEM education as a term is used both to denote education in the separate disciplines, and integration of two or more of the disciplines. It is believed that integrated STEM education increases opportunities for emulating real practices in innovation (Vossen et al., 2020) and could therefore increase relevance and applicability of these disciplines in a rapidly changing world (Kelley & Knowles, 2016; Peterman et al., 2017; Pitt, 2009).

To realise and frame any implications of STEM for learning, contemporary scholars argue that STEM education needs to be authentic (Williams, 2017). In recent years, models and modelling has been argued as a valid premise from which to increase authenticity, relevance and create bridges between the STEM disciplines (e.g., Banks & Barlex, 2020; France, 2018; Herrington et al., 2010; Rau, 2017). Modelling is central to the disciplines as authentic practice in laboratories and design studios (Roth, 1995). Authentic STEM education relies on considering the central functions of models and modelling—physical, symbolic, and mathematical—in learning and practice (e.g., Lesh & Lehrer, 2003). Through modelling processes in STEM education, the disciplines forge a synergistic relationship, often requiring a learner to transit between the learning areas while engaging scientific, mathematical, and technological/engineering activities, which often render them interdependent and thereby facilitate creative and innovative outcomes (Davies & Gilbert, 2003; Hallström & Schönborn, 2019).

In this respect, integrated STEM education is defined as an approach to teaching STEM content of two or more STEM areas. At the same time, integrated STEM education should intersect between STEM subjects while maintaining the integrity of each subject (Williams, 2011). Thus, authentic and integrated STEM education must be based on tested frameworks for authenticity through modelling, to stimulate interaction and transfer of knowledge and skills between contexts. Although authenticity is a widely used term in the literature, little is in fact known about the meaning and application of the concept in education. The concept sometimes refers to the emulation of real-world practices in school settings, but it can also denote—often interdisciplinary—education dealing with complex problem solving that is supposed to stimulate students’ creativity and innovativeness (e.g., English, 2023; Herrington & Oliver, 2000; Lombardi & Oblinger, 2007). Thus, authentic learning shares many similarities with, for example, project-based and problem-based learning, but a more specified definition of what is truly authentic, and for whom something is authentic, remains elusive (McComas & Burgin, 2020; Nicaise et al., 2000; Snape & Fox-Turnbull, 2013; Svärd et al., 2022).

Consequently, one viable way of studying and potentially clarifying integrated, authentic STEM education through models and modelling is by obtaining the views of experts, engaged with (integrated) science, technology, engineering, and mathematics education projects. Therefore, the aim of this study is to identify consensus on significant elements of authentic STEM education through models and modelling.

Models and modelling in STEM education

A model is a simplified representation of a phenomenon (Norström & Hallström, 2023). The phenomenon in question varies between the STEM fields but generally in the science domains aspects of reality are modelled in order to better understand it, while in technology and engineering models could also represent phenomena that do not yet exist such as new innovations. Many models that engineers use are also mathematical. According to Lesh and Lehrer (2003), mathematical models “focus on patterns, regularities, and other systemic characteristics of structurally significant systems” (p. 112). Implementing models and modelling in mathematics helps induce construction, modification, and adjustment of conceptual models. Thus, despite some differences in the nature of the represented phenomena, STEM models and modelling practices are still similar and can be seen as authentic, real-world practices that constitute a bridge between these subjects (Frejd & Vos, 2024; Hallström & Schönborn, 2019; Zawojewski et al., 2008). Gilbert et al., (2000) pointed to the importance of modelling and models in pursuing an authentic science and technology education, by stating:

"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 (pp. 3, 17).

Modelling is thus an authentic practice in science and technology, and this can also be said about engineering and mathematics in which models and modelling are core, real-world practices (e.g., Banks & Barlex, 2020; Gilbert, 2004; Herrington et al., 2010; Lesh et al., 2013; Turnbull, 2002; Vos, 2011; Zawojewski et al., 2008). As English (2023) asserts, STEM contexts are conducive to exploring authentic data, through modelling activities that are used to explain patterns about the studied phenomena. Recent studies have also shown that STEM students possess more advanced “meta-modelling knowledge” (the ability to make sense both of models as representations, and of the modelling process as part of scientific practice) than students of other, single disciplines at tertiary level (Krell & Krüger, 2017).

Although models and modelling can be construed as one of the core tools of integrative STEM, more educational research is needed on how modelling can be developed to meaningfully link the STEM disciplines. The STEM disciplines are not necessarily related in either content or pedagogy, but science, technology, engineering, and mathematics become closely intertwined during modelling practices (e.g., de Vries, 2018; Hallström & Ankiewicz, 2019; Kelley & Knowles, 2016; Tang & Williams, 2019). 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, as well as for whom models and modelling become authentic and in what contexts (Gilbert, 2004).

Authenticity in STEM education

Authenticity in education is a popular but, at the same time, very contested notion (Schriebl et al., 2023; Watson, 2008). Rule (2006) defined authenticity as “learning in contexts that promote real-life applications of knowledge” (p. 1). Shaffer and Resnick (1999, p. 195) also identified four related types of authentic learning, namely, (a) learning that is personally meaningful; (b) learning that relates to the real world outside of school; (c) learning that relates to a particular discipline, and (d) learning where the assessment reflects the learning process. By shifting the focus to learning, one also addresses the problem of for whom education should be viewed as authentic (Anker-Hansen & Andreé, 2019). Teachers’ perspectives or engineers’ perspectives of authentic knowledge and skills are valid alternatives (Turnbull, 2002), as is authenticity of the learning environment which could be both in school or in “real” settings. Students’ perceived authenticity is perhaps most valid, and for them authenticity could also be considered a motivational variable (Behizadeh & Engelhard, 2014; McLure et al., 2022). In this study, we adhere to a socio-cultural definition of authenticity, that is, as students’ participation in practices and activities of professional scientists, technologists, engineers or mathematicians, or activities appropriate for, or corresponding closely to such professional practices (see Murphy et al., 2006). Authenticity thus comes in various forms and degrees that can be combined in a multitude of ways. Using methods and instruments also used in professional activities is one form of authenticity, whilst solving problems similar to those solved by professionals is another.

Previous studies in STEM education have found, however, that teachers find it difficult to motivate students because the students themselves do not view activities as authentic, nor do they connect them to future technology-related everyday activities or professions (e.g., Rees Lewis et al., 2019). A study by Nicaise et al., (2000) that introduced a space mission project in the classroom found that “student learning was anchored around a mock space shuttle mission […] In spite of this complex and weeklong activity, most students viewed the actual simulation more as a theatrical event as opposed to an opportunity for learning” (p. 90). Nicaise et al. (2000) thus attempted to move from merely assuming that certain learning environments are authentic to empirically investigating students’ perceptions of authentic contexts. Nevertheless, few STEM education studies have systematically investigated the meaning of authenticity and authentic learning in relation to what students do in authentic STEM-related activities.

Delphi methodology

Many educational studies have shown that obtaining experts’ views can yield reliable information on learning, teaching as well as curriculum development and implementation (e.g., Osborne et al., 2003). Research that systematically solicits experts’ opinions and reflections about a particular problem or concept is often manifested in the so-called Delphi method (Linstone et al., 2002). In educational research, Delphi approaches aim to seek agreement or stability in a group of experts’ opinions and views about an educational phenomenon. Herein, the presumed power of a Delphi approach is that systematic garnering of experts’ opinion will help increase the validity of the educational problem at hand. In attempting to do so, a Delphi study incorporates two main components, namely participant anonymity and multiple rounds of data collection (e.g., Murry & Hammons, 1995). The initial round usually adopts an open-ended character, where a team of researchers qualitatively analyses the free responses, which in turn informs the construction of more thematic questions. During each round, a result synthesis and extent of agreement is communicated to the expert group, wherein subsequent rounds contain more focused data collections that sharpen the emerging themes. Once group consensus or stability is attained, the approach is considered complete.

The literature reveals that the STEM disciplines are associated with various Delphi studies, although surprisingly lacking in STEM-focused educational journals (Cole, 2019). In science education research, examples of Delphi approaches include Osborne et al.'s (2003) well-cited work on gathering experts’ views of what key ideas should be integrated into science curricula and Häussler and Hoffman’s (2000) Delphi-inspired approach used to develop a curriculum framework for physics education. Kvello and Gericke (2021) studied expert views of what knowledge is important for understanding the nervous system in secondary biology and science education, and recently, Gericke and Mc Ewen (2023) conducted a Delphi study to define an epigenetic literacy framework for secondary education. In a mathematics education context, a recent study by Kallia et al. (2021) adopted a Delphi approach to explore opportunities for addressing computational thinking in mathematics. In technology education, Rossouw et al. (2011) performed a Delphi study to identify key, meaningful and relevant concepts that could be used to inform the teaching of engineering and technology.

One of the key challenges in applying a Delphi method is defining what exactly constitutes an “expert” in relation to the educational phenomenon in focus (e.g., Osborne et al., 2003). Scholars in this area assert that conducting a quality Delphi study requires quality experts, where a “Delphi study is only as good as the experts who participate” (Yousuf, 2007, p. 6). Therefore, it is important to target expert participants that have rich expertise, are highly informed and have knowledge and competencies related to the educational concepts in focus. At the same time, it might also be beneficial to seek experts that can reflect on the phenomenon in the light of wider educational contexts, and who strongly believe in the realisation of educational goals (e.g., Häussler & Hoffmann, 2000).

Conducting the Delphi study

The present study was inspired by the method used by Osborne et al. (2003). This Delphi study consisted of three data-gathering rounds: (i) three open, free text questions; (ii) Likert scale evaluation of representative statements from round 1; and (iii) Likert scale evaluations of statements with a high level of agreement and/or high level of importance revealed in round 2. In all three rounds the respondents were encouraged to provide free text comments in addition to answering or rating. The web-based survey tool Survey and Report was used throughout the study. Respondents answered the questions via a web form, and data were anonymised. The system automatically sent reminder messages. The entire data collection was performed over a period of one year.

Selecting the STEM expert panel

A letter of invitation was sent to 50 persons, deemed to be suitable panel members. The criteria used to decide upon suitable panel members were as follows. Firstly, they should have extensive experience in one or preferably several STEM fields (science—physics, chemistry, biology—technology, engineering, and mathematics), either as a researcher, educator, or industrial practitioner. We sought panel members that would have informed opinions on integrated STEM education, even if they were not necessarily involved in formal implementation of integrated STEM initiatives. Secondly, they should be gender representative and sourced from around the world. The invitation received positive replies from 33 persons, hereafter referred to as the STEM expert panel.

The Delphi study used an online survey to obtain the panel’s views on integrated STEM as an educational enterprise at large (cf. Rossouw et al., 2011). The panel represented three STEM areas, namely (i) disciplinary researchers in the fields of science, technology, engineering, and mathematics, as well as educational researchers in these areas; (ii) STEM education actors such as teacher educators, curriculum specialists and policy makers; and (iii) STEM professionals such as engineers, scientists, and designers working primarily in industry. Following non-response from five persons, the number of respondents analysed in this study was 28, apart from round three where one person did not respond. As per Table 1, most participants were from academia and education with fewer from mathematics, disciplinary research, and industry. Hence, each panel member represented one main professional area and in some cases one or more additional area(s) (in parenthesis). Thus, the degree of actual STEM integration varied among the respondents, whose responses were anonymous as per Delphi method protocol. Approximately half of the panel was made up of women, and all continents were represented.

Table 1 Main (and additional) professional areas and continent of the STEM expert panel (N = 28)

Box 1. Introductory text supplied with the round one questions
The acronym STEM (science, technology, engineering, mathematics) had its beginnings in the 1990s at the American National Science Foundation (NSF). For the last decade or so, STEM has been used internationally as a label for policies, programmes, and practices in research and education. STEM often involves one or several of the STEM disciplines in cooperation, stressing the interaction between these disciplines as commonly used in real-world, collaborative projects.
In STEM learning and practice, modelling refers to the process of creating and representing models, which are simplified versions of reality. Models typically comprise physical, conceptual, verbal, symbolic or mathematical forms.
In education, authentic learning refers to real-world, interdisciplinary STEM practices and complex problems in out-of-school contexts. Furthermore, authentic learning is often characterised by learner-centred scenarios, learning by doing, solving problems, modelling, and finding relevant solutions.

Round 1: discovering themes

The first round of the Delphi study consisted of three free response questions, which were requested to be answered within three weeks. In combination with these questions, the respondents received concise information text that referred to STEM, authentic learning, models and modelling (see Box 1). This information was provided to stimulate the panel’s thinking about concepts of relevance to the Delphi study, as they responded to the following:

• What is your opinion of possible opportunities and limitations of integrating science, technology, engineering, and mathematics (STEM disciplines) in education?

• What is your opinion about the roles of models and modelling in STEM education, and could you give an example of a modelling (learning) outcome?

• Provide and motivate an example based on your own work experiences where modelling is involved in an authentic, real-world relevant STEM learning or work scenario.

Of the 33 potential panellists, 28 eventually answered the questions. One respondent did not answer questions 2 and 3, respectively. Overall, responses were welcomingly extensive and elaborate, with a typical length of between 100 and 200 words (see Table 2).

Table 2 Number of words in round 1 responses (free text questions)

We performed a qualitative content analysis, where we implemented an inductive approach based on a hermeneutic tradition of text interpretation. The approach includes repeated reading of the data set to find and establish patterns. The repeated reading resulted in a step-by-step formulation of categories, which following the last round of the analysis were reduced to main themes (Mayring, 2000). Consequently, the Delphi responses were read thoroughly and repeatedly, and statements related to the research questions about authenticity, models, and modelling in STEM education and—to some extent—STEM practice were extracted. The statements were grouped together according to their core propositions. The analysis resulted in 24 core propositions with supporting statements (direct quotes from the responses) that were communicated to the respondents in the round 2 questions.

Round 2: refining themes

The 24 core propositions from round 2 were developed into 24 Likert item statements presented to the expert panel, grouped into five overarching categories (A–E):

• A. Integrated STEM education (questions 1–7)

• B. Curriculum, teaching practice, and assessment in STEM education (questions 8–12)

• C. The nature and teaching of models in STEM education (questions 13–18)

• D. Authenticity and real-world connection in STEM education (questions 19–21)

• E. Authenticity and real-world connection through modelling in concrete STEM education scenarios (questions 22–24).

Each question consisted of a proposition, and the respondent was asked to rate it on a five-point Likert scale: Strongly disagree, Disagree, Neither agree nor disagree, Agree, and Strongly agree. Two typical items and supporting statements, as shown in the web form, are included in Fig. 1. All the 24 propositions can be found in Table 5. For each of the five categories (A–E), the respondents could provide an optional comment.

Fig. 1

Two example questions from the round 2 questionnaire

Twenty-eight respondents answered the round 2 questionnaire within 18 days. Their Likert scale answers were converted to integers (Strongly disagree—1, …, Strongly agree—5) and mean ($\mu$), standard deviation ($\sigma$), mode (Mo), and median (Md) were calculated for each of the 24 Likert item statements (Table 5, columns $\mu$₂, $\sigma$₂, Mo₂, and Md₂, respectively). Between 13 and 18 respective respondents provided additional free text comments to the categories A–E. Most responses ranged between 25 and 75 words (see Table 3).

Table 3 Number of words in optional free text comments to each question category in round 2

Round 3: establishing consensus

Of the round 2 statements, 16 showed high agreement (mean [$\mu$] ≥ 4 and mode [Mo] = 5) and/or high consensus (standard deviation [$\sigma$] < 1). These were chosen for inclusion in round 3. From the free text comments to round 2, new supporting statements for the items were extracted.

The round 3 questionnaire was similar to that of round 2, with the main difference being that (i) the respondents were prompted to provide a free text comment to each of the 16 statements; (ii) only one supporting statement (from the free text comments to round 2) was listed for each question; and (iii) since there is a well-known risk of questions late in a survey receiving shorter answers or being skipped, the order of the statements was shuffled. The respondents were requested to reply within three weeks.

Synthesising the data corpus

Twenty-seven of the 28 respondents from round 2 also responded to the round 3 Likert scale items. The number of free text replies decreased over the course of the response sequence, with 25 replies to the first question and 21 to the last, respectively. The length of comments and the response rate varied slightly between questions, but with a typical length of between 20 and 40 words (see Table 4).

Table 4 Number of words in motivational free text comments to each question in round 3

Based on Osborne et al., (2003, p. 705), the following criteria were used: consensus was defined as a minimum of two-thirds of the respondents rating the statement as 4 or 5 in round 3. Stability was defined as a shift of 0.2 or less in the ratings between rounds 2 and 3. Nine statements, italicised in Table 5, fulfilled these criteria. Together, they summarise what the panel of STEM experts agree upon concerning models, modelling, and authenticity in STEM education (mainly integrated). These statements, and the respondents’ free text comments to them, are analysed below.

Table 5 Quantitative results from rounds 2 and 3 of the Delphi study

Analysis and findings

Our analysis focussed on the nine propositions for which there was both high consensus and satisfactory stability over time (italicised statements in Table 5). Below they are subsumed as three overarching themes, namely STEM teaching and learning, modelling in STEM education, and authenticity in STEM education.

STEM teaching and learning

Specialised teacher expertise and knowledge dimensions are required to teach STEM

The comments related to this theme discussed teacher expertise mainly along the following three dimensions: pedagogy and subject knowledge, attitude, and organisation. To be able to teach integrated STEM, a broad subject knowledge in many (or all) of the root disciplines is necessary, as well as knowledge about cross-disciplinary teaching and a will to implement it. Difficulties include epistemological and pedagogical differences as well as skills related to, for example, the handling of equipment and tools:

Teaching from a STEM perspective requires the teacher to have a good disciplinary knowledge of the different STEM disciplines, but also an epistemological knowledge of these different disciplines, to be able to deal with various and often complex material devices. [Comment to question 5 in round 3; 5 in round 2]

Several respondents suggested that teams of collaborating teachers from different root disciplines could enhance STEM learning. Examples included primary school through to university level. However, as displayed by the following excerpt, there are organisational obstacles that make this difficult to implement, as teaching tends to be organised along the traditional disciplines:

STEM has the potential to stimulate teacher collaboration and team-teaching. This is not being encouraged in academic institutions. There is need to help teachers to see the strength of team-teaching. This needs institutional transformation through review of the schedule/time-table. [Comment to question 5 in round 3; 5 in round 2]

Integrated STEM learning requires different assessment strategies than the separate disciplines

The panellists were generally of the view that because STEM learning is integrated it will also require different, more authentic assessment strategies that emulate knowledge evaluation in collaborative real-world projects. One such example is presented below:

In order to simulate authentic learning in iSTEM [integrated STEM], assessment needs to take into account collaboration (team/group work) and creativity. Assessment priorities that focus on knowledge could be damaging and a distraction to meaningful iSTEM learning. [Comment to question 6 in round 3; 12 in round 2]

The assessment could thus focus on knowledge requirements in the individual disciplines but should—perhaps primarily—be integrated in itself and incorporate procedural knowledge and competencies needed to fulfil the task. Examples of quotes supporting this argument included the following:

The assessments need to be aligned with the learning objectives. Integrated STEM learning should thus be correspondingly accompanied by integrated assessments. [Comment to question 6 in round 3; 12 in round 2]

We need to develop sustainable assessment […] of competencies, not mere checking of knowledge acquisition and decontextualized skill sets. [Comment to question 6 in round 3; 12 in round 2]

Although it is possible, and indeed necessary to develop appropriate assessment strategies, I do not believe that this will be easily achieved. D&T [the school subject Design and technology] has been bedevilled by assessment difficulties with some arguing for the assessment of procedural competence without the necessity of assessing the acquisition of knowledge, understanding and skills associated with learning in the individual STEM subjects. Others argue that to know the impact of the teaching it is important to know what the students have learned in the individual subjects and to assess the extent to which they use this learning in the way they implement their procedural competence and also to identify the new learning that has taken place through the design activity. [Comment to question 6 in round 3; 12 in round 2]

STEM disciplines should be taught collaboratively and include multiple perspectives

The STEM experts argued that because STEM education addresses real-world challenges, collaboration across disciplinary borders as well as collaborative, integrated STEM teaching should be promoted, although individual learning is also important. Consider the following excerpt in this regard:

All real-world challenges demand collaboration across disciplines, organizational and cultural divides, from analysis and identification, through modelling and decision-making around what approach to follow. Note that while STEM disciplines should be taught collaboratively, it does not follow that there should be no individual learning of skills. It is highly desirable that multiple perspectives are included if the education is to address ethical and sustainability issues. [Comment to question 9 in round 3; 6 in round 2]

Multiple perspectives should be included in the form of input from disciplinary specialists within STEM and from experts outside of schooling. Typical quotes along these lines included:

Ideally iSTEM should be co-taught by multiple specialists, from different disciplines, including educators and experts from outside of schooling. [Comment to question 9 in round 3; 6 in round 2]

Teaching the disciplines collaboratively and according to multiple perspectives would certainly be beneficial, provided they are also taught on their own conditions. [Comment to question 9 in round 3; 6 in round 2]

STEM education supports learning across traditional subject borders through authentic problem solving

The experts collectively asserted that STEM education is not primarily a discrete subject but rather constitutes interdisciplinary cooperation between or cross-curricular themes involving the individual STEM disciplines, in order to solve complex or “wicked” real-world problems and thereby improve students’ learning.

Examples of quotes supporting this emergent argument were as follows:

Solving complex real-world problems often relies on a cross-disciplinary approach. [Comment to question 2 in round 3; 9 in round 2]

Everything depends on the way STEM education is orchestrated. If robustly based on the disciplines involved the statement given may very well be true. If based on integrating the disciplines away in a superficial approach to problems, authentic or not, not much valuable learning may result from STEM education. [Comment to question 2 in round 3; 9 in round 2]

Offering “Integrated STEM” as a discrete subject risks being an artificial construct that explicitly works against the idea of integrating real world experiences into the education. At least if “discrete subject” would include a set of learning outcome descriptions that define a set of knowledges (theories, models), or skills (approaches, methods). Any real-world challenge is characterized by “wicked” aspects that defy recipe-approaches. Having said that—if the “discrete subject” is an introductory course for students in the first semester where the students are introduced to open and wicked challenges, it would make sense, as would a project/problem-based course unit where a challenge is to be addressed. [Comment to question 2 in round 3; 9 in round 2]

Modelling in STEM education

Modelling activities are indispensable for cross-disciplinary learning and the practice of general skills in STEM education

Overall, experts felt that modelling activities are important and common to all STEM enterprises and are fundamental to the notion of an integrated STEM education. Cross-disciplinary movement across STEM subjects cannot meaningfully occur without modelling. Experts also emphasised the crucial role of modelling in mathematics. They also identified modelling as central to developing and executing skills such as making predictions, performing design, systems thinking, as well as transferring knowledge from one context to another. Experts also noted the close relationship between modelling skills and practical application of STEM.

Two quotes from the panel that strongly represent this overall position are as follows:

Modelling is essential not only in the predictive capabilities it directly offers, but also in enabling the modeller and the user of the modelling tool to better understand the underlying physics. [Comment to question 3 in round 3; 15 in round 2]

To me, the application of models and modelling, using tools from mathematics and science, in solving technical and engineering problems is at the core of integrated STEM education. [Comment to question 3 in round 3; 15 in round 2]

Modelling is central to engineering design and therefore essential to STEM education

The panellists revealed consensus in the importance they attributed to modelling for engineering education, even if its central importance is often unacknowledged during teaching practice. In doing so, the experts also communicated the view that in addition to engineering design, modelling is closely connected to the notion of design in all STEM disciplines. Participants emphasised an equally important role of modelling in technology education. Multiple experts were concerned about the danger of attributing design to engineering alone and suggested that design has a more overarching premise applicable to many aspects and skills of the design process as well as across the STEM subjects.

The synthesis above is supported by the following two examples of expert quotes:

Modeling-based instruction emphasizes constructing, evaluating, testing, and using models in engineering education. As one of the disciplines of STEM, modeling is central to engineering education. [Comment to question 7 in round 3; 16 in round 2]

There are different types of models. For example, conceptual models, mathematical models, computational models. Some models will be more relevant during problem scoping, some other models during the problem-solving process, etc. [Comment to question 7 in round 3; 16 in round 2]

Another expert emphasised the philosophical importance of technological design as an integrator of STEM, while also suggesting engineering design as an integrator. This panellist went on to point to the importance of design in all STEM subjects:

Design in science may also be more experimentally oriented—such as, for example, in synthetic chemistry. Design in technology, engineering—and even sometimes in mathematics—will typically lead to the making of an object, or system. The students will also “design” mathematical expressions or functions and do calculations to optimise their design by modelling to test their optimisations. The steps of mathematical modelling resemble, to a large extent, the stages of technological and engineering design. Modelling is pivotal to design in all four subjects. [Comment to question 7 in round 3; 16 in round 2]

Modelling is central to scientific practices and therefore essential to STEM education

Strong agreement in the excerpts portrayed modelling as inherent in each component of STEM and essential for making predictions, for “modelling” the world, as well as for applying knowledge in real world contexts. Overall, despite the strong consensus on the centrality of modelling competences in STEM, there was a sense that experts stopped short of entirely committing to the idea that modelling was always central and foregrounded. In this regard, experts flagged that integrating modelling in practice also depends on the nature of the encountered problem, on the nature of the required modelling competence, as well as on how teachers actively apply modelling during teaching. On this note, experts also suggested that the centrality of modelling extends beyond STEM alone.

Examples of quotes supporting the interpretation above include:

Modelling is a component of each aspect of STEM—the S, the T, the E and the M. [Comment to question 11 in round 3; 17 in round 2]

Modelling is central to each STEM component discipline, but only rarely is modelling applied across disciplines in real world settings. The modelling within subjects needs to be situated in real world contexts. Later courses need to actively make use of theoretical frameworks, skill sets and modelling approaches from earlier courses in such a way that students’ competence progresses. [Comment to question 11 in round 3; 17 in round 2]

Modelling is indispensable for achieving real-world relevance in STEM education

This identified proposition has two inherent complications that several respondents pointed out. The first is that a supporting statement about real-world problems does not mention modelling and is therefore difficult to interpret in this context. The second is the meaning of “real-world”, which can be interpreted in several ways. What is the real world to a pupil in school? As one respondent exemplified, they consider school as real. Another respondent highlighted the differences between countries and regions. The real world experienced by a student in a developing country is different from a European “real world”. A curriculum emphasising vocational training could be interpreted as “real” in the developing world, but not necessarily so in industrialised countries. This opens up for different meanings of “real-world relevance”, wherefore comparison between respondents must be interpreted with care. An example of different meanings coming to the fore around relationships between modelling practices and real-world relevance were communicated by the following view:

Modelling as a practice, where theoretical, scientific, and mathematical models are mapped onto real-world problems and phenomena, is central to the integration of the STEM subjects. However, real-world relevance may be achieved within technology and engineering without modelling, but that risks losing the use of science and mathematics along the way. [Comment to question 8 in round 3; 20 in round 2]

Authenticity in STEM education

Successful STEM education needs to be authentic

The respondents described how STEM education exercises must be authentic and related to the real world. The notion of authenticity was, however, widely questioned and discussed in the comments, for example:

“Authenticity” is an ill-defined notion. What is it that has to be authentic? The problem? The methods for dealing with it? What is the relationship between authenticity and relevance? Relevance for whom? [Comment to question 16 in round 3; 24 in round 2]

Most respondents’ comments supported the idea that authenticity in the STEM education context concerns problems, examples and exercises being derived from, or related to problems or needs that exist outside of the educational context. As communicated by the following quote, it prepares students for a life and career in STEM or related areas, and makes studies more interesting:

Authentic in the meaning being found in the real world, with complex, contradictory, insufficient, and value-conflicting aspects, at least to some degree. If education focuses only on decontextualized desktop in the form of calculation problems or parlour game conundrums, then that is what the students will become good at. [Comment to question 16 in round 3; 24 in round 2]

I think that authentic real-world problems or at least pseudo-realistic, help students to connect their thinking with actual things because they can work concretely and stay better motivated. [Comment to question 16 in round 3; 24 in round 2]

Discussion

This international Delphi study had as its point of departure the premise that models and modelling may be an important part of authentic STEM education. However, we were also mindful of the fact that any consensus on authenticity in STEM education remains elusive in the literature and amongst scholars, as well as what role models and modelling might play. Therefore, given the lack of convergence in what authenticity might mean for STEM and modelling, on top of the fact that integrated STEM education is a rapidly growing pedagogical notion, the aim of the study was to identify consensus on significant elements of authentic STEM education through models and modelling. We structure the discussion by revisiting STEM teaching and learning, modelling in STEM education, and authenticity in STEM education in turn.

When it came to STEM teaching and learning, our findings revealed that specialised teacher expertise and knowledge dimensions are required to teach integrated STEM. In the design of integrated STEM teaching and learning activities, a salient view of the panel was that subject integrity must be maintained (English, 2022). Subject integrity means respecting and maintaining the core epistemological, ontological, and methodological concerns of each STEM subject (cf. Williams, 2011). Furthermore, the panel strongly suggested that teachers therefore require specialised competence for integrating STEM subjects, both in terms of disciplinary knowledge and skills for teaching STEM as a collaborative enterprise (Table 5, especially statements 5 and 6). Integrating modelling strategies during teaching practice requires providing teachers with the necessary skills and opportunities to include their original knowledge in an integrated STEM context (e.g., Gilbert, 2004; Shanta, 2022). Such integration also encourages collaboration and promotes teachers’ creativity. Although challenging to pursue, the panellists stress that STEM disciplines should be taught collaboratively and include multiple perspectives. They are not in favour of STEM as a unified subject but rather as a cooperative endeavour that maintains the integrity of each individual subject (Williams, 2011). These views also find traction in recent work by, for example, Banks and Barlex (2020, p. 28ff) who encourage STEM subject teachers “looking sideways” in collaboration.

The panellists’ responses also suggest that integrated STEM learning requires different assessment strategies than in the separate disciplines, by including more authentic assessment strategies that emulate knowledge evaluation in collaborative real-world projects. Contemporary examples of these are described by Svärd et al. (2022), where students were assessed in terms of the process and evaluated by representatives from a well-established association of inventors. Therefore, an interpretation of the experts’ responses is that integrated STEM teaching and learning requires setting up opportunities for authentic, real-world problems that support innovative and critical thinking capabilities in students.

Furthermore, as revealed by the analysis (Table 5, especially statements 15, 16, and 20) the panellists argued strongly that modelling activities are indispensable for cross-disciplinary learning, real-world relevance, and the practice of general skills in STEM education. Despite there being only two mathematics education panellists, it is notable that many experts emphasised the centrality of mathematical modelling for achieving authentic integrated STEM education (Baker & Galanti, 2017; Kertil & Gurel, 2016), and that computational support was mentioned as important for successful modelling (Denning & Tedre, 2019; Hallström & Schönborn, 2019). Furthermore, many respondents saw modelling as central to scientific practices and therefore important to STEM education. However, a more salient feature of the data is that modelling is considered central to engineering design and therefore an essential feature of design practices across all the STEM subjects (cf. de Vries, 2021). In fact, many respondents mentioned integrated STEM projects that included engineering design elements such as technical problem solving and modelling, although they were not specifically labelled as engineering projects. Thus, as is emerging in the work of contemporary authors (e.g., Kelley & Knowles, 2016; Sung & Kelley, 2022), real-world STEM education scenarios are often being viewed in terms of being primarily technology and engineering based, especially in relation to the engineering design process.

There is a very high consensus among the international expert panel that successful STEM education needs to be authentic (Table 5, especially statements 9 and 24). Furthermore, the panel expressed that integrated STEM education not only requires authentic problems to make it connected to the real world, but also provides opportunities for real-life solutions (e.g., Edström & Kolmos, 2014). However, although they reached consensus on the need for authenticity in STEM education, they were also somewhat baffled about the real meaning of the concept and even suggested alternative concepts such as “pseudo-realistic” and “found in the real world”. This conception of authenticity aligns with Shaffer and Resnick’s notion of authentic learning as relating to the real world outside of school (Shaffer & Resnick, 1999, definition b). Furthermore, the panellists primarily addressed what is meant by authenticity and authentic learning, not for whom something could be regarded as authentic. Recent research shows that the for whom-question is essential to implementing authentic learning in school, that is, it is crucial for the potential success of authentic STEM projects that students really perceive them as authentic and meaningful (e.g., Nicaise et al., 2000; Svärd et al., 2022). A recent example by Melton et al. (2022) on promoting sustainable development showed that authentic science activities provide opportunities for students to transition from novices to experts. The findings of the current international Delphi study signal that more research is needed on authenticity in education in general, which might lead to further refinement and operationalisation of authenticity for STEM education practice. The panel responses also implicate a need for multiple definitions of authenticity for different educational levels because a great deal of the confusion surrounding authenticity seems to originate from the fact that authenticity carries different meanings for different STEM audiences (cf. Anker-Hansen & Andrée, 2019; Schriebl et al., 2023).

Limitations

Due to the anonymous nature of the Delphi method, we were unsure as to the precise prior experience of the panel in implementing integrated or authentic STEM activities. This might have had an important impact on our findings in the sense that the responses were not necessarily always based on first-hand experience of formally integrating STEM. Nevertheless, this means that we also allowed for the development of more unconstrained and visionary ideas about how to integrate STEM. A recent Delphi study by Gericke and McEwan (2023) showed the importance of acknowledging divergent opinions and outliers in pursuit of establishing expert consensus. This is especially important when investigating expert opinions of rapidly developing areas of educational research such as authentic STEM education.

Conclusions and implications

The STEM expert panel reached high consensus concerning the potential of STEM education to support learning across traditional subject borders through authentic problem solving (Table 5, especially statements 6 and 9). A closely related view of high agreement was that model-based integrated STEM teaching approaches provide opportunities to include real-life solutions that are not otherwise possible. In this respect, the panel were in concordance on modelling as indispensable for achieving real-world relevance in STEM education. Furthermore, experts opined that subject integrity in teaching must be maintained for core content, activities, and methods of the individual disciplines to be preserved. Teachers therefore require specialised competence for integrating individual STEM subjects in teaching, both in terms of disciplinary knowledge and skills, and cross-disciplinary STEM teaching (Johnson & Czerniak, 2023).

Three novel conclusions emerge from this study. Firstly, the panellists stress that STEM disciplines should be taught collaboratively and include multiple perspectives, at the same time as they are not in favour of STEM as a subject of its own but rather as a cooperative endeavour that maintains the integrity of each individual subject. Secondly, many respondents mentioned integrated STEM projects that included mathematical and technological modelling as part of engineering design, although they were not specifically labelled as engineering projects. Thus, real-world integrated STEM education scenarios are often viewed as having their primary basis in technology and engineering (Martín-Páez et al., 2019). Thirdly, the panel responses implicate a need for multiple definitions of authenticity for different educational levels since a great deal of the uncertainty surrounding authenticity seems to originate from the fact that the concept carries different meanings for different STEM audiences.

The reported findings of this international Delphi study reveal areas of consensus regarding modelling for authenticity in integrated STEM education. The results can serve to help practically inform the development of teacher education programmes (e.g., include courses aimed at creating active and meaningful integration of STEM disciplines), classroom interventions (e.g., increase collaborative teaching among STEM subjects, see Leung, 2020), and textbook design (e.g., include real-life application, especially in science and mathematics). When it comes to curriculum design there is a need to specify STEM education components and what actually constitutes authenticity at different educational levels.