Learning Progression During Modelling-Based Teaching

  • John K. Gilbert
  • Rosária Justi
Part of the Models and Modeling in Science Education book series (MMSE, volume 9)


Students will inevitably vary in the rate at which they become experts in modelling, that they acquire meta-modelling capability. If this variation is to be accommodated, the compulsory science curriculum must be structured so as to facilitate ‘ learning progression’ (LP) – the progress to expert status – in some way. The nature of a generic LP is presented that addresses both models and modelling. The attainment of an LP in models and modelling will be intertwined with an LP for each of visualisation, analogy, argumentation, and learning about science. Whilst the detailed structure and testing of such an LP has yet to be done, the issues associated with identifying suitable phenomena to be modelled, with gaining access to such phenomena, and with ensuring that transfer of learning occurs between modelling activities, can be discussed. Finally, the core issue of assessing what progression has taken place at any one time is confronted.


Science Education Content Knowledge Target Domain National Curriculum Analogical Reasoning 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Achieving Worthwhile Learning During MBT

A teacher engaged in MBT would hope that the outcome in the finite amount of time available for such an activity would be that all the students had quickly learned how to produce and test models of phenomena that are of scientific interest. Alas, this ambition is rarely attained, quickly and at expert level, because the acquisition of the knowledge and skills entailed in the development of meta-capability is not a unitary process: it actually consists of the development of five distinguishable yet highly inter-related meta-capabilities. An LP in models and modelling must be supported by those in visualisation, analogy, argumentation, and in respect of understanding about science. The evidence from research is that students show different rates of progression in attaining these capabilities, even under the most advantageous circumstances. Moreover, the teacher must seek to enhance all five of them in tandem during MBT if the desired levels of expertise are to be realistically aspired to.

In order to see how this might be done, even in outline, it is necessary to establish what ‘progression’ entails, before describing what the attainment of each of the five meta-capabilities involve in as much detail as current research has made evident. In respect of the LP in models and modelling itself, two approaches can be outlined. They involve respectively: the provision of a set of models- and modelling-related activities, culminating in the construction of a model de novo; and the adoption of a model-based approach to curriculum design.

The Notion of Progression in Learning

The intention behind the provision of an LP in each of the major concepts and skills-sets of science at school level is to support the acquisition of ‘ scientific literacy for all’ (see Chap.  1). A major issue in doing so is the need to bring about a much greater coherence in general than at present between what is taught about models and modelling (the requirements of the curriculum), how it is taught (the pedagogy adopted to do so) and the way that the learning that takes place is assessed (the testing regime adopted) (Duschl, Maeng, & Sezen, 2011). Achieving such a synergy from the present very partial and fragmented provision can be seen as one of the major challenges to be faced by science education over the next decade (and probably more!). The development of such an LP is of great importance because, like LPs on other aspects of science (for example, how scientific methodology has developed historically), it will

… have the potential to organise standards, assessments, and instruction in a way that promotes scientific literacy. Current (…) curricula prioritise the structure of the scientific disciplines, using a top-down approach that creates logical (from scientists’ perspective) sequence of ideas. Learning progressions, which use both top-down and bottom-up ‘design’ approaches, can combine ideas about scientific disciplines with understanding of how students learn (Gotwals & Alonzo, 2012, p. 4).

Thus, while the LP will assume the validity of the current view of models and modelling that is deemed desirable for school-level education, the fact that students have their own interpretations of such matters (as shown, for example, in Grosslight, Unger, Jay, & Smith, 1991) will be recognised at least in the pedagogy adopted.

In somewhat greater precision, the report of a conference by Corcoran and Silander (2009), summarised by Duschl et al. (2011), posited that LPs in general will have four features that permit age- and attainment-related learning in science education to be facilitated by:
  1. 1.

    targeting core and generative disciplinary understandings and practices that merge science content with science practices;

  2. 2.

    (establishing) lower and upper boundaries that describe entry assumptions and exiting expectations for knowing and doing;

  3. 3.

    descriptions of LPs that inform progress levels or steps of achievement;

  4. 4.

    (pointing to) purposeful curriculum and instruction that mediates targeted student outcomes. (Duschl et al., 2011, p. 136)


As we have discussed in Chaps.  2 and  9, modelling is a complex operation that is a vital component in the conduct of scientific enquiry. If an authentic science education is to consist of a series of LPs concerned with specific and scientifically important sets of knowledge and skills, leading to competences in them, then we would argue that an LP on modelling will be a vital component of such an education for all students. Such an LP would therefore have, as its core aim, the attainment of competence in modelling. As has already been said, the development (or exercise) of competences in visualisation, analogy, and the nature of science would necessarily also be required in order for this to happen.

Progression in Models and Modelling

The Nature of a Competence in Models and Modelling

Progression in the knowledge and skills required for modelling necessarily entails progression in knowledge about the nature of models. Thus an overall competence in models and modelling will consist of three elements. These are:
  • Knowledge about models. This is comprised of scientifically acceptable knowledge of: the epistemological and ontological nature of models; the reasons why they are constructed and used; how their scientific value can be assessed.

  • Knowledge about modelling. This is comprised of scientifically acceptable knowledge of: the epistemological and ontological grounds on the basis of which models can be constructed; the procedures involved in constructing models; the procedures involved in evaluating the procedures involved in the construction of models.

  • Skill in the practice of modelling. The emphasis here is on what is actually done when a person is actively engaged in the practice of modelling. These elements are manifest in the skills deployed when:

  • Students construct models consistent with prior experience and theories to illustrate, explain, or predict phenomena;

  • Students use models to illustrate, explain, or predict phenomena;

  • Students compare and evaluate the ability of different models to accurately represent and account for patterns in phenomena and to predict new phenomena;

  • Students revise models to increase their explanatory and predictive power, taking into account additional evidence or aspects of a phenomenon (Schwarz et al., 2009, p. 635, original emphases)

Evidence on the Attainment of Competence in Modelling

Until the last 20 years or so, the theme of models and modelling was not discussed to any great extent in science education. This neglect is reflected in the wide variety of treatments of the themes themselves in textbooks for students over the years, for example in physics (Niss, 2009).

An early and influential enquiry by Grosslight et al. (1991) concerned with the understanding of the nature of models held by students across a range of ages between those of high school and of university suggested that they attained one of three ‘levels’ of understanding. At Level 1, a model was seen as a simple copy of some aspect of reality, while at Level 2 it is basically a copy of reality but produced for a specific purpose, and at Level 3 a model is a construction produced to develop and test ideas, not being a copy of reality. The majority of the school-age students in that study displayed an understanding at the first of these three levels. Later work in the same vein by Chittleborough, Treagust, Mamiala, and Mocerino (2005) showed that the understanding of similarly-aged students had shifted somewhat towards the third, the more scientifically-acceptable, level of understanding. This shift may well have been associated with the growing research, development and teaching interest in the field over the period 1991–2005.

Gobert and Pallant (2004) noted that the work that has since taken place has fallen into three phases in each of which enquiry into understanding has been conflated with attempts to develop that understanding. In the first phase, students were presented with a model and required to learn factual content with its use. In the second phase, students were presented with a problem and required to construct models with which to explain it. In the third phase, an extension of the second, the processes of model construction and use have been defended in discussion with students’ peers.

The more recent work has emphasised the value of modelling per se, this subsuming the development of an understanding of models per se (Schwarz et al., 2009). Situations where the emphasis is on students creating their own models have been found to be especially successful (Abell & Roth, 1995; Lehrer & Schauble, 2012). Closer examination of what is happening during this process of creation, in the context of the use of computer-based modelling systems, showed that students tended to pay attention to the empirical data on the phenomenon in question that is available rather than to their relevant prior knowledge (Sins, Savalsberg, & van Joolingen, 2005). This suggested that there is a clear and major role for teachers in supporting the modelling process if student-initiated work was to be successful. Other work has shown the importance of the adoption of pedagogic practices that closely reflect those in use in scientific enquiry itself (Prins, Bulte, & Pilot, 2011).

The work summarised above does point to the elements of a potentially successful LP. It must: address both models and modelling; be based on an address to phenomena that students see (or merely passively accept) as being of authentic interest; focus on the construction and evaluation of models by the students themselves; involve the provision of scaffolding for student activity by the teacher; involve students reflecting on what they have done during the process of modelling.

Progression in Visualisation

The Nature of Competence in Visualisation

In Chap.  7, we explored the fact that access to the world-as-experienced is provided by the five senses: sight, hearing, smell, taste, touch. From these five, discrete focuses of perception can be identified which have a particular salience. These involve the use of: gesture, concrete objects, vision (especially pictures, diagrams, graphs), and speech. Each of them, together with the many sub-modes in which they exist, differing only in the emphasis placed on their defining attributes, provides particular visualisations. That is, they provide particular links between mental models and the aspect of reality that they depict. The conventions governing the nature of these links are called the ‘codes of representation’ for the modes or sub-modes.

A science student with competence in visualisation fully understands and can use the modes and sub- modes of representation commonly used in science. To do this, an individual must be able to demonstrate:
  • a full understanding of the codes of representation of all the modes and sub-modes of visualisation used in science education. This knowledge will include that about: the entities within models that can be depicted; the relationships between them that can be shown (for example, relative distance and angle between them); the relationships between them that cannot be shown;

  • a capacity to ‘translate’ a given model between those modes of visualisation that are appropriate. For example, that of the human heart between a diagram of it and a material model of it;

  • a capacity to construct a visualisation in any one of the modes and sub-modes used in science education;

  • a capacity to use a suitable visualisation to solve novel problems in respect of a given phenomenon (Gilbert & Eilam, 2014).

Evidence on the Attainment of Competence in Visualisation

Many thousands of studies of competence in visualisation have been reported in the literature. However, they vary widely in terms of: the definition of ‘visualisation’ used, the particular mode (or combination of modes) of representation focused on, the particular element of knowledge or skill focused on, the methodology used to obtain data (ranging within the spectrum of the qualitative to the quantitative), the age gender and educational background of the students, the environment within which data is collected. Review articles have attempted to provide overviews of parts of this complex field (for example, Hegarty & Waller, 2005; Newcombe & Learmonth, 2005), with those concerning sex differences being the most readily comprehensible, for example that of Halbern and Collaer (2005). The consequence is that it is not possible to even approximately answer the question ‘To what extent and in what ways is the ability to visualise attained by individuals?’ The closest approach to doing so was made by Eilam (2012) in identifying what teachers’ might do to promote the status of visualisations in respect of their accompaniment to text. In essence, she suggests that students learn most from visualisations in such a context if:
  • they actually have to memorise the representations, which can only be done if they have learnt the codes of representation involved;

  • they explain a piece of accompanying text by using what is represented in an adjacent visualisation;

  • they explicitly explain elements in a visualisation in terms of the meaning attached to that which is represented;

  • they seek understanding from a visualisation that extends the meaning derived from accompanying text;

  • efforts are being made to extend their general knowledge of that which is being represented.

As emphasised in Chap.  5, studies conducted in MBT (Gilbert, Justi, & Queiroz, 2010; Justi, Gilbert, & Ferreira, 2009) have also shown that students’ involvement in modelling-based activities can support the development of their competence in visualisation when the stage of expressing a proto-model in any of the modes of representation is explicitly focused on and extensively discussed.

Progression in Analogical Reasoning

The Nature of Competence in Analogical Reasoning

In Chap.  8, we established the importance of analogy in MBT. Drawing on that analysis, we suggest that competence in analogical reasoning involves the knowledge and ability to:
  • gain access to memory of a range of domains that have the potential to provide the basis for suitable analogies;

  • systematically map parts of the base domain onto the corresponding parts of a chosen target domain;

  • evaluate the match between the two using the criteria of structural consistency and structural focus;

  • deduce inferences about the target domain, this producing new or enhanced understanding;

  • generalise those inferences to targets that seem similar to the target domain being immediately addressed;

in all the target contexts likely to be met in science education.
These processes of analogical reasoning are used in all the elements of our model for MBT (see Chap.  2). Thus, during the:
  • Creation of a model. Having decided on the aims that a model should address, the modeller collects relevant empirical data, identifies a suitable source for the model, and draws the analogy that leads to its creation as a proto-model. This is the central role for analogy in the modelling process;

  • Expression of a model that has been created. The modeller has to both identify a suitable mode of representation for it and carry out the process of expressing it. In order to do so, an analogy can be drawn to similar contexts where a particular mode of visualisation has been used;

  • Testing phase. The expressed model has to be included in the design and conduct a thought experiment, these processes being preferably based on an analogy to a suitable pre-existing thought experiment. Where this is successful, the next step may be the conduct of an empirical experiment: analogy is again involved;

  • Evaluation of the model. This involves the use of the model to represent a phenomenon in a context different from the one for which it was initially produced.

Evidence on the Attainment of Competence in Analogical Reasoning

The drawing of analogies, as a general learning strategy, has a well-recognised role in First Language education. It is in that context that the problems faced by both young children and students have been identified. For example, Goswami (1992) reports that failure to understand analogy has three fundamental roots: a lack of detailed knowledge of a chosen source, an inability to identify those aspects of the source that might appropriately be mapped onto the target; a lack of understanding of how to draw a relationship between relevant aspects of the two domains.

These problems have also been identified in science education (Aubusson, Harrison, & Ritchie, 2006). The research conducted so far has been largely concerned with students’ ability to understand the ‘teaching analogies’ created by their teachers in the context of direct instruction. Whilst the general problem of lack of background knowledge was impossible to directly address, the ‘Focus, Action, Reflection (FAR) Guide’ for teachers (Treagust, Harrison, & Venville, 1998) has proved an effective way of ensuring that the second and third roots of misunderstanding could be addressed (Harrison & Treagust, 2006).

The little work that has been undertaken into the value of students’ own construction of ‘teaching analogies’ (which we might term ‘self-teaching analogies’), those in teacher-driven contexts have been shown to be successful (Aubusson, Treagust, & Harrison, 2009). As discussed in Chap.  8, the much greater emphasis on students’ construction of analogies during MBT suggests that the process of development of their ability to do so warrants close attention in itself. The Teaching with Analogy (TWA) model and the FAR Guide should prove valuable ways of systematically introducing students to the ideas surrounding the construction and use of analogies. In fact, when the TWA model was used as a base for the initial activity in Mozzer and Justi’s (2012) study, it was found to be very helpful in supporting students’ understanding of the meaning of analogy.

Progression in Argumentation

The Nature of Competence in Argumentation

In Chap.  6, we outlined the skills required for individual participation in argumentation. To do so, a person needed to be able: to deal with evidence, to argue, to counter-argue, to produce alternative theories, to refute arguments (see Table  6.1). Being able to do so in a wide variety of situations constitutes competence in argumentation.

Evidence on the Attainment of Competence in Argumentation

Although a great deal of research into argumentation in science education has taken place in the last decade, it is only fairly recently that overviews of the field have begun to appear (Erduran & Jiménez-Aleixandre, 2008; Mirza & Perret-Clermont, 2009). A review of the literature on student learning (Garcia-Mila & Andersen, 2008) reveals that, in general, students argumentative skills are poor until they are specifically addressed. Most importantly, students:
  • do not engage with the arguments put forward by their peers during collaborative working. They only consider their own claims, ignoring those of other people with whom they are (in theory at least) working;

  • put forward claims without them being accompanied by potentially supportive evidence;

  • put forward evidence, when they do so, that which supports their own claims.

Students’ normal lack of competence in respect of argumentation suggests that engagement in modelling activities, of the type that we have outlined in MBT, will lead to the gradual development of these skills. Evidence that support this affirmative is discussed in Mendonça and Justi (2013) and in Chap.  8.

Progression in Understanding About Science

The Nature of Competence of Understanding About Science

Chapter  9 outlined the different perceptions of nature of science that might inform school science education. A combination of the ‘Family Resemblance’ and the ‘Whole Science’ views does present a compelling account of the field, but implementing this with the school curriculum would require major changes both to syllabuses and to teacher education.

Evidence on the Attainment of Understanding About Science

Given the complexity of the ideas involved, it is not surprising that such research as exists shows that, in the absence of teaching focused on ‘understanding about science’, only a relatively small proportion of students show an acceptable grasp of those ideas at any one place in the school curriculum (Kang, Scharmann, & Noh, 2005). In a large-scale, interview-based, study Driver, Leach, Millar, and Scott (1996) showed that students aged from 9 to 16 years in the UK demonstrated a slow and uneven progression in successively using three forms of understanding:
  • Phenomenon-based reasoning.

    No distinction is made between observation and explanation. The former involves enquiry by carefully observing objects and events, whilst the latter involves a re-description of those objects or events.

  • Relation-based reasoning.

    Whilst students do distinguish between observation and explanation, the latter is thought to emerge from generalisations about the former.

  • Model-based reasoning.

    Explanations are based on a model of a phenomenon which has a distinct ontological status. A model arises by the act of imagination, whilst the observations made play a substantial role in its acceptance via the making and testing of predictions.

In the light of these results, it would be expected that explicit attempts to teach ‘understanding about science’ would yield some positive results. Leach, Hind, and Ryder (2003) showed that, for some 16–18 year old senior high school students at least, the insertion of single lessons spread throughout the school year did lead to a distinctive improvement in an understanding of the epistemology of science. In an associated study, Ryder, Leach, and Driver (1999) showed that undergraduate science students who were conducting project work, but without explicit instruction on epistemological matters, showed a significant improvement in their grasp of ‘understanding about science’. In the light of these results, it is not surprising that Khishfe (2008) showed that adopting an inquiry-based approach to teaching, which entailed an explicit address to epistemological issues, led to a improvement in ‘understanding about science’ on the part of many of the students.

In all these studies it is puzzling why only some students showed the desired change in understanding. A clue may lie in the finding by Hogan (2000) that there seems to often be a distinction between what she terms students’ distal knowledge of what is entailed in ‘understanding about science’ – their declarative knowledge of the subject – and their proximal knowledge of what is entailed in it – their personal beliefs and commitments. Whilst a failure to grasp the ideas they are taught about ‘understanding about science’ may be widespread among students – those ideas are multiple, complex, and abstract – it may also be the case that they do not believe what they are being taught. Supporting progression may thus be even more demanding that at first sight seems to be the case. At the same time, there does seem to be confusion about the theoretical foundations about both nature of ‘understanding about science’ and how to effectively and efficiently evaluate the progression of learning in and about it (Deng, Chen, Tsai, & Chai, 2011).

As has been shown in the previous five sections of this chapter, our grasp of the manner and extent of students’ knowledge of models and modelling, visualisation, analogical reasoning, argumentation, and ‘understanding about science’, is far from complete. However, this must not excuse us from trying to design an LP in modelling based on current ‘best practice’.

A Potential Strategy for Designing an LP About Models and Modelling

The major question that has to be addressed here is: What notion of learning should form the basis of an LP? One approach would see all learning as completely idiosyncratic, such that no firm, generalised, structure for an LP can be proposed: this would be what Ford (2015) describes as “hopelessly tailored to fleeting fluctuations of situation and setting” (p. 407). Most importantly, it would leave teachers without any real guidance on how to design lessons. The other approach would be to provide what Ford (2015) calls “context-free accounts (…) that have questionable validity” (p. 407). This approach, which has been found to be generally ineffective in facilitating learning, based on the reflection of a sequence of ideas and activities derived from a simplified view of the history of the development of the notion of models and modelling, has been widely used up to the present. We feel that an approach that lies between these two is likely to be both the most supportive of the attainment of scientific literacy in respect of models and modelling by all students and to be within with ‘subject knowledge’ and ‘pedagogic content knowledge’ (Shulman, 1987) of many teachers (but see Chap.  11).

Such an approach would recognise the validity of what has been learnt about learning in science education over the last few decades and which has been assimilated by teachers. Thus, preconceptions/misconceptions by students have been identified for a large number of the concepts used by science (Gilbert & Watts, 1983). It may thus be assumed that students will have some ideas about many of the ideas that comprise an LP on modelling before they are taught them. We can be more certain about what students should know and be able to do when they are fluent in the knowledge and practice of modelling. However, as they will have started to be taught about modelling at very different points in their educational development, we can be far less certain about the status of their relevant knowledge and skills when they start to experience that process. The essence of any curriculum that addresses ‘models and modelling’ must therefore involve an address to all the elements of competence in modelling at an elementary level, followed by a progressive re-address to those elements at a higher level, perhaps in successive school years. We have identified two possible strategies based on existing best practice that meet these criteria. It first is self-evident: the explicit provision of a progressive exposure to all the components of a capability in models and modelling. The second is wider in ambition: the design and provision of a curriculum based on ideas about models and modelling. We now address these two alternatives.

Model 1: An Explicit and Progressive Exposure to Competence in Modelling

This approach consists of a direct and progressive acquisition of the elements of knowledge and practical skill that comprise a competence in modelling. It is produced by linking together the conduct and outcomes of activities that have, individually or in conjunction with each other and over a period in time, already been reported in the research literature.

As a result of working with teachers to produce a description of a ‘modelling environment’ that was suitable for (USA) grades K to 6 in respect of precursors to the study of notions of ‘evolution’, Lehrer and Schauble (2012) identified some principles that seem Competence in Modellingrelevant to all content-themes in the science curriculum (that is, including that of ‘models and modelling’) and all student age-ranges. Thus, in order to provide a structured knowledge of modelling, investigations should take place:
  • using phenomena (systems, contexts, problems) that are capable of supporting enquiries at a progressively greater depth;

  • using varied exemplars of such phenomena so that ‘transfer of learning’ is facilitated;

  • in such a way that meaningful questions about the phenomena can readily be raised by both the teacher and the students;

  • in such a way that support the development of a repertoire of types of representations (graphs, diagrams etc.);

  • in such a way that support the development of progressively improved practice in the use of those types of representation;

  • in such a way that support the development of the practice of measurement and hence of the skills of assessment.

Turning these principles into an actual LP in models and modelling could be produced by successively providing students with opportunities to:

Learn and Use a Model of Models and Modelling

The theme of ‘models and modelling’ is often first met at the beginning of different phases of education. In these circumstances a conservative, transmission, model of teaching must be (alas) assumed for many such occurrences, perhaps augmented by student-led practical work, in either physics, or chemistry or biology. Many of the recorded instances relate to study at university level, although there seems no a priori reason why they should not found at school level. Thus, for example:
  • In biology, Passmore and Stewart (2002) directly taught several models of evolution, including Darwin’s Theory of Natural Selection, to high school students and had them successfully use it to explain a number of phenomena using self-made representations.

  • In physics, Redfors and Ryder (2001) taught university students about the structure of metals and found that their understanding was best when the examples chosen were familiar to the students. Arnold and Millar (1996) introduced the notions of heat, temperature, and thermal equilibrium to 12 year-olds and then had apply them in a range of contexts, thus showing the power of a concept to provide generalise understanding.

  • In chemistry, Luxford and Bretz (2013) taught university students in the USA about covalent and ionic bonding and subsequently interviewed them where they were found to be better able to show their understanding when using self-made play-dough representations.

In general, this initial phase consists of: direct teaching of a curriculum model by the teacher, augmented by practical work in which students attempt to relate how that model explains the behaviour of phenomenon by use of representations of it (usually in a concrete/material form).

Learning to Revise Models

In this addition to the ‘learn and use a model’ approach, students are required to learn and subsequently alter a model that explains a simple phenomenon so that it successfully represents more complex phenomena (Halloun, 1998). Here, a model is adapted to address changing purposes, for example having represented the behaviour of a phenomenon then going on to represent the causes of that behaviour.

In this phase, the emphasis is on changing a model so that it can meet revised/altered different purposes.

Learning to Reconstruct a Model

In this approach, students are provided with all the elements of an established model and with a series of questions, the answers to which will lead them to build that model.

Two examples stand out in the literature. Barab, Hay, Barnett, and Keating (2000) provided undergraduate students with the elements of the standard solar system model and had them assemble the components in order to explain various phenomena shown by the Earth-Sun system. The emphasis here is on the construction of a model, probably heavily ‘scaffolded’ by the teacher. Louca, Zacharia, and Constantinou (2011) familiarised 11–12 year old students with a computer-based modelling system and required them to work in groups. They attempted to recreate models to explain ‘the free-fall of an object’, ‘relative motion’ and ‘diffusion’. With the teacher providing supportive questions only, activity by the students passed through three phases: the description of the phenomenon (objects were identified); causal reasons for behaviour were speculated on; the construction of ‘stories’ about what was happening to individual objects in the production of a comprehensive causal explanation.

At this stage of learning about modelling, the main precepts become present. Whilst the teacher may set the problem, the questions to be addressed are identified by the students, as is the proposal of a model, together with the collection, analysis and evaluation of data. Whilst the main elements of modelling are present then, they are carried out within the psychological safety of a known-model of a phenomenon.

Learning to Construct a Model de Novo

This can be based on the ‘ Model of Modelling’ approach that has be presented and discussed in Chaps.  3 and  4. All the criteria for models and modelling are met. As discussed in Chap.  4, this means that students would need to experience all the stages of modelling, starting from doing so in situation involving simpler entities to be modelled and questions related to them to be answered, and gradually moving to situations involving more complex entities and questions. However, by taking into account what is discussed in this chapter, the progression would not only be related to the target of modelling. Perhaps more important than this, the progression concerning learning to construct a model de novo would require a series of simultaneous progressions in the major epistemic practices that permeate modelling ( visualisation, analogical reasoning, and argumentation), thus supporting the main cognitive processes involved in performing it (as discussed in Chap.  2). Therefore, students learning would not be focused only on learning a given scientific or socio-scientific topic through modelling-based activities, but also on simultaneously learning to perform the related epistemic practices. Such progressions would result in (and, in some sense, constitute) progressions in the understanding of the entity being modelled, the development of the competence on models and modelling, and the understanding about science.

In a simplified way, the progression concerning learning to construct a model de novo could be represented through a series of interconnected multiple spirals, each one representing the progression in visualisation, analogical reasoning, argumentation, understanding about science, etc. (Fig. 10.1). It seems impossible to predict or to identify the meanings of each point where two or more spirals cross each other in a theoretical manner or outside a given context. On the other hand, Fig. 10.1 emphasises that:
Fig. 10.1

Representation of the progression concerning learning to construct a model de novo

  • the learning process represented is dynamic and non-linear (as it is modelling itself);

  • specific points in one spiral may influence and/or support turnings points in a distinct spiral.

The latter aspect was partially observed in some of the studies conducted from the Model of Modelling perspective discussed in Chaps.  4,  5,  6,  7, and  8 when the authors showed, for instance, how the development of students’ argumentation supported their better performances during production, expression, tests and evaluation of models (Mendonça & Justi, 2013), or how the development of students’ visualisation skills was essential for their learning of both abstract chemical topics and meta-modelling knowledge (Gilbert et al., 2010; Justi et al., 2009; Maia & Justi, 2009). However, in those studies, the empirical data were analysed in order to address questions that did not focus on the relations between distinct L.P. Therefore, this new approach requires other studies from which (i) Fig. 10.1 could be tested, and (ii) the meaning of specific representational aspects in Fig. 10.1 could be better characterised. Certainly, there is a lot yet to be done!

Model 2: Basing the Curriculum Substantially on the Ideas of Models and Modelling

A Basis in Teacher-Led Development Work

This approach has been developed during the work of the ‘Cams Hill Science Consortium’ which began in 2001 and which continues to evolve to this day. Although only a more detailed account of the first 5 years of the project are available (Newberry & Gilbert, 2007), the general outlines of the project have remained the same throughout the whole period. Thus:
  • the work covers the whole age range of compulsory science education in England and Wales (5–16 years);

  • the basic objective was to support teachers in the professional provision of a science curriculum based on constructivist principles. It must also meet the requirements of the mandatory National Curriculum (which was undergoing a process of change throughout the period 2001–2015);

  • participation is by the invitation of teachers who had shown a capability for curricular innovation. Although participation changes somewhat, as teachers changed their schools, 27 schools were directly involved in 2013. Funding was largely provided by participating schools;

  • ideas were initiated, developed, and discussed during meetings spread throughout the ‘school year’;

  • between these meeting, the teachers tried out their ideas in the classroom as they saw fit, reporting the outcomes (both positive and negative) to the next meeting of one of the three geographical sectors of the Consortium.

The Outputs of the Consortium

The initial impetus for the Consortium was the belief by the initiators (Matthew Newberry and John Gilbert) that the ideas of models and modelling had much to contribute to a science curriculum that would engage students. The outputs of the Consortium can be summarised under four headings reflecting themes that were addressed roughly sequentially during the project:
  1. 1.

    Providing a coherent basis for the development of understanding.

A careful reading of the National Curriculum convinced the members of the project that the progressive ‘levels of attainment’ that were expected to be achieved by students were based to Bloom’s taxonomy of educational objectives (Bloom, 1956). Being initially focused on the higher ‘levels of attainment’ (i.e. 4–7), the project initially developed a ‘ levels mountain’, which provided a simple empirical guide simultaneously to the nature of the ‘steps in understanding’ that were expected, the magnitude of the increased cognitive demands that they successively required, and the relative time that the full attainment of each required (see Fig. 10.2).
Fig. 10.2

The ‘Levels Mountain’ representing the increased ‘Levels of Understanding’ required by the National Curriculum (Newberry, Grevatt, & Gilbert, 2009, p. 21)

The Levels Mountain was readily understood by both teachers and students, being widely used to suggest, in classrooms in the south of the UK, what understanding was required if the ‘next Level’ was to be attained. While intended initially as a guide for teachers in lesson planning, students also found it helpful in grasping what was expected of them.

However, towards the end of the 2000s, the designers of the National Curriculum abandoned the explicit expectation of ‘Levels of Understanding’ on the grounds that students’ parents found the idea difficult to understand. In order to accommodate the change in terminology that ensued, whilst retaining the notion of models in an implicit form, the ‘Progress Pathway’, in which the nature and quality of the explanations that students were expected to understand were set out for each academic year of the primary school (1–5) and across the sum of the first three academic years of the secondary (junior high) school (7–9) (see Figs. 10.3, 10.4.a, and 10.4.b).
Fig. 10.3

An example (Year 3) of the ‘Progress Pathway’ for the progression of learning in the Primary School (Newberry & Cams Hill Science Consortium, 2014)

Fig. 10.4.a

The ‘Progress Pathway’ expected to students in Years 7 to 9 (Newberry & Cams Hill Science Consortium, 2014)

Fig. 10.4.b

The ‘Exceptional Progress Pathway’ designed to challenge able students in Years 8 + 9 (Newberry & Cams Hill Science Consortium, 2014)

Notice that the emphasis has shifted to ‘the attainment of explanatory’ competence, recognising that, with advancing school years, the pace of learning spreads out across a student cohort whilst the nature of that understanding expected of all is increasingly precise. This approach assumes the notion of ‘model’ as the driving force in the production of explanations: the more advanced the understanding of the nature of models, the more sophisticated the explanations that are possible.
  1. 2.

    Providing a basis for a constructivist approach to learning about and with models.

The project developed an outline ‘scheme of work’, based on constructivist principles, that would enable any one of the ways of using models (learning, using, revising, recreating, producing) to be addressed. Called the ‘Thinking Frame’, its basic structure is given in Fig. 10.5.
Fig. 10.5

A generic ‘Thinking Frame’ (Newberry, 2006)

An interactive website with further details and videos of the Cams Hill Science Consortium’s Thinking Frames Approach can be found on

The initial impetus for a class based on the use of a Thinking Frame was the identification of a problem associated with a phenomenon that was readily accessible to students. Every effort was to pick on examples of phenomena that were drawn from everyday life: books such as Press (1995) provided the basis for problems as did the ‘scientific toys’ commercially available, for example ‘the sonic gun’.1 The first step with a class would be elicit brainwaves about what was happening in or causing the phenomenon observed. These would be models, whether preconceptions or previously taught models. The next step would be for students to produce a visualisation of what was happening or causing the phenomenon. This would involve the various modes of representation. As the use of the Thinking Frame became more common in a given class, students would develop competence in a repertoire of modes. The third step was to produce a thinking sequence of a possible explanation as a series of bullet points which was then tested empirically. The fourth step was to produce a paragraph that linked the thinking sequence into prose. In a variety of guises, dependent on the purpose of the initial question asked and the wide range of phenomena that could be explored, the thinking frame provided a flexible pedagogic teaching tool that was widely used in the south of England. It enabled all the ways of learning about models and modelling to be explored, up and including ‘learning to model de novo’.
  1. 3.

    Providing a basis for evidence of learning.

Students in schools in England and Wales are required to demonstrate their learning in a series of public examinations. Of the types of written questions that they are asked, the most challenging is the ‘short answer’, where a series of sentences have to be composed by the student. This has been found to be very challenging to students. In the light of this experience, the Cams Hill Science Consortium developed a ‘Literacy Ladder’ to help teachers integrate writing skills into their use of the ‘Thinking Frame’ (see Fig. 10.6.).
Fig. 10.6

The literacy ladder (Newberry & Cams Hill Science Consortium, 2007)

When the sequence of activities in the ladder was undertaken with classes jointly with colleagues from the corresponding English Department, the outcome was found to be most successful: students could express themselves both more concisely and precisely.
  1. 4.

    Providing a scheme of work for the National Curriculum.


As the substantially nature of the revised National Curriculum became apparent during the 2010s, the Consortium was concerned that teachers would devalue their own extensive professional experience and instead purchase new published textbook schemes, some of which might have been inadequately field-tested. So it was decided, perhaps as a culmination of the work of the Consortium, to produce a model of the curriculum that, whilst faithfully adhered to the mandatory requirements of the National Curriculum, also enabled teachers to develop lesson plans that valued their professional experience.

The basis for the model curriculum was the topic overview. A generic structure of a topic overview is given in Fig. 10.7.
Fig. 10.7

The structure of a topic overview (Newberry & Cams Hill Science Consortium, 2014)

The key aspects of a topic overview were:
  • The topic title.

  • The background colour allocated of the theme in the National Curriculum to which the topic belonged. The themes were: Survival (animals); Survival (plants); Changes; Forces; and Materials. In each of the 6 years of the primary school, students would study 6 topic overviews. In each of the 3 years of the junior high school, students would study 13 or 14 topic overviews. By junior high school the names of the key themes were updated to be called: Life & Survival; Energy; Forces; and Particles.

  • The ‘key vocabulary’ would list both words that had been previously listed and the new words associated with the particular topic overview.

  • The key concept that underlay the topic being studied.

  • The other ‘bubbles’ indicate the facts about specific phenomena that are to be studied.

Examples are given in Figs. 10.8 and 10.9.
Fig. 10.8

A topic overview from a Year 3 forces topic (Newberry & Cams Hill Science Consortium, 2014)

Fig. 10.9

A topic overview from a Year 7 forces topic (Newberry & Cams Hill Science Consortium, 2014)

Further details of the Cams Hill Science Consortium can be found on, where copies of these resources may be purchased. At the time of writing (June 2015), over 150 primary and secondary schools have adopted the scheme.

Addressing the Challenges of Implementing an LP on Modelling

Whilst a broad framework for the design and implementation of an LP on modelling is a necessary first step in its implementation, teachers must take practical steps to realise its potential in the particular realities of the classroom, laboratory, field centre or other learning environment. Several such steps are discussed below.

Gaining Access to Phenomena

The phenomena that can sustain an LP on modelling must, of course, be able to support both the acquisition of all the elements of both the knowledge of modelling and of the development of the practice of modelling. It also must, in the realities of a school science curriculum, lead to the attainment of a high-level understanding of some of the core content concepts required by that curriculum. When should this be attempted with students and how might it be organised?

Unless a step-wise ‘cognitive capability’ model of conceptual development is adopted by teachers, there seems every reason why attempts to implement an LP on modelling might be undertaken with students of any age. A few detailed examples have been published on the use on such work with younger pupils. One example is that of framing an evidently successful enquiry into ‘the action of a solar still’ by Kenyon, Schwarz, and Hug (2008) with Grade 5 classes. These authors also give sketch outlines of LPs for modelling for such students built around: the life cycle of insects, electrical circuits, condensation, human sight, how smell works. However, in a review of papers that have appeared on modelling- oriented assessment in the period 1980–2013, Namdar and Shen (2015) showed that only a very low proportion (1/3) of the students could grasp the purpose of the empirical work required when at high school level. However, as the notion of teaching towards an LP on modelling gains ground with teachers, textbook writers, and curriculum designers in the next few years, it must be expected that reports of classroom experience will begin to define the lower age-limit at which such work can realistically begin, if one is in fact necessary.

Another perspective on the issue of ‘access’ is: how should that be provided? The traditional valuation of ‘direct empirical experience’ in science education (see, for example, Hofstein & Lunetta, 1982) strongly suggests that this should be the preferred form. However, the pressure on curriculum time, the complexity of arranging such direct access, particularly for the long periods of time and for large numbers of students that modelling work entails, coupled with the wish to have that work be decisive and leading to clear cognitive gains, has led to the introduction of computer-based ‘experience’. This has been coupled with guided instruction, especially in the examples authored by the Concord Consortium in the USA (The Concord Consortium, 2014).

If we have clear ideas both of what can reasonably be achieved with a particular group of pupils and of the means by which suitable access to appropriate experiences can be provided, what then might the characteristics of those experiences be? They must:
  • address phenomena in which the students have an interest (or can be persuaded to find interesting!);

  • be such that exemplar forms can be made available to students;

  • depend on a few scientific concepts for its explanation.

However, the most important criterion must be that phenomena chosen must be capable of sustaining ‘authentic modelling practices’.

Identifying and Modelling Phenomena that Are Candidates for ‘Authenticity’

Authentic modelling practices in science are those that are characteristic of a group of workers in the field, who, as a result of addressing purposes in common, come to use a set of research skills based on the same pool of knowledge. Such practices, once identified with the help of the scientists, can be adapted for learning purposes, the major gain of this being that students will come to understand and use the epistemology that underpins them. Situations that are capable of doing so have to meet a number of criteria. They must be capable of:
  • provoking interest in students because they relate directly to the impact of science on society;

  • being enquired into by groups of students in an autonomous manner;

  • involving the use of a coherent model of modelling;

  • conveying the same subject knowledge as is required to understand the original scientific practice. This implies that details descriptors of that practice are needed;

  • being enquired into safely using the equipment available in a school;

  • not requiring too much curriculum time (after Prins, Bulte, van Driel, & Pilot, 2008).

In the 2008 paper, Prins et al. also identified three topics as meeting all their criteria: the modelling of microbiological contamination in food chains to predict food safety; the modelling of the water treatment process used to predict the quality of drinking water that can be produced from surface water; and the modelling of human exposure to and uptake of chemicals emitted by consumer products in order to predict the safety of consumer products. Prins et al. (2011) reported the evidently broadly successful implementation of the ‘water treatment’ case with ten groups of four 16–17 year-old (Grade 10 and 11) chemistry students in The Netherlands. However, the procedure occupied 8 lessons, each of 50 min, and suggests that such authentic modelling activities are not to be undertaken lightly, given their considerable expense of curriculum time. It is also the case that the implied effort and commitment needed to establish the scientific practice being taught authentically are considerable. There seems no way of short-circuiting access to the scientific knowledge and skills involved.

Ensuring That ‘Transfer of Learning’ Takes Place

Successful ‘transfer of learning’ means that knowledge which is learnt in one context can be employed in another context (Gick & Holyoak, 1980). Attaining such transfer when an LP on modelling is the focus of attention is especially important for two reasons, both of which have got to do with the use of time. First, developing students’ full understanding of modelling will take a lot of curriculum time, so there is pressure to ensure that the investment is worthwhile. Second, whilst the LP on modelling is being addressed, students will have necessarily been learning concepts that are core components of the curriculum: it is important to show that the latter has been fully effective.

The issue of ‘transfer’ in relation to the knowledge and skills of modelling has not yet been the focus of many empirical studies. Bamberger and Davis (2013) differentiate between two idealised contexts in which transfer may take place. ‘Near transfer’ is when learning in situation A is similar to that required for situation B and the similarity between the two situations is readily apparent to students: they also call this ‘transfer-in-situation’. ‘Far transfer’, on the other hand, is when learning in situation A is considerably different to that in needed for situation B and the relationship between the two is not readily apparent to students: they call this ‘transfer-between-situations’. One would expect that ‘transfer-between-situations’, of the two, is much harder to achieve.

This same paper also rehearses the three levels of increased understanding attainable for each of the

… four dimensions of the epistemic criteria that capture growth in students’ performance and understanding of the practice (of an LP in modelling): (A) attention to abstraction and representation of the features of the model; (B) attention to clarity of communication and audience understanding; (C) attention to evidentiary support (for claims made); (D) attention to mechanistic and process-oriented versus illustrative/descriptive accounts (Bamberger & Davis, 2013, p. 216 as originally set out in; Schwarz et al., 2009).

From this, they set out three increasing levels of modelling performance that deal with each of:

The explanation domain (which) refers to the extent to which the model (produced by a student) answers questions about how and why the scientific phenomenon happened. (…) The comparative domain refers to the extent to which the model compares the two situations. (…) The abstraction domain refers to which aspects of the model include elements that are inaccessible to our eyes. (…) The labelling domain refers to the extent to which the model includes a key and labels of the model’s elements (Bamberger & Davis, 2013, p. 223).

The Bamberger and Davis (2013) study drew on standard four-level models of the understanding of ‘the particle nature of matter’ and of ‘friction’, and was conducted with Grade 6 students. They were taught an LP module on ‘the particle nature of matter’ (PNM) as manifest in ‘smell’, taking tests both before and after this experience of their understanding of ‘smell’,’evaporation’, and ‘friction’. The results showed that for:
  • the same topic as that of the teaching (‘smell’), the students improved both their understanding of the PNM and their modelling performance. In respect of the latter, students showed improvement in the ‘explanation’ and ‘communication’ domains but less so in the ‘comparativeness’ domains and not at all in the ‘abstraction’ domains;

  • a question concerning ‘evaporation’, a topic that is in a near-content transfer-in-situation to ‘smell’, the students showed significant improvement in their understanding of PNM but only in that of the ‘explanation’ domain of their model. In short, their modelling capabilities of explanation increased as long as the content was readily perceived as familiar;

  • a question concerning ‘friction’, a far-content transfer-in-situation topic, the students did not improve their content knowledge, but did improve their modelling performances in the ‘explanation’, ‘abstraction’ and ‘labelling’ domains.

The results of this study show that, when an LP on modelling is the focus of teaching, students can transfer that knowledge to new content areas, provided that this calls for ‘near transfer’ (also known as ‘transfer-in-situation’), but that this transfer was not necessarily reflected in their knowledge of the content of the new area. These results also suggest that what students perceive to be the focus of the teaching is all important in deciding what they learn. In practice, therefore, teachers have to strive to give a balanced emphasis on ‘ modelling skills’ and ‘content knowledge acquisition’ for transfer to be achieved in even ‘near transfer situations’. Another implication that might then be drawn, by extrapolation from these results, is that ‘far transfer’ may require even more prolonged and focused attention when modelling is used in order to achieve an improved content knowledge.

Establishing LPs in Modelling

Whilst some progress has been made in identifying the characteristics of LPs in modelling, they will only be widely facilitated if:
  • a ‘library’ of phenomena that are readily capable of providing opportunities for work on ‘models and modelling’ is established with the skills and knowledge of modelling entailed for each point of entry having been identified;

  • the ‘entry’ and ‘exit’ characteristics of attainment for students of different ages are established for each phenomenon;

  • the intermediate steps in progression are established, recognising that this will be far easier in terms of ‘knowledge’ than for ‘skills’;

  • detailed strategies for teaching these ideas are established.

This list implies a major effort of research and development by the science education community. There is one more theme that cannot be overlooked: assessment.

The Assessment of Progression Towards Competence in Modelling

If students are to achieve meta-competence in models and modelling, then a major factor must be their engagement in ‘self-assessment’ (James, Black, McCormick, & Wiliam, 2006). This will contribute to the formative evaluation conducted by the teacher, which is defined as:

Evaluation conducted while a creative process is under way, designed and used to promote growth and improvement in a students’ performance or in a program development (Gullickson, 2002)

and no doubt contained within an overall strategy focused on inquiry-based science education (Csapo, 2014).

Despite the centrality of this activity, a recent review by Nicolau and Constantinou (2014) found that only 23 published papers about it were substantial, concerned with school-age students, and were empirically-based. It seems that, in general, data is collected by use of interviews, open- and closed-questionnaires, video, and concept mapping. The data collected was concerned with modelling practices, the products of modelling (i.e. models), the acquisition of meta-knowledge, and the cognitive processes involved. The authors observe that “in the reviewed papers, modelling competence was neither defined nor assessed in a unified manner” (p. 71).

The theme of the assessment of models and modelling, both for formative and summative purposes, does then require considerable additional work, not least because their inclusion in the ‘Next Generation National Standards for Science’ for the USA, which is likely to be very influential at world-level, is clearly signalled (NGSS Lead States, 2013).


  1. 1.

    Sonic Gun is a circular flexible membrane stretched over a circular frame is drawn back at its center and released. The force produces a shock wave in the air that is detectable at a short distance.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • John K. Gilbert
    • 1
  • Rosária Justi
    • 2
  1. 1.The University of ReadingBerkshireUK
  2. 2.Universidade Federal de Minas GeraisBelo HorizonteBrazil

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