Khine M.S., Saleh I.M. Models and Modeling: Cognitive Tools for Scientific Enquiry

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Part I

Theory Formation and Modeling

in Science Education

Chapter 1

Modeling and the Future of Science Learning

Richard K. Coll and Denis Lajium

Introduction

Models and modeling are of such importance in science that the appropriate under-

standing of, and ability to use, models is seen by many authors as central to an

understanding of science (Gilbert & Boulter, 1998; Harrison & Tr eagust, 2000;

Ramadas, 2009). In this chapter we consider key aspects of models and model-

ing. We begin by describing the nature of models and modeling. We then discuss

how models and modeling relate to the nature of science and scientiﬁc enquiry. This

followed by a description of modeling as a cognitive tool and consideration of how

models and modeling relate to the learning of science. We conclude the chapter

by highlighting the areas of needed research in science education with respect to

models and modeling.

The Nature of Models and Modeling

Three principal purposes for modeling in the sciences are reported in the sci-

ence education literature: (1) to produce simpler forms of objects or concepts;

(2) to provide stimulation for learning or concept generation, and thereby support

the visualization of some phenomenon; and (3) to provide explanations for scien-

tiﬁc phenomena (Gilbert & Rutherford, 1998a, 1998b; Passmore & Stewart, 2002;

Ramadas, 2009; Thomas & McRobbie, 2001). The process of modeling involves

the transfer of some features of the source of the model to the target of the model

(Brodie et al., 1994) (Fig. 1.1). We thus have a target, something we want to under-

stand; a source, something known to us from our everyday life or prior experiences;

and the model which helps us bridge between the two (Brodie et al., 1994; Suckling,

Suckling, & Suckling, 1978).

R.K. Coll (B)

Science and Engineering Faculty, University of Waikato, Hamilton, New Zealand

e-mail: r.coll@waikato.ac.nz

M.S. Khine, I.M. Saleh (eds.), Models and Modeling, Models and Modeling

in Science Education 6, DOI 10.1007/978-94-007-0449-7_1,



Springer Science+Business Media B.V. 2011

4 R.K. Coll and D. Lajium

Model

SourceTarget

Fig. 1.1 The relationship between a model, its source and target (after Brodie et al., 1994)

model (R

)

analog (R

)

target (R

)

analogy (A)

Fig. 1.2 Analogical transfer by structural mapping between two domains (from Duit, 1991)

A useful visualization of such mapping from target to source is provided by Duit

(1991) (Fig. 1.2). In Duit’s representation, the process of modeling involves analog-

ical mapping—many authors believe that all models are in fact analogies and that

all modeling consist of mapping via the use of analogy (A) (see, e.g., Gilbert, 2004;

Harrison, 2008). In this mapping, there are features in parts of the structures of the

analog (R

) and target (R

) that are shared (R

From Fig. 1.2 it can be seen that modeling involves s impliﬁcation of the target.

In other words, the model is a simpler version of the target and shares only some

attributes with the target (i.e., R

). As a consequence, the extent to which the target

and source share attributes varies (Maksic, 1990), and because of this the model and

target may in some cases be very different and may be different in numerous ways.

This is an inherent feature of models and modeling and should not be seen as some

sort of ﬂaw or limitation of models; indeed as we shall see it is a key component

of models and modeling. The fact that the model is simpler than the target means

is in fact beneﬁcial, because we can ignore less relevant or unimportant details, and

instead focus on the most interesting or important facets—selected and dominant

features that help us understand key attributes of the target. Consequently, the use

of a model enables scientists to identify key aspects of the target without becoming

distracted by unimportant detail or attributes (Gilbert & Boulter, 1998). The initial

grasping or generation of an abstract concept is more readily achieved when the

concept has been stripped to the bare necessities required for understanding—a pro-

cess of what Weller (1970, p. 118) describes as providing “a basic outline of the

‘forest’.”

So the nature of the target and the purpose of models, and subsequent modeling,

vary, and so the models themselves vary considerably (Gilbert & Osborne, 1980).

1 Modeling and the Future of Science Learning 5

Some are quite simple such as a two-dimensional drawing or a ball-and-stick model

used to illustrate aspects of molecular geometry in a small molecule. Others are

highly complex and might, for example, be used to provide detailed predictions

of physical or chemical properties (e.g., quantum mechanical modeling of atomic

structure, modeling of spectroscopic data such as nuclear magnetic resonance—

NMR).

Although many authors emphasize the importance of models in science, there is

much variation in the use of the terms model and modeling, and as a consequence

numerous typologies of models have been developed. Examples of types identi-

ﬁed in the literature include knowledge models scale models target systems mental

models, and expressed models (see, e.g., Brodie et al., 1994; Gilbert & Boulter,

1998; Harrison & Treagust, 1998; Justi & Gilbert, 1999; Smit & Finegold, 1995;

Suckling et al., 1978). These typologies can, however, be distilled down to a few

key types. These are target models—the concept or phenomena of interest— and

the user’s model—the model possessed or used by an individual, often a mental

model (Norman, 1983). A users’ mental model is a personal mental construct and,

according to radical constructivists, such a model is only accessible by another up

to a point (Gilbert, 2004; von Glasersfeld, 1993). When users’ models or mental

models are shared and aspects of these are agreed they become consensual models

(and after time an historical model, see Gericke & Hagberg, 2007). A consensus

or historical model is a model that has been subject to some form of “testing” (e.g.,

physical testing or argumentation) by a particular social group. In the case of science

this group is the scientiﬁc community, and this group or community agrees on the

attributes and value of the model. Teaching models, as the name implies, are mod-

els using during instruction. Expressed models are models as they are expressed,

or communicated, to others. This may take the form of actual expression (e.g., in

language or drawings), or as one can interpret the model from analysis of presented

models (e.g., in textbooks or scientiﬁc writing). This notion recognizes a model

as the construct of an individual, or a particular community of practice, consistent

with the view that any model is a mental model (Gilbert, 2004), and thus a personal

mental construct (von Glasersfeld, 1993).

The above description of the nature of models is driven by the purpose or use of

the model. Models also may be classiﬁed on the basis of the nature of the model.

Obvious examples are physical models and mental models; but there also are numer-

ous other types of models identiﬁed in the science education literature. Interestingly,

the model typologies based on model nature or type throw up some things that we

may not have thought of as models, for example, chemical equations. But if one

considers the nature of models (viz, they are a representation of an entity or phe-

nomena), then such classiﬁcation is logical and appropriate. Again, classiﬁcation

schemes can be summarized in broad terms. So models have been classiﬁed on the

basis of their nature as falling into two broad types physical models and concep-

tual/symbolic models (Brunner, 1967; Coll, 1999; Suckling et al., 1978). Physical

models include things such as concrete physical models such as scale models used

in engineering design or architecture and ball-and-stick or space-ﬁlling models used

in chemistry (Black, 1962;Harré,1970; Smit & Finegold, 1995; Tomasi, 1988

6 R.K. Coll and D. Lajium

Conceptual models consist of diagrams such as reaction schemes and metabolic

pathways (Gilbert, 2004; Harrison & Treagust, 1996), and formulae (Gilbert, 2004;

Harrison & Treagust, 1996; Trindle, 1984). Some models, like analog models, may

be physical or conceptual/symbolic (Black, 1962; Duit, 1991; Peierls, 1980; Tomasi,

1988). Conceptual/symbolic models represent mental constructs; in other words,

they are mental models (Brunner, 1967; Suckling et al., 1978) or expressed mental

models (Gilbert, 2004).

Models, Modeling, and the Nature of Science

Here we delve into the nature of models and modeling in a little more detail,

and consider how this relates to the nature of science. As noted above models

possess a number of fundamental properties, a key feature being that they are

human inventions or (mental) constructions. As such, they represent an approxima-

tion of reality (Portides, 2007), or a limited “version” of the target, and inevitably

present an incomplete understanding of the entity or phenomena (Carr & Oxenham,

1985; Ganguly, 1995; Greca & Moreira, 1997). We might say they are “wrong”

or “limited” in some key aspect (Tomasi, 1988; Trindle, 1984). Here, we mean

they are inherently limited, because human understanding can never match real-

ity (Harding & Hare, 2000). But many models possess notable limitations that are

clearly recognized in advance, and these limitations may be unhelpful in the use

or function of the model. Two examples illustrate our meaning here. First is the

Aufbau principle used to explain the electron conﬁguration of the elements. It is

well recognized that many elements do not agree with predictions of the Aufbau

principle (e.g., chromium and copper). But it “works” for most elements, so it is

retained, and explanations are developed for the anomalous elements (e.g., inter-

electron repulsion, Zumdahl & Zumdahl, 2003). Perhaps a more dramatic example

is ligand ﬁeld theory. Ligand ﬁeld theory models bonding in organometallic com-

plexes and is based on simple electrostatic attraction between a metal center and

electron-rich ligands (atoms, ions, or groups) that surround it. This attraction leads

to perturbation of energy levels for the metal d orbitals in particular, and the model

allows for predictions of electron distribution and bonding. A major use of model

is in the interpretation of electronic absorption spectra in the UV–visible portion

of the electromagnetic spectrum. However, there is much evidence to suggest that

ligand ﬁeld theory fails in many ways; the simplest example relates to the failure of

ligand ﬁeld theory to explain the spectrochemical series. Interestingly, despite these

obvious, and fairly serious, limitations, ligand ﬁeld theory is still widely used by

modern scientists (see, e.g., Nakamoto, 2009); simply because in many instances it

is able to correlate some experimental data adequately, and it is therefore useful in

some circumstances.

What is of particular interest here, to our discussion of the nature of science, is

that even when models like ligand ﬁeld theory possess severe limitations this does

not necessarily mean that they are automatically discarded—particularly if not eas-

ily replaced (students often think once a model fails, it is discarded, see Shen &

1 Modeling and the Future of Science Learning 7

Confrey, 2010). It is this highly pragmatic use of models that are known to pos-

sess quite signiﬁcant limitations that distinguishes scientists from students (Shen &

Confrey, 2010; Williamson & Abraham, 1995). Hence, a key aspect of the nature

of science, as it pertains to models and modeling, is that scientists understand the

nature of models and see models in a very functional, utilitarian, manner (Portides,

2007). They instinctively, or as a result of their training, recognize that models

are intended to serve the user and frequently require modiﬁcation (e.g., when new

experimental data are obtained, see Borges & Gilbert, 1999). Grosslight, Unger, J ay,

and Smith (1991) observe that one reason for this difference between scientists and

students is that students and non-scientists tend to think of models in concrete terms,

effectively as scale models of reality (see also, Abell & Roth, 1992; Bent, 1984b;

Carr, 1984; Clement, 1998), and thus do not appreciate their limitations (Ogan-

Bekiroglu, 2007). This, it is argued, occurs because some well-known models have

proven spectacularly successful. Examples include the Watson–Crick model for t he

structure of DNA (Rodley & Reanny, 1977; Watson & Crick, 1953), Einstein’s rela-

tivity (Clark, 1973; Kline, 1985), and Schrödinger’s wave-mechanical model of the

atom (Kline, 1985; Moore, 1989). What this may mean is that successful models

are so powerful at explaining well-understood observationsthat they end up being

regarded as “facts” (Schrader, 1984). In other words, a student or novice may con-

fuse a highly successful, well established, model with reality, or the target it is being

used to model.

Another aspect of the nature of science and models is the fact that it is com-

mon for scientist to use multiple models to describe an entity (Flores-Camacho,

Gallegos-Cázares, Garritz, & García-Franco, 2007) or explain phenomena/data

(Barnea, Dori, & Finegold, 1995; Birk & Abbassain, 1996; Lin & Chiu, 2007). The

use of multiple models is particularly prevalent in some sciences such as physics

and chemistry, especially when it comes to developing an understanding of abstract

microscopic concepts like atomic structure and chemical bonding (Brodie et al.,

1994; Chiu, Chou, & Liu, 2002; Comba & Hambley, 1995; Eilam, 2004; Glynn &

Duit, 1995; Lin & Chiu, 2007; Lopes & Costa, 2007). Again, as might be expected,

there are signiﬁcant differences in how scientists view and use multiple models (see,

e.g., Clement, 1998; Flores-Camacho et al., 2007; Grosslight et al., 1991; Harrison

& De Jong, 2005), with scientists again acting in a highly pragmatic fashion. As

an illustration, there are numerous models for chemical bonding, and scientists

use whichever model seems appropriate and convenient (Coll & Treagust, 2003a,

2003b). Consider reactions of aromatic chemical substances. Molecular orbital the-

ory provides the most comprehensive explanation for the bonding in aromatics (viz,

delocalization of electron density across the molecule), but scientists routinely use

electron dot Lewis structure-type notations and formulae when presenting reaction

schemes (Coll & Treagust, 2002a). Key here, again, is that the scientist retains in his

or her mind an acute appreciation of the limitations that such simple models possess,

and that there are often apparent “contradictions” between models (Flores-Camacho

et al., 2007) because they are used for different purposes.

The ﬁnal aspect of models related to the nature of science we wish to raise here is

the success or otherwise of models. We have already noted that all models possess

8 R.K. Coll and D. Lajium

some limitations or fail in some way, that is, the very nature of the models and mod-

eling. We also suggested above that scientists still use these models, in ways they

ﬁnd useful. Maksic (1990) makes an interesting point, noting that a good match

between the predictions of a given model and experimental data indicates that a

model is reliable and useful. But Maksic goes on to observe that this should not

be taken to infer that complex and sophisticated quantitative models are necessarily

superior to simpler qualitative counterparts. Simple qualitative models, despite their

apparent “lack of accuracy” or lack of sophistication, possess considerable value in

science, for example, in theory generation (Koponen, 2007). Likewise, construct-

ing an analogical model allowed Maxwell to gain access to a systematic body of

knowledge, consisting of a structure of causal and mathematical relationships, dur-

ing the development of his famous equations (Nersessian, 1992; Franco, de Barros,

Colinvaux, Krapas, Queiroz, & Alves, 1999).

Models and Modeling in Scientiﬁc Enquiry

The literature thus suggests that models and modeling are an important part of doing

science and that models play a key role in scientiﬁc enquiry. Models can play a

number of roles in scientiﬁc enquiry, and four distinct functions have been identi-

ﬁed: discovery development evaluation, and exposition (Cosgrove, 1995; Holyoak &

Thagard, 1996, 1997). Discovery occurs when model contributes to the formation or

generation of a new knowledge or the formulation of a hypothesis (Ganguly, 1995;

Johnson-Laird, 1989; Stavy & Tirosh, 1993). When a hypothesis or discovery has

been made, the model may then be used to further its development—either from

a theoretical or from an experimental perspective. As the model is developed, we

need to test the model, and so models play an important role in the evaluation of a

hypothesis, and in evaluating arguments for or against the hypothesis. Finally, mod-

els are commonly used for exposition, that is, they are used to explain hypotheses

or theories to others.

Some authors argue that all models are analogy; whether one believes this or

not, analogies are an important model type used for concept generation. Because

such analogy or model use in concept generation is a personal mental process, it

is difﬁcult to document, although there are numerous scientiﬁc theories for which

models clearly contributed to some vital stage of a scientists’ thinking, whether it

was in discovery or the development of an idea (as described above). There are

a number of well-known models that clearly illustrate the role that models can

play in concept generation during the development of scientiﬁc theories (Sutton,

1993). Holyoak and Thagard (1996) identiﬁed a number of models that they say

have played a role in theory development (mostly analogies). Examples include the

Kekulé’s snakes biting their tails used to model the structure of benzene. Model use

thus plays a generative role—mostly when in situations for which prior knowledge

is weak or when there is little connection between ideas (Silva, 2007; Wong,

1993a, 1993b). The generative function here comes from the way we use models

(see Duit’s model described in Fig. 1.2 above), in that the scientist, trying to solve

1 Modeling and the Future of Science Learning 9

a problem or explain some data, engages in the mapping of attributes from the

known to the unknown (Harrison, 2008; Wong, 1993a). In doing so, the analogy or

model provides insights and inferences. As Wong sees it, these generative models

are dynamic tools rather than static representations used for understanding. In such

circumstances, individuals seek to ﬁnd ways of making it easier to explain observed

phenomena and so develop their own models to advance their understanding (see

also, Johnson-Laird, 1989).

Justi and Gilbert (2002) analyzed how models are produced in science and devel-

oped a “model of modeling” (Fig. 1.3). This model of modeling exempliﬁes the

Fig. 1.3 A “model of modeling” (after Justi & Gilbert, 2002)

10 R.K. Coll and D. Lajium

essential features of scientiﬁc modeling as used in scientiﬁc enquiry. Notable is

the dynamism of the model (Maia & Justi, 2009), in that data are “reconsidered”

constantly, and the relationship between data and the mental models developed

by scientists to explain these data is examined in an on-going, iterative fashion.

Considerable emphasis is placed on testing any scientiﬁc model and re-examination

of relationships between data and models (as we might expect). Acceptance or

rejection of a model is related to the purpose of the model, which remains

paramount—consistent with the literature described above. Sins, Savelsbergh, van

Joolingen, and van Hout-Wolters (2009) sum the use of models and modeling in

scientiﬁc enquiry nicely, describing it as a process of developing, comparing, and

testing competing models.

Modeling as a Cognitive Tool

The above discussion indicates that models, particularly analogical models, func-

tion as cognitive tools. The literature also suggests that students fail to appreciate

that the principal function of mental models in science is to aid in the understand-

ing of some phenomenon, as mentioned above. This lack of insight is highlighted

in studies across different science disciplines. For example, studies by Grosslight

et al. (1991); Abell and Roth (1992) in the biological sciences, Bent (1984b)in

chemistry, and by Raghavan and Glaser (1995) in physics support this conclu-

sion. Gabel, Briner, and Haines (1992) suggest that mismatch between scientists’

and students’ perceptions of the role of models may be due to the inability of

novices to operate at the formal level. To illustrate, chemistry can be described

on three distinct levels, sensory, atomic/molecular, and symbolic. Usually a chem-

ical substance is represented on the atomic/molecular level using models such as

three-dimensional representations (Ke, Monk, & Duschl, 2005). However, students

typically attempt to address chemical problems on one level alone, for example,

using a purely symbolic approach (Jansoon, Somsook, & Coll, 2008, Jansoon,

Coll, & Somsook, 2009; Tan et al., 2008). Consequently, some authors argue that it

is essential for instructors to design problem-solving exercises that utilize all three

levels in an integrated manner to foster genuine understanding, as opposed to merely

achieving competence in the use of algorithms (Gabel et al., 1992; Green, 1996;

Jansoon et al., 2008, 2009; Nakhleh, Lowrey, & Mitchell, 1996; Pestel, 1993), or

to involve students in concrete sensori-motor experiences (Ke et al., 2005) that pro-

vide a range of experiences that develop p-prims that can be incorporated into their

schema.

Given the complexity of some speciﬁc models, the huge variety of models, and

the issues associated with model use, it is not surprising that many authors regard the

appropriate use of models as a complex task. Bent (1984a) makes parallels between

learning chemistry via models and learning a language. Hence, the literature recom-

mends that science teachers introduce a model only when necessary to explain an

experiment or an observation (Coll, France, & Taylor, 2005; Harrison & Coll, 2008).

Students appreciate more about how scientists actually use models when led through