ESSAY FOR THE ERANUS CLUB ON SCIENCE AND FREE WILL
11 FEBRUARY 1873
From Campbell and Garnett, Life of Maxwell, Chapter XIV, pp.434-444
DOES THE PROGRESS OF PHYSICAL SCIENCE TEND TO GIVE ANY ADVANTAGE TO THE OPINION OF NECESSITY (OR DETERMINISM) OVER THAT OF THE CONTINGENCY OF EVENTS AND THE FREEDOM OF THE WILL?
Maxwell sees many causes, some coming from before our birth through heredity, others since birth as education, etc.According to Mr F. Galton, it is derived from structureless elements in our parents, which were probably never developed in their earthly existence, and which may have been handed down to them, still in the latent state, through untold generations. Much might be said in favour of such a congenital bias towards a particular scheme of philosophy; at the same time we must acknowledge that much of a man's mental history depends upon events occurring after his birth in time, and that he is on the whole more likely to espouse doctrines which harmonise with the particular set of ideas to which he is induced, by the process of education, to confine his attention. What will be the probable effect if these ideas happen mainly to be those of modern physical science? The intimate connexion between physical and metaphysical science is indicated even by their names. What are the chief requisites of a physical laboratory? Facilities for measuring space, time, and mass. What is the occupation of a metaphysician? Speculating on the modes of difference of coexistent things, on invariable sequences, and on the existence of matter. He is nothing but a physicist disarmed of all his weapons — a disembodied spirit trying to measure distances in terms of his own cubit, to form a chronology in which intervals of time are measured by the number of thoughts which they include, and to evolve a standard pound out of his own self-consciousness. Taking metaphysicians singly, we find again that as is their physics, so is their metaphysics. Descartes, with his perfect insight into geometrical truth, and his wonderful ingenuity in the imagination of mechanical contrivances, was far behind the other great men of his time with respect to the conception of matter as a receptacle of momentum and energy. His doctrine of the collision of bodies is ludicrously absurd. He admits indeed, that the facts are against him, but explains them as the result either of the want of perfect hardness in the bodies, or of the action of the surrounding air. His inability to form that notion which we now call force is exemplified in his explanation of the hardness of bodies as the result of the quiescence of their parts.
Neque profecto ullum glutinum possumus excogitare, quod particular durorum corporum firmius inter se conjungat, quhni ipsarum quies. Princip., Pars II. LV.Descartes, in fact, was a firm believer that matter has but one essential property, namely extension, and his influence in preserving this pernicious heresy in existence extends even to very recent times. Spinoza's idea of matter, as he receives it from the authorities, is exactly that of Descartes; and if he has added to it another essential function, namely thought, the new ingredient does not interfere with the old, and certainly does not bring the matter of Descartes into closer resemblance with that of Newton. The influence of the physical ideas of Newton on philosophical thought deserves a careful study. It may be traced in a very direct way through Maclaurin and the Stewarts to the Scotch School, the members of which had all listened to the popular expositions of the Newtonian Philosophy in their respective colleges. In England, Boyle and Locke reflect Newtonian ideas with tolerable distinctness, though both have ideas of their own." Berkeley, on the other hand, though he is a master of the language of his time, is quite impervious to its ideas. Samuel Clarke is perhaps one of the best examples of the influence of Newton;(') while Roger Cotes, in spite of his clever exposition of Newton's doctrines, must be condemned as one of the earliest heretics bred in the bosom of Newtonianism. It is absolutely manifest from these and other instances that any development of physical science is likely to produce some modification of the methods and ideas of philosophers, provided that the physical ideas are expounded in such a way that the philosophers can understand them. The principal developments of physical ideas in modern times have been 1st. The idea of matter as the receptacle of momentum and energy. This we may attribute to Galileo and some of his contemporaries. This idea is fully expressed by Newton, under the form of Laws of Motion. 2nd. The discussion of the relation between the fact of gravitation and the maxim that matter cannot act where it is not. 3rd. The discoveries in Physical Optics, at the beginning of this century. These have produced much less effect outside the scientific world than might be expected. There are two reasons for this. In the first place it is difficult, especially in these days of the separation of technical from popular knowledge, to expound physical optics to persons not professedly mathematicians. The second reason is, that it is extremely easy to show such persons the phenomena, which are very beautiful in themselves, and this is often accepted as instruction in physical optics. 4th. The development of the doctrine of the Conservation of Energy. This has produced a far greater effect on the thinking world outside that of technical thermodynamics. As the doctrine of the conservation of matter gave a definiteness to statements regarding the immateriality of the soul, so the doctrine of the conservation of energy, when applied to living beings, leads to the conclusion that the soul of an animal is not, like the mainspring of a watch, the motive power of the body, but that its function is rather that of a steersman of a vessel — not to produce, but to regulate and direct the animal powers!") 5th. The discoveries in Electricity and Magnetism labour under the same disadvantages as those in Light. It is difficult to present the ideas in an adequate manner to laymen, and it is easy to show them wonderful experiments. 6th. On the other hand, recent developments of Molecular Science seem likely to have a powerful effect on the world of thought. The doctrine that visible bodies apparently at rest are made up of parts, each of which is moving with the velocity of a cannon ball, and yet never departing to a visible extent from its mean place, is sufficiently startling to attract the attention of an unprofessional man. But I think the most important effect of molecular science on our way of thinking will be that it forces on our attention the distinction between two kinds of knowledge, which we may call for convenience the Dynamical and Statistical. The statistical method of investigating social questions has Laplace for its most scientific and Buckle for its most popular expounder. Persons are grouped according to some characteristic, and the number of persons forming the group is set down under that characteristic. This is the raw material from which the statist endeavours to deduce general theorems in sociology. Other students of human nature proceed on a different plan. They observe individual men, ascertain their history, analyse their motives, and compare their expectation of what they will do with their actual conduct. This may be called the dynamical method of study as applied to man. However imperfect the dynamical study of man may be in practice, it evidently is the only perfect method in principle, and its shortcomings arise from the limitation of our powers rather than from a faulty method of procedure. If we betake ourselves to the statistical method, we do so confessing that we are unable to follow the details of each individual case, and expecting that the effects of widespread causes, though very different in each individual, will produce an average result on the whole nation, from a study of which we may estimate the character and propensities of an imaginary being called the Mean Man. Now, if the molecular theory of the constitution of bodies is true, all our knowledge of matter is of the statistical kind. A constituent molecule of a body has properties very different from those of the body to which it belong:. Besides its immutability and other recondite properties, it has a velocity which is different from that which we attribute to the body as a whole. The smallest portion of a body which we can discern consists of a vast number of such molecules, and all that we can learn about this group of molecules is statistical information. We can determine the motion of the centre of gravity of the group, but not that of any one of its members for the time being, and these members themselves are continually passing from one group to another in a manner confessedly beyond our power of tracing them. Hence those uniformities which we observe in our experiments with quantities of matter containing millions of millions of molecules are uniformities of the same kind as those explained by Laplace and wondered at by Buckle, arising from the slumping together of multitudes of cases, each of which is by no means uniform with the others. The discussion of statistical matter is within the province of human reason, and valid consequences may be deduced from it by legitimate methods; but there are certain peculiarities in the very form of the results which indicate that they belong to a different department of knowledge from the domain of exact science. They are not symmetrical functions of the time. It makes all the difference in the world whether we suppose the inquiry to be historical or prophetical — whether our object is to deduce the past state or the future state of things from the known present state. In astronomy, the two problems differ only in the sign of t, the time; in the theory of the diffusion of matter, heat, or motion, the prophetical problem is always capable of solution; but the historical one, except in singular cases, is insoluble. There may be other cases in which the past, but not the future, may be deducible from the present. Perhaps the process by which we remember past events, by submitting our memory to analysis, may be a case of this kind. Much light may be thrown on some of these questions by the consideration of stability and instability. When the state of things is such that an infinitely small variation of the present state will alter only by an infinitely small quantity the state at some future time, the condition of the system, whether at rest or in motion, is said to be stable; but when an infinitely small variation in the present state may bring about a finite difference in the state of the system in a finite time, the condition of the system is said to be unstable. It is manifest that the existence of unstable conditions renders impossible the prediction of future events, if our knowledge of the present state is only approximate, and not accurate. It has been well pointed out by Professor Balfour Stewart that physical stability is the characteristic of those systems from the contemplation of which determinists draw their arguments, and physical instability that of those living bodies, and moral instability that of those developable souls, which furnish to consciousness the conviction of free will. Having thus pointed out some of the relations of physical science to the question, we are the better prepared to inquire what is meant by determination and what by free will. No one, I suppose, would assign to free will a more than infinitesimal range. No leopard can change his spots, nor can any one by merely wishing it, or, as some say, willing it, introduce discontinuity into his course of existence. Our free will at the best is like that of Lucretius's atoms — which at quite uncertain times and places deviate in an uncertain manner from their course. In the course of this our mortal life we more or less frequently find ourselves on a physical or moral watershed, where an imperceptible deviation is sufficient to determine into which of two valleys we shall descend. The doctrine of free will asserts that in some such cases the Ego alone is the determining cause. The doctrine of Determinism asserts that in every case. without exception, the result is determined by the previous conditions of the subject, whether bodily or mental, and that Ego is mistaken in supposing himself in any way the cause of the actual result, as both what he is pleased to call decisions and the resultant action are corresponding events due to the same fixed laws. Now, when we speak of causes and effects, we always imply some person who knows the causes and deduces the effects. Who is this person? Is he a man, or is he the Deity? If he is man — that is to say, a person who can make observations with a certain finite degree of accuracy — we have seen that it is only in certain cases that he can predict results with even approximate correctness. If he is the Deity, I object to any argument founded on a supposed acquaintance with the conditions of Divine foreknowledge. The subject of the essay is the relation to determinism, not of theology, metaphysics, or mathematics, but of physical science – the science which depends for its material on the observation and measurement of visible things, but which aims at the development of doctrines whose consistency with each other shall be apparent to our reason. It is a metaphysical doctrine that from the same antecedents follow the same consequents. No one can gainsay this. But it is not of much use in a world like this, in which the same antecedents never again concur, and nothing ever happens twice. Indeed, for aught we know, one of the antecedents might be the precise date and place of the event, in which case experience would go for nothing. The metaphysical axiom would be of use only to a being possessed of the knowledge of contingent events, scientia simplicis intelligentiae – a degree of knowledge to which mere omniscience of all facts, scientia visionis, is but ignorance. The physical axiom which has a somewhat similar aspect is 'That from like antecedents follow like consequents.' But here we have passed from sameness to likeness, from absolute accuracy to a more or less rough approximation. There are certain classes of phenomena, as I have said, in which a small error in the data only introduces a small error in the result. Such are, among others, the larger phenomena of the Solar System, and those in which the more elementary laws in Dynamics contribute the greater part of the result. The course of events in these cases is stable. There are other classes of phenomena which are more complicated, and in which cases of instability may occur, the number of such cases increasing, in an exceedingly rapid manner, as the number of variables increases. Thus, to take a case from a branch of science which comes next to astronomy itself as a manifestation of order: in the refraction of light, the direction of the refracted ray depends on that of the incident ray, so that in general, if the one direction be slightly altered, the other also will be slightly altered. In doubly refracting media there are two refracting rays, but it is true of each of them that like causes produce like effects. But if the direction of the ray within a biaxal crystal is nearly but not exactly coincident with that of the ray-axis of the crystal, a small change in direction will produce a great change in the direction of the emergent ray. Of course, this arises from a singularity in the properties of the ray-axis, and there are only two ray-axes among the infinite number of possible directions of lines in the crystal; but it is to be expected that in phenomena of higher complexity there will be a far greater number of singularities, near which the axiom about like causes producing like effects ceases to be true. Thus the conditions under which gun-cotton explodes are far from being well known; but the aim of chemists is not so much to predict the time at which gun-cotton will go off of itself, as to find a kind of guncotton which, when placed in certain circumstances, has never yet exploded, and this even when slight irregularities both in the manufacture and in the storage are taken account of by trying numerous and long continued experiments. In all such cases there is one common circumstance – the system has a quantity of potential energy, which is capable of being transformed into motion, but which cannot begin to be so transformed till the system has reached a certain configuration, to attain which requires an expenditure of work, which in certain cases may be infinitesimally small, and in general bears no definite proportion to the energy developed in consequence thereof For example, the rock loosed by frost and balanced on a singular point of the mountain-side, the little spark which kindles the great forest, the little word which sets the world a fighting, the little scruple which prevents a man from doing his will, the little spore which blights all the potatoes, the little gemmule which makes us philosophers or idiots. Every existence above a certain rank has its singular points: the higher the rank, the more of them. At these points, influences whose physical magnitude is too small to be taken account of by a finite being, may produce results of the greatest importance. All great results produced by human endeavour depend on taking advantage of these singular states when they occur.
There is a tide in the affairs of menThe man of tact says 'the right word at the right time', and, 'a word spoken in due season how good is it!' The man of no tact is like vinegar upon nitre when he sings his songs to a heavy heart. The ill-timed admonition hardens the heart, and the good resolution, taken when it is sure to be broken. becomes macadamised into pavement for the abyss. It appears then that in our own nature there are more singular points – where prediction, except from absolutely perfect data, and guided by the omniscience of contingency, becomes impossible – than there are in any lower organisation. But singular points are by their very nature isolated, and form no appreciable fraction of the continuous course of our existence. Hence predictions of human conduct may be made in many cases. First, with respect to those who have no character at all, especially when considered in crowds, after the statistical method. Second, with respect to individuals of confirmed character, with respect to actions of the kind for which their character is confirmed. If, therefore, those cultivators of physical science from whom the intelligent public deduce their conception of the physicist, and whose style is recognised as marking with a scientific stamp the doctrines they promulgate, are led in pursuit of the arcana of science to the study of the singularities and instabilities, rather than the continuities and stabilities of things, the promotion of natural knowledge may tend to remove that prejudice in favour of determinism which seems to arise from assuming that the physical science of the future is a mere magnified image of that of the past.
Which, taken at the flood, leads on to fortune.
Letter to Francis Galton, 26 February 1879
Normal | Teacher | Scholar
Drawing-to-Learn: A Framework for Using Drawings to Promote Model-Based Reasoning in Biology
Kim Quillin*‡ and Stephen Thomas†
Mary Lee Ledbetter, Monitoring Editor
*Department of Biological Sciences, Salisbury University, Salisbury, MD 21801
†Department of Zoology, Michigan State University Museum, Center for Integrative Studies in General Sciences, Michigan State University, East Lansing, MI 48823
‡Address correspondence to: Kim Quillin (ude.yrubsilas@nilliuqxk).
Author information ►Article notes ►Copyright and License information ►
Received 2014 Aug 16; Revised 2014 Oct 3; Accepted 2014 Oct 11.
Copyright © 2015 K. Quillin and S. Thomas. CBE—Life Sciences Education © 2015 The American Society for Cell Biology. This article is distributed by The American Society for Cell Biology under license from the author(s). It is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).
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The drawing of visual representations is important for learners and scientists alike, such as the drawing of models to enable visual model-based reasoning. Yet few biology instructors recognize drawing as a teachable science process skill, as reflected by its absence in the Vision and Change report’s Modeling and Simulation core competency. Further, the diffuse research on drawing can be difficult to access, synthesize, and apply to classroom practice. We have created a framework of drawing-to-learn that defines drawing, categorizes the reasons for using drawing in the biology classroom, and outlines a number of interventions that can help instructors create an environment conducive to student drawing in general and visual model-based reasoning in particular. The suggested interventions are organized to address elements of affect, visual literacy, and visual model-based reasoning, with specific examples cited for each. Further, a Blooming tool for drawing exercises is provided, as are suggestions to help instructors address possible barriers to implementing and assessing drawing-to-learn in the classroom. Overall, the goal of the framework is to increase the visibility of drawing as a skill in biology and to promote the research and implementation of best practices.
It is difficult to imagine teaching, learning, or doing biology without the use of visual representations. As in physics, chemistry, and other science, technology, engineering, and math (STEM) disciplines, the spatial and temporal dimensions of biology span many orders of magnitude and involve complexity that challenges the limits of human comprehension. Visual representations are a powerful tool, because they help to make the unseen seen and the complex simple.
This power of visuals has been used by scientists from the representational anatomical works of Leonardo da Vinci to the theoretical phylogenetic work of Charles Darwin. In this essay, we encourage biology instructors of students ages K–16 and beyond to explicitly train students not only to interpret visual information in textbooks, journal articles, slide presentations, websites, and classroom whiteboards, but also to create drawings, for two reasons: 1) drawing is a powerful tool for thinking and communicating, regardless of the discipline (e.g., Roam, 2008); and 2) drawing is a process skill that is integral to the practice of science, used in the generation of hypotheses, the design of experiments, the visualization and interpretation of data, and the communication of results (e.g., Schwarz et al., 2009; Ainsworth et al., 2011).
Even though biology has a rich tradition of illustrating natural history, it lags behind physics and chemistry in acknowledging and explicitly teaching drawing as a skill, especially the drawing of abstract visual models as a tool for reasoning (National Research Council [NRC], 2012). Model-based reasoning is a type of problem solving that enables analysis of complex and/or abstract concepts. Different types of models are used for problem solving across STEM disciplines, including verbal, mathematical, visual, dynamic, and physical models (Table 1; e.g., Harrison and Treagust, 2000; Koba and Tweed, 2009). Model-based reasoning is a powerful tool for fostering conceptual change and meaningful learning in students (e.g., Jonassen et al., 2005; Blumschein, et al., 2009). When used in science, these abstract, explicit representations of systems can be used singly and in combination to generate predictions and explanations (Schwarz et al., 2009).
Types of models for model-based reasoning
The vast majority of illustrations in biology texts, in primary literature papers, and on whiteboards in classrooms are abstract, visual models. Many biology instructors draw models in their classrooms and prompt students to draw as well, but rarely with a self-awareness of this strategy as a teachable science process skill and rarely from the perspective of modeling.
In a recent study of faculty perceptions of teaching the process of science in biology, drawing or making models was not included among the 22 science skills assessed, except in the creation of graphs from data (Coil et al., 2010). Likewise, the Vision and Change document (American Association for the Advancement of Science [AAAS], 2011) includes Modeling and Simulation as one of the core competencies in biology, yet defines modeling narrowly in the mathematical sense. We advocate for the revision of the Vision and Change definition to align with the Discipline-Based Education Research report (NRC, 2012) to include visual model-based reasoning as embraced in physics (e.g., vector diagrams), chemistry (e.g., bonding diagrams), engineering (e.g., circuit diagrams), and math (e.g., diagrams to solve word problems).
The goals of this essay are to increase the visibility of drawing as a skill in biology and to provide a framework to promote the research and implementation of best practices. We have experienced a number of barriers to progress as we have researched the literature on drawing-to-learn. These barriers include a diffuse literature scattered across diverse disciplines ranging from nursing and cognitive psychology to secondary education and math; diverse study subjects ranging from kindergarteners to adults; inconsistent use of terminology; lack of clearly articulated goals or best practices for assigning drawing in science class; seemingly contradictory results in drawing studies; and a number of complicating factors that raise the question of transferability of the results from one study to the next. These frustrations have inspired us to distill the complexity of drawing into a “big picture” framework that can serve as a launching point to facilitate future work in biology.
This essay will deliver a framework in three parts: 1) a definition of drawing with an explanation of its facets; 2) a clear articulation of the diverse pedagogical goals of drawing-to-learn; and 3) a proposed set of teaching interventions that can serve both as prompts for interested instructors and also as testable hypotheses for researchers. This essay is not intended as a comprehensive literature review but rather as a sampling and synthesis of insights gleaned from diverse fields.
WHAT IS A “DRAWING”?
There is no consensus in the literature on the definition of “drawing,” and many terms (e.g., sketch, diagram, external representation, external model, visualization, illustration, picture) are used differently in different papers. We embrace an inclusive definition of drawing to encourage drawing-to-learn as a parallel endeavor to other pedagogical movements such as writing-to-learn (e.g., Klein, 1999; Libarkin and Ording, 2012; Reynolds et al., 2012; Mynlieff et al., 2014), and talking-to-learn (e.g., Tanner, 2009). That is, we define drawing broadly as
a learner-generated external visual representation depicting any type of content, whether structure, relationship, or process, created in static two dimensions in any medium.
This definition, while inclusive, masks a number of complicating factors central to the use of drawing in the biology classroom. The following discussion will illuminate four of these factors.
Drawings Vary in the Extent to Which They Are Learner Generated
Visual literacy is the ability of students both to interpret visual representations that are provided by instructors and also to create visual representations on their own (e.g., Schönborn and Anderson, 2010). But interpretation and creation are not distinct categories—they represent ends of a continuum (Figure 1). At one end of the continuum, students can be asked to view and interpret an instructor-generated or instructor-selected model in class or in homework. At the other end of the continuum, students can be asked to draw their own model starting from a “blank slate.” The entire range of the continuum represents visual learning (learning using images), but the degree to which students are engaged in active learning (constructing their own knowledge based on prior knowledge and experience; e.g., Freeman et al., 2014) increases as the students take on more responsibility for their drawing. For the remainder of this essay, “drawing” will include any visual representation that is either partially or fully learner generated.
Drawings vary in the extent to which they are learner generated.
Drawings Are External Models That Involve the Formation of Internal Models
It may seem self-evident that drawings are external representations (physically visible outside the mind of the creator); however, the literature suggests that an important interaction occurs between external models and internal models (mental models in the “mind’s eye”; e.g., Johnson-Laird, 1980; Seel, 2003; Jonassen et al., 2005).
First, consider that the brain naturally uses spatial information to encode other kinds of information, such as verbal information, increasing the brain’s capacity for memory and learning (e.g., Chun and Jiang, 1998; Guida and Lavielle-Guida, 2014). It follows, then, that students learn more from combining verbal and visual information than from verbal information alone (Pavio, 1986), which appears to be true regardless of “learning style” (Rohrer and Pashler, 2012; Kirschner and Merriënboer, 2013).
Next, consider how verbal and visual information are integrated. Mayer (2009) proposes in his cognitive theory of multimedia learning that students create a mental model in their working memory by performing three cognitive tasks: 1) selecting verbal and visual information from materials presented (sensory processing) and from prior knowledge (long-term memory), 2) organizing verbal and visual information, and 3) integrating those elements into a mental model. Van Meter and Garner (2005) extended this theory in their generative theory of drawing construction, proposing that the drawing of a physical model can occur after the creation of a mental model or in parallel with selecting, organizing, and integrating information. We have created a visual model to summarize these ideas in Figure 2. Note that the creation of an external model requires not only mental processes but also motor coordination to manipulate the drawing medium into the desired image.
Visual framework for the generative theory of drawing construction. In this model, the circles represent verbal and/or visual information. The arrows show that a drawing may be an endpoint, developed after the creation of a mental model, or a means to...
This framework helps to make sense of seemingly contradictory results in the literature. For example, Leutner et al. (2009) observed that students who created only a mental model experienced higher learning gains than students who created a mental model plus a drawing. In this case, it appears that the creation of a mental model was itself the critical step in learning and that the drawing process increased cognitive load in a way that was unproductive to learning (Sweller, 1988; de Jong, 2010), possibly because the students had little experience or confidence with drawing and used their time inefficiently. Other studies suggest that the generation of an external model is important both as a catalyst to create a mental model, and as a way to improve cognitive efficiency while learning. For example, drawings can be used to offload information to free up working memory (Larkin and Simon, 1987; Harrison and Treagust, 2000; Jonassen et al., 2005; Koba and Tweed, 2009). Further, it is difficult to assess a student’s internal model.
In sum, it is important to recognize that when an instructor assigns a drawing exercise to a student or when a scientist draws a model to think with, the actual drawing that results may be the desired outcome (e.g., to communicate to instructors or colleagues) or may be a means to the creation of a mental model (to construct knowledge) and, therefore, an effective strategy for instructors to access and assess the student’s learning and identify misconceptions (e.g., Köse, 2008; Dikmenli, 2010).
Drawings Vary in the Extent to Which They Are Representational or Abstract
One variable that contributes to the varied use of terms for drawings is the extent to which the drawings are intended to be representational (“true to life”) or abstract (analogical). Some authors use “drawings” to refer only to representational drawings (e.g., Van Meter and Garner, 2005), wherein drawings are a subset of the larger category, diagrams (e.g., Uesaka and Manalo, 2011). Others use “drawings” to refer to any learner-generated visualization, including those with quantitative information, such as graphs (e.g., Ainsworth et al., 2011). We embrace the latter approach for drawing-to-learn, with “drawings” embracing the full continuum from representational to abstract (Figure 3).
Drawings range in the extent to which they are representational or abstract. In theory, all drawings are analogical, because they cannot truly represent the real world, but they vary in the extent to which they are intended to be representational.
Structures or objects are often the first category to come to mind when a student or instructor thinks of drawings, but processes and relationships can also be depicted and explored via drawings. For example, students in a biology lab may be asked to draw cells or anatomical structures as viewed through a microscope, but they may also be asked to draw a flowchart to understand the process of meiosis or a phylogenetic tree to decipher the relationships among taxa. A few examples are illustrated in Table 2.
Examples of biology content that can be explored via drawings, including references as an entrée to the literature in these areasa
When viewing these examples from biology, there are three points to recognize: drawings can vary across scale; drawings can vary in their integration of text; and drawings can vary in the level of abstraction that is suitable to the context. First, consider that, because drawings can be used across scales and all levels of organization from atomic to global—even within the same representation—they are appropriate for all fields of biology, ranging from biochemistry and molecular biology to genetics, evolution, and ecology. Further, some drawing types, such as flowcharts, graphs, and concept maps, can be applied to all disciplines.
Drawings can also range in the extent to which they contain words. Some drawings contain no words at all, such as a drawing depicting the wing pattern of a particular species of butterfly or the leaf morphology of a particular species of oak tree. Other drawings contain a few labels, such as a drawing of a cell containing labeled organelles or a drawing of a flower containing labeled reproductive structures. At the other end of the spectrum, some drawings are composed mostly of words, numbers, lines, and/or arrows, but with obvious spatial relationships, such as in flowcharts, concepts maps, graphs, and phylogenetic trees (see Table 2).
Finally, drawings can vary to the degree in which they should be representational or abstract, depending on context. For example, a highly representational drawing of a wolf might be appropriate to a study of wolf behavior (where the stance and position of ears and tail is germane to the point), but a mere box with the word “wolf” might be appropriate in a food web or concept map (Figure 3). This distinction is important, because many students and instructors are insecure about their ability to draw. Artistry is not a prerequisite for most uses of drawing as a tool. In many cases, structures or processes can be represented by simple shapes that are easy to create. Thus, the fear of drawing is a barrier that can be overcome with transparency about intended use in a given context (“A box with ‘wolf’ is all that is needed!”) and practice in the intended use in that context (K.Q., unpublished data).
Drawings Can Be Made in Any Two-Dimensional Medium
Just as there is variation in the level of abstraction of drawings, so too is there variation in how they are produced. The word “drawing” often suggests paper and pencil—reminiscent of art class—but student drawings can vary in medium from pencil on paper to marker on whiteboard to stylus on tablet. An increasing number of programs enable students to draw/construct images online and in classroom management systems, improving the number of options available to instructors, especially of large-enrollment or digitally delivered courses (e.g., BeSocratic, Learning Catalytics). Three-dimensional physical models and kinesthetic activities are closely related to drawing and are certainly of educational and scientific value but are beyond the scope of this essay, as are dynamic animations and computer simulations.
In terms of cognitive processes, the principle of selecting, organizing, and integrating information (Figure 2) applies to drawing no matter the medium (e.g., Mayer, 2009). However, this does not mean that all students (or instructors or scientists) will draw equally well in all media. There are two types of barriers that might be important regarding medium. One is experience—the ability of a student to draw in one medium, such as pencil on paper, does not necessarily transfer to ability in another medium, such as stylus on tablet, and depends on the student’s familiarity with the new medium. Differences in the sensory-motor experience, the needed hand–eye coordination, and knowledge of the functional capacity of the medium could require practice to master.
Second, some media have inherent limitations. Color coding is not possible when only a black pen is available, and precise markings are not possible using a fingertip on a touch screen. More research on the effects of drawing medium on learning is needed (e.g., Mayer et al., 2005; Templeman-Kluit, 2006; Ainsworth, 2008). Meanwhile, instructors should be mindful of the opportunities and limitations of different drawing media.
WHY ASK STUDENTS TO DRAW?
With the definition of drawing established, the next task is to make sense of the many reasons for using drawing. The effective use of drawing in the classroom and the effective measurement of drawing as a tool depend on the alignment between desired outcomes, assessment, and activities (e.g., Cohen, 1987; Wiggins and McTighe, 1998). Thus, transparency regarding goals is essential. We have created a matrix (Table 3) to serve as a framework for distinguishing the variety of pedagogical goals found in the literature (Table 4). The matrix categorizes the goals according to whether drawings are on the representational or abstract ends of the continuum (Figure 3) and whether they are intended as formative or summative exercises. Formative exercises are used to help students build their own knowledge and practice skills and are used by instructors to enable targeted feedback to students. Summative exercises are used by students to communicate their knowledge and skills and are used by instructors for evaluating student performance, such as for course grades.
Pedagogical goals for assigning drawing exercises with sample instructor promptsa
A sample of references for entrée into the drawing-to-learn literature
One common goal cited in the formative-representational quadrant is the use of drawings to enhance observational skills (e.g., Baldwin and Crawford, 2010; Ridley and Rogers, 2010). Louis Agassiz of the Harvard Museum of Comparative Zoology captured this sentiment in his assertion that “A pencil is one of the best eyes” (Lerner, 2007, p. 382). For example, students can be asked to draw cells as seen through the microscope to explore cell structure.
The summative-representational quadrant focuses less on seeing and more on communicating what has been observed and learned. Before the advent of photography, representational drawing was essential to science as a means of recording and disseminating knowledge. In terms of teaching and learning, representational drawings are a means of assessing student performance, such as the accuracy and completion of a lab exercise on plant growth. Overall, seeing and communicating are distinct, but aligned, goals—a student (or instructor or scientist) with more practice seeing will be better equipped to communicate what has been seen.
Goals for drawings are quite diverse in the formative-abstract quadrant of the matrix, in the top, right-hand section of Table 3. For students, the goal of this quadrant is to make visual models to help them construct their own knowledge, which involves the creation of both internal and external models (Figure 2). The creation of these models helps students to acquire and remember content knowledge, connect concepts into a big picture, process data, solve problems, and design and interpret experiments. Drawing models can also help motivate students and make them more self-aware of their own learning. For instructors, this quadrant can be used as a diagnostic tool to elicit students’ mental models, such as their conception of the relationship between genes and evolution (Dauer et al., 2013), and to reveal misconceptions, such as the common misconception that photosynthesis turns CO2 into O2 (Köse, 2008) or that DNA replication occurs during mitosis and meiosis (Dikmenli, 2010). Instructors can then design interventions appropriate to students’ needs.
The abstract-summative goals are aligned with many of the abstract-formative goals; they are similar in their use, yet distinct. The focus of this quadrant is for students to reveal their knowledge and problem-solving skills to the instructor, to fellow students, or to others, usually for points that determine grades. Familiarity with the visual conventions that are used in the discipline and acceptable for the audience dictates how well the students can accurately communicate concepts through abstract representations. In this manner, the student experience in this quadrant prepares them for the communication of scientific information that is integral to the practice of science.
To our knowledge, there has been no formal measure of instructor practice in the formative and summative use of drawing in biology classrooms nationally. However, our informal surveying of colleagues around the United States has revealed a diversity of practices. For example, one college biology instructor said that she uses abstract drawings on exams but does not give students formative opportunities to draw in class. Another instructor said that he uses extensive abstract drawing in class but not on exams due to his large class sizes. Further, some instructors use drawings extensively all semester, while others use them only in one topic area. And some instructors are extremely enthusiastic and purposeful about their use of drawings, outlining several pedagogical goals for their use, while others were surprised by this novel topic and had to consider for a few moments whether or not they used drawing (“What does ‘drawing’ mean exactly?”) in class. This variety of practices reveals a need for alignment between formative and summative elements of Table 3. If drawing skills are an important skill, they should be part of a summative assessment of students. And if drawing skills are part of a summative assessment, they should be aligned with formative experiences in the same drawing category (i.e., representational or abstract).
In sum, the purpose of the matrix is to help add clarity to discussions of why instructors would invest time and effort into assigning and assessing drawing exercises. Assigning drawings to students to help them engage (improve motivation) or see (improve observation skills) are very different pedagogical goals than assigning drawings to help students understand (lower-order cognitive skill) or solve a problem (higher-order cognitive skill), but all are important. Likewise, assigning drawings to students to help them learn (student-centered goal) and assigning drawings so that instructors can assess learning (instructor-centered goal) are very different pedagogical goals, but both can be used to improve student learning. Finally, teaching drawing as a learning tool (such as the use of concept maps to help memorize content or see the big picture) is a different goal than teaching drawing as a science process skill (such as drawing models to design an experiment), but both are valid and worthwhile. Overall, the key is for instructors and researchers to articulate goals clearly so that appropriate interventions can be designed and aligned between the formative and summative quadrants to achieve those goals.
WHAT ARE SOME SUGGESTED PRACTICES FOR TEACHING DRAWING FOR MODEL-BASED REASONING IN BIOLOGY?
With the goals for drawing-to-learn in mind, the next step is to consider how to scaffold drawing skills to meet those goals—that is, how can instructors provide a sequence of support that helps students to eventually achieve mastery of the skill on their own? It is beyond the scope of this essay to propose teaching practices to support all of the diverse goals for drawing-to-learn. For the remainder of this essay, we will focus on using drawings for model-based reasoning, because this is an area with enormous, yet unrealized potential (e.g., Ainsworth et al., 2011; NRC, 2012; see Introduction). This example also serves to model how drawing could be scaffolded to help achieve other pedagogical goals in biology.
When planning an intervention to help students draw models for model-based reasoning, it is helpful to have an endpoint in mind in terms of desired modeling skills. The literature has articulated some of the differences between novice and expert learners regarding the drawing and use of models in various STEM disciplines (e.g., NRC, 2012; see other references in Table 4). We have simplified and synthesized these differences into a framework in Table 5 to show where students typically start, and where we intend for them to end up. In general, novice learners tend to view models as static summaries of reality created by others, which they must memorize, whereas expert learners tend to view models as flexible thinking tools. Explicit instruction can help novice learners to develop more expert-like skills in model-based reasoning.
Differences between novices and experts in how they draw and use models
Given the goal of moving students to more expert-like practices, and based on the constellation of factors discussed in the literature (see Table 4 and the discussion here), we propose three major categories of interventions that may improve the ability of students to draw models to learn. These interventions can serve as a starting framework for interested instructors and also as testable hypotheses for biology education researchers. To ground these interventions in learning theory, we invoke the theory of cognitive capacity (see Sweller, 1988; de Jong, 2010). This theory predicts that learning will be efficient when distractors to learning are minimized and the full cognitive capacity of the student is focused on the learning goal. Conversely, learning will be inefficient if the learner experiences cognitive load that is unproductive to the learning goals (e.g., Mayer et al., 2001; Mayer, 2009). Thus framed, the three interventions are as follows:
Affect: interventions to improve student motivation and attitudes toward drawing-to-learn will encourage students to assign more cognitive capacity to these activities.
Visual literacy: interventions that explicitly teach the skill of translating verbal-to-visual information and visual-to-verbal information as well as accepted symbol use within biology subdisciplines will enable students to spend more of their cognitive capacity on important concepts and principles rather than on the act of drawing.
Model-based reasoning: interventions that model and give students practice with the flexibility of models as reasoning tools, as well as feedback on the efficacy of their models, will enable students to spend more of their cognitive capacity on problem solving rather than the act of modeling and will increase the likelihood that students will draw models to solve problems on their own, without prompting.
First, we will outline the teaching and learning challenges in each of these categories, and then we will offer suggestions for practices that might address these challenges. At the end, we will consider some of the practical considerations to ease the use of drawing-to-learn in the classroom.
A student’s affect, or emotional state, is critical to learning success, because it influences motivation—the amount of time and effort a student is willing to commit to learning (Bransford et al., 2000). Affect changes over time and context and can be positively or negatively influenced by instructor behavior and interventions in the classroom (Anderson and Bourke, 2000). While some aspects of affect are resistant to change, such as strongly held values or deep anxieties stemming from childhood experiences, others can be influenced relatively quickly and effectively, providing instructors with opportunities to improve student motivation and thus learning (Kobella, 1989).
There are multiple interacting dimensions to affect, which are beyond the scope of this paper (see Anderson and Bourke, 2000). Here we offer a framework of four affective dimensions as an introduction to the subject: attitude, value, self-efficacy, and interest (Figure 4).
How does the student feel about drawing models?
For example, a student might have a poor attitude toward drawing models because of negative associations or experiences or simply because they do not enjoy the activity. Some students feel so uncomfortable drawing that they do not want to participate (e.g., Mohler, 2007; Baldwin and Crawford, 2010). Other students may like drawing in general but feel that drawing is something to be done in art class, not in science class (K.Q., unpublished data). As such, they will not value the approach and will not be motivated to use it.
Similarly, students may be unmotivated to draw models, because they have poor self-efficacy. “I’m not good at drawing” is a common classroom refrain. Students with low self-efficacy may also suffer anxiety due to the threat of harsh judgment of their work (Anderson and Bourke, 2000). Further, students may not be interested in drawing models due to a perception that the costs outweigh the benefits. For example, some students do not bother to draw models to help them solve math problems due to the perception that drawing models will be difficult, even though students are more likely to solve problems correctly when using models (Uesaka et al., 2007; Uesaka and Manalo, 2011). Similarly, in physics, students must be consistently encouraged and incentivized to draw models to solve problems early on but eventually create their own models spontaneously, even when credit is not given to do so (Rosengrant et al., 2009). Affective instruments have been used in other STEM disciplines to measure attitudes toward drawing (e.g., engineering; Alias et al., 2002), but there are little published data on student affect toward drawing in biology (but see Lovelace and Brickman, 2013; Trujillo and Tanner, 2014).
By applying the general principles of affect (e.g., from Anderson and Bourke, 2000) toward, drawing, we propose several interventions for addressing problems of affect in Table 6. The efficacy of these interventions is testable using the methods outlined in Lovelace and Brickman (2013).
Proposed interventions for improving affect regarding drawing models to reason
Overall, the goal is to be explicit with students about the importance of models, to scaffold their use in class to make models easier to use, and to be transparent about expectations to avoid frustration and fear on the part of the students.
Models are composed of multiple elements that are abstractions of the real world. To successfully interpret and draw visual models, students must develop visual literacy—the skill to read and write visual or symbolic language, including the ability to translate verbal to visual (e.g., Stern et al., 2003; Van Meter et al., 2006; Schwamborn et al., 2010), visual to visual (e.g., Johnstone, 1991; Novick and Catley, 2007; Hegarty, 2011), or visual to verbal (e.g., Schönborn and Anderson, 2010). These components of visual literacy are illustrated in Figure 5.
Visual literacy requires translation (→) from verbal to visual, visual to visual, and visual to verbal.
When a student translates visual to visual, the translation process can be “horizontal,” from one drawing to another at the same scale (such as two different representations of “chromosome”), or “vertical,” from a drawing at one scale to a drawing at another scale (such as a condensed chromosome viewed at the cellular level vs. a chromosome viewed as a segment of DNA double helix; see Figure 5). Students across STEM disciplines struggle particularly with vertical translations (e.g., NRC, 2012).
Note that these visual translation steps may occur internally as a student develops an internal model or can require the additional translation from internal model to an external model (see Figure 2), which involves not only sensory and cognitive modalities, but also motor coordination and familiarity with the drawing medium used.
Symbols vary in the degree to which they are representational, or isomorphic, to the concepts they represent. For example, a wolf in a food web can be represented with varying levels of detail (see Figure 3); each wolf symbol is nonetheless easily interpreted. Visual language also differs across subdisciplines of biology (e.g., Novick, 2006; NRC, 2012). For example, an arrow used to represent transcription in a diagram of biology’s central dogma infers base pairing of DNA and RNA nucleotides; an arrow in a food web infers the transfer of energy and matter via consumption in a trophic relationship; and an arrow in a chemical reaction indicates a change in the state of matter. This heterogeneity can lead to misunderstandings and misconceptions, such as the interpretation of a DNA→RNA arrow in the central dogma to mean that DNA is itself converted into RNA (Wright et al., 2014).
Visual literacy is rarely taught explicitly by instructors; this occurs, in part, because instructors tend to be experts in their discipline and do not experience the foreign language–like appearance of visual representations to some students (e.g., Mioduser and Santa María, 1995; Schönborn and Anderson, 2010; Wright et al., 2014). Unfortunately, when students lack the skill to create effective external models, the creation of external models can hinder learning compared with the creation of mental models alone, either due to the increased cognitive demands incurred from the unscaffolded mental processes (Leutner et al., 2009) or due to the creation of inaccurate models that impair learning (e.g., Schwamborn et al., 2010).
With practice, however, students can learn to pick out important information, avoid distraction by surface features, and focus on making connections among important concepts (Mioduser and Santa María, 1995; Gobert and Clement, 1999; Harrison and Treagust, 2000; Van Meter et al., 2006; Hegarty, 2011; Dauer et al., 2013). We offer some proposed interventions for addressing problems of visual literacy in Table 7.
Proposed interventions for improving visual literacy when drawing models
As Table 5 summarized, novice learners tend to view models as static, authoritative “truths” and tend to be distracted by surface features, whereas expert learners view models as a flexible abstraction of reality that can be manipulated and used as a thinking tool. Overall, novices allocate more time and effort to creating models, whereas experts allocate more time and effort to using their models to find solutions (NRC, 2012). Modeling is challenging, because it requires the investment of cognitive effort (e.g., Uesaka and Manalo, 2011) and cognitive flexibility (DeHaan, 2009). Fortunately, this skill can be improved with instruction and practice (see references in Table 4).
The creation and use of models can be parsed into four tasks: construction, use, evaluation, and revision (Schwarz et al., 2009). To succeed in drawing models to reason, students must not only be able to create a model, but must also apply it to solve a problem or make a prediction, evaluate its efficacy, and revise as necessary. For example, students who draw highly accurate models benefit more from drawing models than those who draw low-accuracy models (Van Meter et al., 2006; Rosengrant et al., 2009), so iteration and revision is needed to develop expert-like modeling skills. Table 8 proposes some interventions for instructors in each of the four categories. Overall, the goal for instructors is to be transparent with students about what they are asking them to do and to give students plenty of practice and feedback.
Proposed interventions for improving visual model-based reasoning via drawing
HOW CAN DRAWING-TO-LEARN BE MADE MORE PRACTICAL FOR INSTRUCTORS?
The above discussion is framed in terms of the student experience, but the same principles apply to instructors, who vary in their experiences and skills. Thus, interventions in affect, visual literacy, and model-based reasoning have the potential to help instructors (and scientists) improve their skills in using drawings to reason in the same way that they are helpful to students (see references in Table 4).
What else can help instructors? Fortunately, some minor changes to instruction have the potential to produce meaningful learning gains for students. For example, the mere reference to illustrations in the textbook as “models” could possibly help to move a student closer to an expert perspective on the dynamic nature of knowledge in science. Similarly, increased attention to the affect of students regarding the drawing of visual models could result in a valuable increase in motivation (Anderson and Bourke, 2000). We have consolidated the prompts from Tables 6–8 and formatted them into a summary timeline (Figure 6) to serve as a visual guide to help instructors scaffold drawing-to-learn in the classroom. Other resources in the literature provide alternate teaching guides (Harrison and Treagust, 2000) and learning progressions (Schwarz et al., 2009) for drawing models to learn in science.
Visual guide on drawing-to-learn for instructors.
To further facilitate both the scaffolding and assessment of drawing models to learn, we have adapted the Blooming Biology Tool created by Crowe et al. (2008) to focus specifically on several commonly used modeling topics in biology (Table 9). Because drawing exercises can occur at all levels of thinking as defined by Bloom’s taxonomy (Bloom et al., 1956; Anderson et al., 2001), an instructor can scaffold modeling by first introducing formative exercises at lower-order cognitive levels and then working up to assignments at higher-order cognitive levels.
Blooming Biology Tool for drawing visual models to reasona
The assessment of drawings can be daunting to instructors, especially those teaching large-enrollment courses. For example, it is important that students receive quality formative feedback on their models to make sure they are not harboring misconceptions or are not adrift from the intent of the exercise. But how is an instructor to give thoughtful feedback on graphs, concept maps, phylogenetic trees, or meiosis diagrams in a class of 500 students?
In an effort to suggest some possible solutions, we have generated a list of strategies from our own experience, from colleagues teaching undergraduate biology, and from the literature (Table 10). For example, we have learned from personal experience that it helps to prescribe drawing activities by providing a starting point (see Figure 1) or key of symbols to use, both to help students understand expectations and to limit the possible range of solutions. Instructors can also use different technology-based modeling tools to help their students build models (e.g., Jonassen et al., 2005) and a rubric to facilitate assessment (see Allen and Tanner, 2006). Other colleagues have had success with a random-call method, selecting a few student models at random to critique in class. Peer review can also be effective, especially when used in combination with a rubric, with the caveat that this method tends to be more successful with lower-order cognitive tasks than higher-order cognitive tasks (Freeman and Parks, 2010). In sum, there are a number of possible solutions to facilitate assessment, the effectiveness of which will depend on context in the class. These proposed solutions represent hypotheses that can be tested and ranked under different conditions and with different student populations via biology education research.
A selection of proposed solutions to facilitate assessment of drawn models
CONCLUSION AND NEXT STEPS
Every biology instructor asks his or her students to interpret biological models, because we all offer visuals to students, and many of these visuals are models. Further, many instructors ask their students to draw their own models at some point—whether lipid bilayers, chromosomes in meiosis, graphs, phylogenetic trees, concept maps, or food webs—either as formative or summative activities. Biology instructors do this because model-based reasoning is intuitively a powerful tool for conceptual change and is inherent to the process of science. However, many instructors are not self-aware of drawing as a science process skill, and thus do not value the skill and do not scaffold it explicitly for their students.
We have argued in this essay that the drawing of visual models deserves more attention as a science process skill in biology, akin to efforts in other STEM disciplines. The Vision and Change list of core competencies (AAAS, 2011) should be augmented to reflect this change, as supported by evidence in the Discipline-Based Education Research report (NRC, 2012) and elsewhere. We have also provided a synthetic, multifaceted framework to help structure future use of drawing-to-learn and further research on best practices in biology.
There is a great deal that we do not know about drawing-to-learn in biology, and thus a wealth of opportunities for more work, including the testing of many of the hypotheses proposed in this essay and in the literature. For example, which types of interventions are most successful in improving
students’ ability to draw and reason with their models? What are the barriers that limit the utility of drawing exercises in class? How do gender, ethnicity, background experience, and content knowledge influence student abilities and/or affect regarding drawing-to-learn? Are insights from research on drawing one type of model transferable to other types?
We look forward to lively and productive discussions of drawing-to-learn in biology as part of the larger movement toward teaching problem solving (not just memorization) and science process skills (not just content) to cultivate the next generation of educated scientists and citizens.
We thank the many colleagues who have discussed drawing-to-learn with us on our campuses, at conferences, and beyond. Special thanks to Tessa Andrews, Norris Armstrong, Peggy Brickman, Alison Crowe, Cara Gormally, Robin Heyden, Scott Freeman, Karin Johnson, Julie Libarkin, David Quillin, Julie Stanton, Mary Pat Wenderoth, and two anonymous reviewers for their constructive criticism on various drafts of this article.
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