OLD WINE IN NEW BOTTLES:
A PROBLEM WITH CONSTRUCTIVIST EPISTEMOLOGY

Michael R. Matthews
University of Auckland

I. INTRODUCTION

Constructivism is one of the major influences in present day science and mathematics education. Perhaps with only slight exaggeration one participant at the 1991 US National Association for Research in Science Teaching annual conference announced “now we are all constructivists.” Constructivism inspires science education reform programmes, infuses textbooks, is commended as the theoretical foundation for science curricula,¹ is the subject of major international conferences and of numerous journal articles, and is the foundation of many science-teacher training courses. Constructivist teaching methods are widely advocated and great hopes are held for their transformative effects, one advocate saying that: “If the theory of knowing that constructivism builds…were adopted as a working hypothesis, it could bring about some rather profound changes in the general practice of education.”²

Constructivism has been no less prominent in mathematics education. One well-placed writer has said: “Anyone who observes mathematics education has to be impressed by the quite sudden eruption of ‘constructivism’ as a central concern of so many researchers.”³ A glance at the Annual Conference Proceedings of the large “International Group for the Psychology of Mathematics Education” (PME) will confirm the observation, as will a perusal of the pages of most mathematics education journals.

There is much that is laudable, insightful, and progressive about constructivist theory and practice. It is far superior to the wooden and limiting behaviourist theory of mind and learning against which Piaget, and early cognitive psychologists such as Bruner, struggled. Constructivism’s stress on pupil engagement in learning, and the importance of understanding student’s current conceptual schemes in order to teach fruitfully, are progressive; as is its stress on dialogue, conversation, argument, and the justification of student and teacher opinions in a social setting. Importantly, constructivism’s stress on understanding as the purpose of education is a major advance over the rote learning and mantra-like repetition of formulae that characterises so many science classrooms — classrooms like the graduate class of which Richard Feynman said “the students had memorised everything, but they didn’t know what anything meant.”⁴

The positive pedagogical aspects of constructivism have been amply developed by others, this paper will try to highlight what I regard as a fundamental, and fatal, epistemological error in the doctrine; in so highlighting this error I wish to rescue good constructivist pedagogy from the deficient theory that parented it.

My criticism in brief is that constructivism maintains the widespread, commonsensical, subject-centred, Aristotelian-empiricist epistemological paradigm, and by correctly pointing to a major error in empiricist assumptions, it then swings to a relativist epistemology without abandoning the paradigm itself. The relativist conclusion only follows within the empiricist paradigm, if this paradigm is rejected — and there are good reasons for so doing — no such relativist epistemological conclusions follow, and certainly no idealist ontological conclusions follow. Epistemologically, constructivism is the well-known old empiricist wolf in contemporary sheep’s clothing; to change metaphors, it is the empiricist wine, so criticised by constructivists, served up in new bottles.

II. CONSTRUCTIVIST PHILOSOPHY

Constructivism bristles with philosophical questions: it explicitly assumes positions in the philosophy of science, the philosophy of mind, and the philosophy of education. This is not surprising. It is at once a theory of science, of human learning, and of teaching; and there is a consciously normative element to much constructivist writing as signaled in the title of one recent journal article: “Toward a Humanistic Constructive Model of Science Learning.”⁵ Some extracts from constructivist writings indicate the range of these epistemological and ontological positions:

Such [constructivist] approaches view knowledge as personally and socially constructed, rather than “objective” and revealed; theories as provisional, not absolute.⁶

Science as knowledge is an intellectual construct, and what are referred to as the laws of nature are merely the result of this human activity. Nature as such does not have laws.⁷

The fact that scientific knowledge enables us to cope does not justify the belief that scientific knowledge provides a picture of the world that corresponds to an absolute reality.⁸

Although we may assume the existence of an external world we do not have direct access to it; science as public knowledge is not so much a discovery as a carefully checked construction.⁹

Put into simple terms, constructivism can be described as essentially a theory about the limits of human knowledge, a belief that all knowledge is necessarily a product of our own cognitive acts. We can have no direct or unmediated knowledge of any external or objective reality. We construct our understanding through our experiences, and the character of our experience is influenced profoundly by our cognitive lens.¹⁰

Scientific knowledge is invented in order to make sense of observations which are themselves theory-laden. There is no great book of nature that can be consulted in order to check if the models or theories correspond to an ontological reality.¹¹

Constructivism is, logically, a post-epistemological position. The standard questions of epistemology cannot be answered — or even reasonably asked — from this perspective. Its premises suggest, rather, abandonment of traditional epistemological language.¹²

Although most constructivists are ontological realists — the world although unknowable does actually exist apart from our thinking about it, some “radical constructivists” are idealists — the world is created by human thought and dependent upon such thought. Ernst von Glasersfeld’s radical constructivism is perhaps the best known. He says:

The realist believes his constructs to be a replica or reflection of independently existing structures, while the constructivist remains aware of the experiencer’s role as originator of all structures…for the constructivist there are no structures other than those which the knower constitutes by his very own activity of coordination of experiential particles.¹³

Although there are variations in constructivist epistemology, the common thread is that it is subject-centred, experience-based, and relativist. But its relativism needs to be distinguished from other relativisms in which the goal of science as a search for truth about the world is accepted, and it is then asserted that we cannot know of different accounts which one is actually true or better. In contrast for most constructivists our knowledge does not tell us about the world at all, it tells us about our experiences, and how they are best organised.

Lerman,¹⁴ following Kilpatrick,¹⁵ suggests that the core epistemological theses of constructivism are:

(1) Knowledge is actively constructed by the cognizing subject, not passively received from the environment.

(2) Coming to know is an adaptive process that organizes one’s experiential world; it does not discover an independent, pre-existing world outside the mind of the knower.

The first thesis (1) is a psychological claim, the second (2) is an epistemological claim. (As will be pointed out, Lerman believes (1) implies (2).) Wheatley offers a nearly identical summation of the epistemological core of constructivism. He says

The theory of constructivism rests on two main principles…. Principle one states that knowledge is not passively received, but is actively built up by the cognizing subject…. Principle two states that the function of cognition is adaptive and serves the organisation of the experiential world, not the discovery of ontological reality…. Thus we do not find truth but construct viable explanations of our experiences.¹⁶

III. CONSTRUCTIVISM AS A FORM OF EMPIRICISM

Given the influence of constructivism, surprisingly few critiques of its epistemology have appeared in the educational literature. Strike¹⁷ provided one early criticism; there has been some skirmishing between main-stream Piagetian personal-constructivists and Vygotskian social-constructivists; and there have been some adjustments around the epistemological edges, for example by Kilpatrick,¹⁸ Lerman¹⁹ and Goldin²⁰ — but all of these can be regarded as domestic disputes. It is as if a period of Kuhnian normal-science has descended upon the science and mathematics education communities. The President of the US National Association for Research in Science Teaching suggests as much: “A unification of thinking, research, curriculum development, and teacher education appears to now be occurring under the theme of constructivism[; there is] a lack of polarized debate.”²¹ An insightful article by Wallis Suchting²² may turn out to be the cat that fell among the pigeons: his critique strikes at the fundamentals of constructivism, and locates the doctrine in an anti-scientific philosophical tradition.²³

To understand my argument it is necessary to retrace in a highly schematic way the history of epistemology which since the 4th century BC has been dominated by the empiricist-Aristotelian paradigm in one guise or another.

Aristotle assumed a world independent of people populated by individual substances that formed classes or species in virtue of their essences or forms. To know something was to know its essence, or nature. Knowers were in two important senses passive in the Aristotelian theory of knowledge: first, the world imprinted empirical knowledge on the subject through ordinary unmediated sense-perception, this had to be unmediated in order for the object of knowledge to be known as it actually was; second, the rational faculty, nous, by a process of induction or epagoge intuited the universal forms inherent in the real. Observation, vision, and looking, were the key elements in the subject side of Aristotle’s epistemological equation, on the other object side the key element was undisturbed nature. Knowledge was obtained when the subject side accurately mirrored the object side.

Despite their anti-Aristotelian rhetoric, the British empiricists of the seventeenth century — Bacon, Locke, Berkeley, and Hume — maintained in all essentials this Aristotelian paradigm of knowledge. Knowledge was an individual matter, it was grounded in experience or sense impressions, its criterion was adequacy between thought and reality or the correspondence of ideas with objects.

Any epistemology which formulates the problem of knowledge in terms of a subject looking at an object and asking how well what they see reflects the nature or essence of the object, is quintessentially Aristotelian, or more generally empiricist.

It is not coincidental that modern constructivists once having formulated the epistemological problem in Aristotelian-Lockean terms then endorse versions of Berkeley’s savage critique of it and end up with relativism, and for the more consistent, idealism. It is not for nothing that von Glasersfeld says that 1710 was a very good year: being the year of publication of both Vico’s major work and Berkeley’s Treatise.²⁴

Constructivism’s acceptance of the fundamentals of the Aristotelian-empiricist epistemological problematic is indicated when von Glasersfeld speaks of “looking through distorting lens and [agreeing] on what they see,” and Confrey speaks of “cognitive lens,” and Desautels and Larochelle write of “making sense of observations which are themselves theory-laden”; and when numerous others have recourse to this looking/seeing/observing vocabulary for stating the problem of knowledge, or when use is made of the Kuhnian/Hansonian ambiguous or hidden figures to establish facts about the theory dependence of observation, or when gestalt-switch terminology is used to describe scientific revolutions. Whether subjects are seeing through lens clearly or darkly, it is the metaphor of seeing through lens which signals commitment to an empiricist theory of knowledge.

The one-step argument from the psychological premiss “the mind is active in knowledge acquisition” to the epistemological conclusion “we cannot know reality” is endemic in constructivist writing. Lerman speaks for many when he says of the two theses — (1) and (2) above — that “the connections between hypothesis (1) and (2) seem to be quite strong.”²⁵ But this conclusion only follows on the assumption that Aristotle had in fact correctly delineated the problem of knowledge; the conclusion only follows if the terms of the problem as stated by Aristotle are accepted. If this assumption is rejected then none of the skeptical conclusions of constructivism follow.

IV. THE SCIENTIFIC-EPISTEMOLOGICAL REVOLUTION

The scientific revolution associated with Galileo effectively destroyed the Aristotelian epistemological paradigm. Unfortunately the seventeenth-century empiricist champions of the new science saw only Aristotelian science as being refuted in the work of Galileo and Newton, they interpreted this scientific revolution in terms of the old epistemology — saying that the new science gave a better fit between thought and reality, that it was more adequate to experience, that the scientist-philosophers were better thinkers than their predecessors.

Galileo’s accomplishment is to make the important distinction between the theoretical object of science, which is a system of mathematically expressed definitions, principles, concepts and relations; and the real objects of science, which are the materials, events, objects in the world that are grasped, described, and by suitable instrumentation and experimentation, manipulated by scientists, and others, in accordance with the former. These theoretical objects are not Lockean ideas in contrast to material bodies; neither are they Humean ideas arising automatically from sense impressions.

Galileo’s account of pendulum motion well illustrates the difference between the theoretical objects of Galileo’s science and the real objects in the world, pendulums, which are the occasion for this particular theory.

Mythology not withstanding Galileo did not look carefully at pendulums swinging and then derive his law of isochronic motion. In fact his Aristotelian patron, and on this occasion opponent, Guidibaldo del Monte did just this and not surprisingly thought that Galileo had taken leave of his senses when he formulated his law. Real pendulums in no way behave isochronically — if they did, an immediate consequence of Galileo’s law would make pendulums perpetual mobiles, which clearly they are not. Rather Galileo began with a collection of concepts in dynamics, with a mathematical means of depiction and analysis that dealt with abstracted circumstances where many features of real pendulums were ignored — their colour, massiveness, etc., and with idealised situations where the bob was regarded as a point mass, where there was no mechanical friction at the fulcrum nor air resistance in the swing, and where the string had no weight and hence did not damp the motion. When the real object — the briefly swinging, non-isochronic, material pendulum — was described in terms provided by the theoretical object, and depicted geometrically, it was then in a suitable form for analysis by Galilean science. The result was the law of isochronic motion. Del Monte said that this was a world on paper, and that science was to be about the real world. Crucially Galileo’s science was about the real world, he was not a Platonist or idealist, but it was not immediately about this world as naturally disposed: it was mediated by the conceptual-theoretical object which clearly did not correspond to the real world.

Galilean science applied to a highly constrained experimental situation formed only on the design provided by the theoretical object. The real was altered, that is refined and perfected, to correspond with the theoretical, not the other way around as del Monte the Aristotelian, and more generally empiricists would insist in their claim that theory should be brought into line with reality. That the theoretical object did not correspond with the real was beside the point. Subsequently an interplay of theory — abandoning for instance Galileo’s view that the circle was the brachistochrone, or curve of quickest descent — and experimental refinement lead to Huyghen’s improvement of the law of pendulum motion.

Seeing or observing things differently was just not important in the debate between Galileo and del Monte. Galileo did not see point masses at the end of weightless strings, nor did he see continuous motion at the zenith of swing, he saw exactly what del Monte saw — chandeliers on the end of chains, lead balls on the end of wire, pendulums which momentarily stopped at their zenith, and pendulums which came to a halt within about two-dozen oscillations etc. Observation — whether theory dependent or not — was barely relevant to the dispute. Galileo described things differently, he did not see things differently. The new descriptions did not come from looking — after all one of the greatest observers of all time, Leonardo da Vinci, had long looked at pendulums without describing them in the way Galileo did — the descriptions came from an intellectually constructed theoretical object. Once described mathematically these statements were able to be worked upon by his mechanical system.²⁶

V. CONSTRUCTIVE CRITICISM

Constructivism takes correspondence between ideas and reality to be the sine qua non of knowledge; when this is shown to be in principle problematic, constructivists conclude that knowledge claims must in principle also be problematic, if not down-right chimerical. But correspondence does not have this central role in knowledge claims. What correspondence theories have correctly appreciated is that the truth of a scientific claim, or the worth of a theory, is ultimately determined by something beyond the claim or the theory: people propose, but the world disposes. But the determiner of knowledge is not correspondence. What can it mean to say that a statement, a collection of words, corresponds to a material state of affairs? At any rate it is not the raw, material state of affairs that is supposed to correspond to the scientific claim, rather it is a delimited, specified, and usually idealised, aspect of the material state of affairs that is supposed to so correspond — to repeat, colourless point masses in no sense correspond to coloured billiard balls, nor does a chemical equation mirror the messy reactions of exceedingly impure substances that are mixed in the typical laboratory crucible; the equation “captures” the reaction, it does not mirror the reaction. Correspondence theories are based upon an important realist intuition, but beyond this they are incoherent. Pleasingly this does not affect our claims to knowledge.

Constructivism is correct in stressing the inventive, humane, culturally and historically dependent aspects of creating the theoretical objects of science — but none of this bears, of itself, upon truth. Further although constructivists stress this creative aspect of knowledge production, they seldom extend the analysis: their model of creation is a sort of personal, cottage-industry, model; it is the personal, Robinson Crusoe, model of knowledge construction that leaves aside the necessary social and communitarian dimensions of cognition — the dimensions that inclined Freire, following Hegel, to say that “it is the ‘we think’ that determines the ‘I think’ and not the other way around.”

Lerman’s thesis (1) above nicely encapsulates the difference between an empiricist (and constructivist) conception of knowledge and an objectivist view. Lerman speaks of the individual constructing knowledge in contrast to it being imprinted from the environment. This is meant to contrast constructivism to empiricism, but it needs to be noted that: First no empiricist would possibly disagree with this claim, as all empiricist epistemologies conceive of the mind as active in some sense in knowledge acquisition; and secondly objectivists would reject the notion of individuals constructing knowledge. Individuals have language, concepts and beliefs that are entirely dependent upon their social-historical circumstances, some of the systems of belief in their culture may constitute knowledge, others of them may constitute ignorance, superstition, ideology, and falsehood. Which particular patterns of belief, or theories, in a society constitute knowledge is not a matter of individual construction; individuals may appropriate intellectual useful understandings, but such appropriation is dependent upon knowledge being available.

The idea of theoretical production is much more verdant than is usually realised. Marx said that people create history, but they do not create it as they choose; they create it in definite circumstances over which they have little control. As with material production, so also theoretical production depends upon raw materials (words, concepts, language, formulae), means of production (mathematical systems, logic, computional devices, instruments), productive relations (ways in which science is organised and funded, ownership of intellectual property, educational arrangements), and finally the social and legal context of the productive activity (religious constraints, economic pressures, cultural values). Knowledge is a form of theoretical production and can usefully be analysed as such.

Once the real/theoretical object distinction is made, and knowledge is recognised as a process of intellectual production working with real objects that have been described, apprehended, or incorporated by a theoretical object, then the interesting epistemological tasks of evaluating different modes of knowledge production — in terms of fecundity, simplicity, utility — can be commenced. Relativism short-circuits all of this.

Impiricism, and constructivism, conceives the enterprise of science in terms of individuals looking at the world and trying to ascertain whether their ideas, concepts, and conceptualisations make sense. Objectivist epistemology distinguishes between the raw material and events of the world (the real objects of science), the theoretical structures and concepts of science, the material and events as described by the theory (the theoretical objects of science), and the experimental and technical procedures of science. Individual understanding and conceptualisation is parasitic upon this extra-individual scientific domain. Science education can then be conceived in terms of the appropriate introduction of individuals into this world of concepts, understandings, techniques and community standards.

It needs to be said in passing that one does not need to be a constructivist to agree with most of their pedagogical claims — Socrates’ teaching of Pythagoras’ theorem to the slave boy is an early and enduring model of teaching for understanding, Aquinas and the medievals stressed personal engagement with and attachment to the subject matter being taught, they spoke of a “love of learning,” Montaigne’s essays on education advocate dialectical rather than didactic teaching, Dewey and the progressives emphasised class discussion, debate, the testing and scrutiny of teacher and pupil opinions, as of course has Paulo Freire in his many publications. Recently Richard Peters, Paul Hirst, Israel Scheffler, Jane Martin and other philosophers of education have stressed the importance of pupil comprehension and understanding for education.²⁷ Leading constructivists have of course recognised that progressive and good pedagogy has pre-dated their writings.²⁸

Von Glasersfeld says often that the orthodox epistemological problematic has to be abandoned, and that correspondence as a mark of truth needs to be rejected. This is because on his terms we cannot see reality, we only have our sensations to reflect upon, and so we are never able to judge correspondence between our ideas and the world (a restatement of Berkeley’s argument). He sometimes replaces correspondence with pragmatism, and in other places with coherence among experience. This leads him, and Noddings for instance, to speak of constructivism as being post-epistemological. His original subject-observing-an-object formulation does lead to an impasse, and one appreciates why he wants to abandon epistemology. My suggestion is that this is a case of old, unpalatable, empiricist wine in a new bottle; there are other non-empiricist, objectivist wines which allow epistemological imbibing to proceed with interest, enjoyment and profit.²⁹

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¹ R. Driver and V. Oldham, “A Consructivist Approach to Curriculum Development in Science,” Studies in Science Education 13 (1986): 105-122.

² E. von Glasersfeld, “Cognition, Construction of Knowledge, and Teaching,” Synthese 80, 1 (1989): 121-140.

³ R.B. Davis, “Discovery Learning and Constructivism,” in Constructivist Views on the Teaching and Learning of Mathematics, eds. R.B. Davis, C.A. Maher, and N. Noddings (Reston, Virginia: National Council of Teachers of Mathematics, 1990), 93-106.

⁴ R.P. Feynman, Surely You’re Joking, Mr.Feynman (London: Allen and Unwin, 1985).

⁵ K.C. Cheung and R. Taylor, “Towards a Humanistic Constructivist Model of Science Learning: Changing Perspectives and Research Implications,” Journal of Curriculum Studies 23, 1 (1991).

⁶ R. Millar and R. Driver, “Beyond Processes,” Studies in Science Education 14 (1987), 57.

⁷ R. Nadeau and J. Destautels, Epistemology and the Teaching of Science (Ottawa: Science Council of Canada, 1984), 19.

⁸ E. von Glasersfeld, 135.

⁹ Driver and Oldham, 109.

¹⁰ J. Confrey, 108.

¹¹ J. Desautels and M. Larochelle, “A Constructivist Pedagogical Strategy: The Epistemological Disturbance,” (Experiment and Preliminary Results) in More History and Philosophy of Science in Science Teaching, ed. D.E. Herget (Tallahassee, Florida: Florida State University, 1990), 236.

¹² N. Noddings, “Constructivism in Mathematics Education,” in Constructivist Views on the Teaching and Learning of Mathematics, eds. R.B. Davis, C.A. Maher, and N. Noddings, 18.

¹³ E. von Glasersfeld, 104.

¹⁴ S. Lerman, “Constructivism, Mathematics, and Mathematics Education,” Educational Studies in Mathematics 20 (1989): 211-223.

¹⁵ J. Kilpatrick, “What Constructivism Might Be in Mathematics Education,” in Psychology of Mathematics Education, eds. J.C. Bergeron, N. Herscovics, and C. Keiran (Montreal: Proceedings of the Eleventh International Conference, 1987), 3-27.

¹⁶ G.H. Wheatley, “Constructivist Perspectives on Science and Mathematics Learning,” Science Education 75 (1), (1991): 10.

¹⁷ K.A. Strike, “Towards a Coherent Constructivism,” in Misconceptions and Educational Strategies, ed. J.D. Novak (Education Department, Cornell University, 1987), v. 1, 481-489.

¹⁸ J. Kilpatrick, “What Constructivism Might Be in Mathematics Education.”

¹⁹ S. Lerman, “Constructivism, Mathematics, and Mathematics Education.”

²⁰ G. Goldin, “Epistemology, Constructivism, and Discovery Learning in Mathematics,” in Constructivist Views on the Teaching and Learning of Mathematics, eds. R.B. Davis, C.A. Maher, and N. Noddings.

²¹ R.H. Yeany, “A Unifying Theme in Science Education?,” NARST News 33 (2), (1991): 1-3.

²² W.A. Suchting, “Constructivism Deconstructed,” Science & Education 1 (3), (1992).

²³ Jeremy Kilpartick’s 1987 article, read at International Psychology of Mathematics conference polarised debate in the mathematics education community.

²⁴ That a leading constructivist identifies Vico and Berkeley as the founders of constructivism and lauds their philosophy is indicative of the ambiguous relationship between constructivism and modern science, including science education: Vico and Berkeley were the avowed opponents of the Scientific Revolution and of the work of Galileo, Newton and others. Both of them were defenders of orthodox Christianity against the perceived irreligious philosophy of the new science. Berkeley’s 1710 Treatise was subtitled ‘Wherein the Chief Causes of Error and Difficulty in the Sciences, With the Grounds of Scepticism, Atheism, and Irreligion are Inquired Into’. That so many today are defending science education with the doctrines of two deeply anti-scientific thinkers is cause for some reflection.

²⁵ S. Lerman, “Constructivism, Mathematics, and Mathematics Education,” 212.

²⁶ A more detailed account of this pendulum debate is developed in M.R. Matthews, “Galileo’s Pendulum and the Objects of Science,” in Philosophy of Education Proceedings 1987, eds. B. and D. Arnstine (Normal, Illinois: Philosophy of Education Society, 1987), 309-319; and in M.R. Matthews, “Galileo and Pendulum Motion: A Case for History and Philosophy of Science in the Science Classroom,” The Australian Science Teachers Journal 36 (1), 7-13.

²⁷ Neil Cooper is representative of these philosophers of education in claiming that: “My thesis is that education ought to be the transmission of understanding-knowledge and that an educated person will properly be one who not only has understanding-knowledge but understands the nature of that knowledge.” N. Cooper, “The Transmission of Knowledge,” in Philosophers on Education, eds. R. Staughton and J. Wilson (Totowa, New Jersey: Barnes and Noble, 1987), 61-78.

²⁸ Ernst von Glasersfeld has realistically commented that: “Good teachers…have practised much of what is suggested here, without the benefit of an explicit theory of knowing…but…constructivism may provide the thousands of less intuitive educators an accessible way to improve their methods of instruction.” E. von Glasersfeld, 138.

²⁹ For some elaboration of non-empiricist, objectivist epistemology see Suchting (1986, ch. 1), Chalmers (1982, chs. 10, 11), Matthews (1980), Baltas (1989).