CONSTRUCTIVISM IN SCIENCE AND MATHEMATICS EDUCATION
Michael R. Matthews
University of New South Wales, Sydney, 2052 Australia
Constructivism is undoubtedly a major theoretical influence in contemporary science and mathematics education. Some would say it is the major influence. In its post-modernist and deconstructionist form, it is a significant influence in literary, artistic, history and religious education. Constructivism seemingly fits in with, and supports, a range of multicultural, feminist and broadly reformist programmes in education. Although constructivism began as a theory of learning, it has progressively expanded its dominion, becoming a theory of teaching, a theory of education, a theory of the origin of ideas, and a theory of both personal knowledge and scientific knowledge. Indeed constructivism has become education’s version of the ‘grand unified theory’.
Although there have been some critics of constructivism (Suchting 1992, Matthews 1993, Phillips 1995, Osborne 1996), and some urging caution in its adoption (Millar 1989, Solomon 1993), few would dispute Peter Fensham’s claim that ‘The most conspicuous psychological influence on curriculum thinking in science since 1980 has been the constructivist view of learning’ (Fensham 1992, p. 801).
THE SCOPE OF CONSTRUCTIVISM
The range of constructivist concerns can be seen in the subheadings of a recent science education article, where we are informed of: ‘A constructivist view of learning’, ‘A constructivist view of teaching’, ‘A view of science’, ‘Aims of science education’, ‘A constructivist view of curriculum’ and ‘A constructivist view of curriculum development’ (Bell 1991). The expanded purview of constructivism is also apparent in the remarks of another constructivist that: ‘this approach [constructivism] holds promise for the pursuit of educational objectives other than those associated exclusively with cognitive development … the constructivist point of view makes it possible to develop a vision of the whole educational phenomena which is comprehensive and penetrating’ (Pépin 1998, p. 173). Another author writes, ‘Constructivism is a postmodern theory of knowledge with the potential to transform educational theory’ (Fleury 1998, p. 156). It is not surprising then that, ‘For several years now, across the country [USA], preservice and in-service teachers have been considering constructivism as a referent for their philosophies of education’ (Bentley 1998, p.244). And constructivism is not just a theory about education, it is a theory about one of culture’s greatest and most enduring achievements, namely science. As Bentley says ‘Indeed as an epistemology, constructivism speaks to the nature of science’ (Bentley p. 243).
Constructivism spreads to still further fields. It increasingly presents itself as an ethical and political theory, as well as a learning, a teaching and an epistemological theory. As a recent paper says ‘There is also a sense in which constructivism implies caring – caring for ideas, personal theories, self image, human development, professional esteem, people – it is not a take-it-or-leave-it epistemology’ (Watts 1994, p. 52). This ethical dimension is manifest in the frequency with which notions of emancipation and empowerment occur in constructivist writing. Constructivism is thought to be a morally superior position to its rivals in learning theory and pedagogy. It offers teachers ‘a moral imperative for deconstructing traditional objectivist conceptions of the nature of science, mathematics and knowledge, and for reconstructing their personal epistemologies, teaching practices and educative relationships with students’ (Hardy & Taylor 1997, p. 148).
The well elaborated social constructivism of Paul Ernest certainly includes ethical and political dimensions. For instance, he says:
Each culture, like each individual, has the right to integrity. Thus, the system of values of each culture are ab initio equally valid. In absolute terms, there is no basis for asserting that the values of one culture or society is superior to all others. It cannot be asserted, therefore, that Western mathematics is superior to any other form because of its greater power over nature. (Ernest 1991, p. 264)
It is important that the ethical and political arguments for different multiculturalist positions not be confused with epistemological arguments. (1) In the foregoing quotation, the epistemological conclusion that different values, much less systems of mathematics, are equally valid simply does not follow from the ethical premise that each culture has a right to integrity. The ethical, or political, premise can be agreed to without any commitment at all to the relativistic epistemological conclusion. The right to individual or cultural integrity is simply not dependent upon individual beliefs, or cultural norms, being right. Being silly does not nullify one’s right to respect from others.
There is also a political dimension to much constructivist writing. Two constructivist writers say that they are ‘committed to the philosophy and principles of composite grades and mixed-ability groupings’ (Brass & Duke 1994, p. 100). Another writer has identified the Progressive Education tradition as constructivist, and the British Plowden Report of the mid-1960s as the embodiment of constructivist school organisation (Hawkins 1994).
A number of constructivists align themselves with the Critical Theory of Michael Apple, Henry Giroux and Stanley Aronowitz. One New Zealand commentator says that ‘There are many parallels between the literature on the development of critical pedagogy [and] the literature on constructivist learning’ (Gilbert 1993, p. 35). This is because, ‘Critical theorists question the value of such concepts as individualism, efficiency, rationality and objectivity, and the forms of curriculum and pedagogy that have developed from these concepts’ (Gilbert 1993, p. 20).
For some, constructivism is even larger than a theory of learning, education and science; it is almost a worldview or weltanschuung. Yvon Pépin, quoted above, goes on to say that constructivism: ‘also offers a global perspective on the meaning of the human adventure, on the way human beings impart meaning to their whole existence in order to survive and adapt’ (Pépin 174). Whilst another constructivist writes:
To become a constructivist is to use constructivism as a referent for thoughts and actions. That is to say when thinking or acting, beliefs associated with constructivism assume a higher value than other beliefs. For a variety of reasons the process is not easy. (Tobin 1991, p. 1)
Thus one problem posed for the appraisal of constructivism, for determining whether it has been a help or hinderance in educational reform, is being clear about what aspect of constructivism is being appraised: the learning theory, theory of knowledge, pedagogical theory, theory of science, educational theory or more all-encompassing worldview. Frequently the different aspects are treated as a package deal, whereby being a constructivist in learning theory is deemed to flow on to being a constructivist in all the other areas, and being a constructivist in pedagogy is deemed to imply a constructivist epistemology and educational theory. But these aspects can all be separated and each can stand alone. Thomas Kuhn, for instance, held a constructivist theory of science yet was an advocate of anti-constructivist pedagogy (Kuhn 1959). Socrates might be seen to be a constructivist in pedagogy, yet he was an anti-constructivist in his theory of knowledge. On the other hand, Ernst Mach was a most vigorous champion of instrumentalist (constructivist?) views of science, yet was quite didactic in his pedagogy.
Thus at least the following dimensions, or fields, of constructivism need to be separated:
1. Constructivism as a theory of learning.
2. Constructivism as a theory of teaching.
3. Constructivism as a theory of education.
4. Constructivism as a theory of cognition.
5. Constructivism as a theory of personal knowledge.
6. Constructivism as a theory of scientific knowledge.
7. Constructivism as a theory of educational ethics and politics.
8. Constructivism as a worldview.
A former president of the US National Association for Research in Science Teaching (NARST) has said that ‘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 polarised debate’ (Yeany 1991, p.1). Another past president of the same organisation wrote that ‘there is a paradigm war waging in education. Evidence of conflict is seen in nearly every facet of educational practice. ..[but] there is evidence of widespread acceptance of alternatives to objectivism, one of which is constructivism’ (Tobin 1993, p. ix). A review of research in mathematics education notes that ‘In the second half of the 1980s public statements urging the introduction of radical constructivist ideas in school mathematics programs also began to assume bandwagon proportions’ (Ellerton & Clements 1991, p. 58).
A 1990 bibliography produced at Leeds University, a major centre of constructivist research, listed over 1,000 works (Carmichael et al 1990). Reinders Duit, at the Institute for Science Education in Kiel, has been performing the Herculean task of keeping up-to-date with research in this field, and in the early 1990s he estimated that there were 2,500 constructivist-inspired scholarly research articles in journals and anthologies (Duit 1993). At the end of the 1990s, that number could probably be quadroupled. A periodic series of research conferences held at Cornell University under the guidance of Joseph Novak reflects this same almost exponential growth of constructivist scholarship. Sixty papers were presented at the first international conference in 1983 (Helm & Novak 1983), 160 papers were presented at the second conference in 1987 (Novak 1987), 250 at the third conference in 1993 and about 300 at the fourth in 1995.
In the past decade there have been scores of constructivist-inspired books and anthologies in science and mathematics education. (2)
Constructivist influence has extended beyond just the research and scholarly community: it has had an impact on a number of national curricular documents and national education statements. Speaking of recent US science and mathematics education reforms, Catherine Twomey Fosnot has commented that ‘Most recent reforms advocated by national professional groups are based on constructivism. For example the National Council for Teachers of Mathematics … and … the National Science Teachers Association’ (Fosnot 1996, p. x). (3) The US National Science Teachers Association Standards for Teacher Preparation – standards according to which the value of institutions’ teacher education programmes are to be evaluated – is replete with the endorsement of constructivism.
Constructivism influenced the recently released US National Science Education Standards (NRC 1996). The 1992 Draft Standards recognised that the history, philosophy and sociology of science ought contribute to the formation of the science curriculum. But when the contribution of philosophy of science was, in an Appendix, elaborated, it turned out to be constructivist philosophy of science. After dismissing a caricature of logical empiricism, the document endorses ‘A more contemporary approach, often called postmodernism [which] questions the objectivity of observation and the truth of scientific knowledge’. It proceeds to state that ‘science is a mental representation constructed by the individual’, and concludes, in case there has been any doubt, that ‘The National Science Education Standards are based on the postmodernist view of the nature of science’. Not surprisingly these endorsements caused some scientific and philosophical eyebrows to be raised, and sleeves to be rolled up. (4)
The revised 1994 Draft emerged sans the Appendix, but its constructivist content was not rejected, merely relocated (NRC 1994). Learning science was still identified with ‘constructing personal meaning’. And the history of science was seen in terms of the ‘changing commitments of scientists [which] forge change commonly referred to as advances in science’. As one commentator, sympathetic to constructivism, remarked:
even though the term constructivism is not used even once in the NSES, it is clear that individual constructivism … is the driving theory of teaching and learning throughout the document … the theoretical underpinning of the document is made to be invisible. (Rodriguez 1997, p. 30)
And constructivist influence is not just confined to the US. The New Zealand National Science Curriculum is heavily influenced by constructivist theories and ideals (Matthews 1995). Comparable documents in Spain, the UK, Israel, Australia, and Canada bear to varying degrees the imprint of constructivist theory.
High hopes are held for constructivism, with two proponents in science education saying that it ‘can serve as an alternative to the hunches, guesses, and folklore that have guided our profession for over 100 years’ (Mintzes & Wandersee 1998, p. 30). The introductory essay of a recent constructivist anthology announces that: ‘ “critical-constructivism” stands in opposition to the unmitigated sociopolitical vaporousness only too frequently encounted nowadays’ (Larochelle & Bednarz 1998, p. 20). Another leading advocate has, understatedly, said: ‘If the theory of knowing that constructivism builds upon were adopted as a working hypothesis, it could bring about some rather profound changes in the general practice of education’ (Glasersfeld 1989, p. 135).
These comments resonate with a certain Manicheeism commonly found in constructivism. There is a widespread sense that constructivism will lead teachers, students and researchers out of the wilderness and into the educational Promised Land; that one’s back can be turned on ‘sociopolitical vaporousness’ and emancipation achieved. There are goodies and baddies, and references to ‘warfare’. Jeremy Kilpatrick, in his plenary address to a major international mathematics education conference in 1987, criticised the insularity and fervour of constructivists, observing that constructivism was akin to waves of religious fundamentalism that periodically sweep America. He said of constructivism that it has:
A siege mentality that seeks to spread the word to an uncomprehending, fallen world; a band of true believers whose credo demands absolute faith and unquestioning commitment, whose tolerance for debate is minimal, and who view compromise as sin; an apocalyptic vision that governs all of life, answers all questions, and puts an end to doubt. (Kilpatrick, 1987, p. 4)
And constructivism is understood as not just another flag to march behind; it is not just an ideal, or purely normative theory: it purports to give scientific guidance about human learning and the process of knowledge production; and philosophical guidance about the epistemological status of what is being learned, especially the nature of scientific and mathematical knowledge claims. Constructivism is not just a banner flapping idly in the breeze, as Luis Althusser once said of the role of Marxism in the French Communist Party and as could be said of so many educational slogans: rather constructivism is meant to connect with the reality of human cognitive processes and thus guide effective teaching and learning across the curriculum: in science, mathematics, literature, religion and history. Children are said to learn in a certain way, and what they learn is said to be characterised in a certain way and thus teaching, curriculum, school organisation are all supposed to reflect these realities, not just hopes or aspirations.
AN EVIDENTIAL DILEMMA
Although constructivists appeal to realities about human learning and science, there is a problem because, for many constructivists, reality collapses into ‘my experience of reality’. (5) This is comparable, and not accidently so, to what happened to reality in the classic empiricism of Bekeley. (6) Antonio Bettencourt is just one of many constructivists who say: ‘... constructivism, like idealism, maintains that we are cognitively isolated from the nature of reality. ... Our knowledge is, at best, a mapping of transformations allowed by that reality’ (Bettencourt, 1992, p.46).
Thus there is an ‘Evidential Dilemma’ for constructivists: they wish to appeal to the nature of cognitive realities (learning processes) and epistemological realities (especially the history of science and mathematics) to support their pedagogical, curricular and epistemological proposals. Thus one researcher who champions ‘sociotransformative constructivism’ (STC), and who supports the position with a study of 18 students in a secondary science methods class, is impelled to remark that:
Note that by using the term empirical evidence, I am not taking a realist or empiricist stance, nor any other Western orientation. I use the term ‘empirical evidence’ with the understanding that knowledge is socially constructed and always partial. By ‘empirical evidence’ I mean that information was systematically gathered and exposed to a variety of methodology checks. Hence in this study I do not pretend to capture the real world of the research participants (realism), nor do I pretend to capture their experiential world (empiricism). What I do attempt is to provide spaces where the participants’ voices and subjectivities are represented along with my own voice and subjectivities. (Rodriguez 1998, p. 618)
That constructivists suffer this ‘evidential dilemma’ or ‘evidential discomfort’ in not surprising. As a prominent constructivist in mathematics education has written:
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. (Confrey, 1990, p. 108)
As lenses change, so seemingly does reality, and researchers with different lenses live in different worlds, and necessarily have to appeal to different ‘realities’ to support their claims. Just whose reality is the most real, or whose reality ought to drive education policy and funding, is left obscure. There are of course difficult interpretative problems regarding the relationship of evidence to theory, and good methodologists are aware of them and do their best to make the relationship more transparent, but constructivism creates an in principle barrier between evidence and theory. This then leaves legitimate methodological space for ideology, personal and group self interest, or just ‘feel-goodness’, to determine theory choice and acceptance.
VARIETIES OF CONSTRUCTIVISM
There are three major constructivist traditions: educational constructivism, philosophical constructivism, and sociological constructivism. Educational constructivism itself divides into personal constructivism having its origin with Piaget and at present most clearly enunciated by Ernst von Glasersfeld; and social constructivism which has its origins with Lev Vyotsky, the Soviet contemporary of Piaget, and has been enunciated by researchers such as Rosalind Driver in science education and Paul Ernest in mathematics education. Philosophical constructivism has its immediate origins in Thomas Kuhn’s work, and is most robustly represented by Bas van Fraasen, a recent President of the US Philosophy of Science Association. This philosophical constructivism has its roots in Berkeley’s philosophy of science, and further back in intrumentalist philosophy of Ancient Greece. This tradition has been, since Aristotle, opposed by realists in the philosophy of science (see Matthews 1994, chap. 8). Sociological constructivism is identified with the Edinburgh ‘Strong Programme’ and their research on the Sociology of Scientific Knowledge (SSK). In this tradition the growth of science, and changes in its theories and philosophical commitments, is interpreted in terms of changing social conditions and interests. The explanatory power of cognitive content and rational reasoning is discounted. Psychological processes are not much referred to in this tradition: the individual mind is treated like a ‘black box’, with the sociologists concentrating mainly on sociological inputs or context and theoretical outputs or statements of belief. That is, that something is true and reasonable is not thought, by adherents to the Edinburgh Programme, to constitute an explanation of why it is believed. They believe in the Symmetry Principle: the explanation of false beliefs and of true beliefs has to be of the same form. (7)
This chapter will be concerned chiefly with the first tradition, educational constructivism. Even here there are many varieties. (8) One review identified the following varieties: contextual, dialectical, empirical, information-processing, methodological, moderate, Piagetian, post-epistemological, pragmatic, radical, realist, and socio-historical (Good, Wandersee & St Julien 1993). To this list could be added humanistic constructivism (Cheung & Taylor 1991), didactic constructivism (Brink 1991), sociocultural (O’Laughlin 1992), pragmatic social constructivism (Garrison 1998), and sociotransformative constructivism (Rodriquez 1998).
Thus constructivism is clearly a ‘Broad Church’ doctrine, and this presents problems for its appraisal. These ‘identity problems’ are exacerbated when some educational constructivists simply identify constructivism with non-behaviourist learning theory. Indeed for many writers, teachers and students this is what constructivism means. Dennis and Valentina McInerney, for instance, in their text on educational psychology say that: ‘We discuss the cognitive theories of Gestalt Psychology and of Bruner as examples of personal constructivism’ (McInerney 1998, p. 90). This identification is a cause of some confusion: what is a reasonable necessary condition for constructivism, becomes both a necessary and sufficient condition. Bruner and the Gestalt theorists paid little attention to epistemology, which is the defining feature of serious constructivism. Certainly many realists in epistemology embrace non-behaviourist learning theory: to label these people ‘constructivists’ is to invite confusion.
These identity problems are likewise exacerbated when writers simply identify constructivism with all views that recognise the social, cultural and historical dimension of cognition. Many, since at least Hegel and Marx, have recognised that the ‘we think’ determines and sets limits on the ‘I think’. Paulo Freire is one of many who have championed this view (Matthews 1980). Constructivists rightly stress this insight, but are frequently blind to its major import: the individual does not confront the world and experience as a Robinson Crusoe figure, but needs to absorb, learn, and be formed by, his or her social milieu and language. Language, especially scientific and mathematical language, needs to be mastered and, at the end of the day, transmitted. Many constructivists want the ‘historical-cultural omelette’ but are reluctant to break the ‘knowledge cannot be transmitted’ egg.
Constructivists’ paradigmatic case of knowledge is the individual confronting the world and making sense of their experiences: socialisation, enculturation and language is pushed into the background. Alan Morf, for instance, in an article elaborating constructivist epistemology, wrote that ‘I consider knowledge as experience-generated potentialities for action’ (Morf 1998, p. 36), and he refers to an infant’s first interactions with their environment as exemplary of this kind of knowledge. Anthony Lorsbach and Kenneth Tobin, in an article explaining the implications of constructivism for practising science teachers, wrote:
The constructivist epistemology asserts that the only tools available to a knower are the senses. It is only through seeing, hearing, touching, smelling, and tasting that an individual interacts with the environment. With these messages from the senses the individual builds a picture of the world. Therefore, constructivism asserts that knowledge resides in individuals. (Lorsbach & Tobin, 1992, p. 5)
Ernst von Glasersfeld has had great influence on the development of constructivist theory in mathematics and science education in the past decade. He has published well over one hundred papers, book chapters and books in fields such as mathematics and science education, cybernetics, semantics and epistemology. (9) Von Glasersfeld is an advocate of ‘Radical Constructivism’, a position based on ‘the practice of psycholinguistics, cognitive psychology, and . . . the works of Jean Piaget’ (Glasersfeld 1990, p. 1). As he provides perhaps the most systematic account of the epistemological and ontological underpinnings of psychological constructivism that can be found in the educational literature, his work will be examined here in some detail. The examination intends to illustrate some philosophical problems with constructivist theory, and more generally illustrate how the history and philosophy of science can bear upon important disputes in educational theory.
Von Glasersfeld sees himself in a constructivist tradition begun in the ‘18th century by Giambattista Vico, the first true constructivist’ and continued by ‘Silvio Ceccato and Jean Piaget in the more recent past’ (Glasersfeld 1987, p. 193). This tradition tends to undermine a large ‘part of the traditional view of the world’, above all ‘the relation of knowledge and reality’ (Glasersfeld 1987, p. 193). Von Glasersfeld concludes his discussion of Vico with the claim that, for constructivists:
The word ‘knowledge’ refers to a commodity that is radically different from the objective representation of an observer-independent world which the mainstream of the Western philosophical tradition has been looking for. Instead ‘knowledge’ refers to conceptual structures that epistemic agents, given the range of present experience within their tradition of thought and language, consider viable. (Glasersfeld 1989, p. 124)
This can be referred to as von Glasersfeld's principle, or perhaps von Glasersfeld's philosophy (VGP), as it subsumes a number of epistemological and ontological theses, among which are the following:
Knowledge is not about an observer-independent world.
Knowledge does not represent such a world; correspondence theories of knowledge are mistaken.
Knowledge is created by individuals in a historical and cultural context.
Knowledge refers to individual experience rather than to the world.
Knowledge is constituted by individual conceptual structures.
Conceptual structures constitute knowledge when individuals regard them as viable in relationship to their experience; constructivism is a form of pragmatism.
There are some ambiguities and obscurities in this formulation, but there are other statements of VGP which illuminate some of these constitutive theses. In one place von Glasersfeld says:
Our knowledge is useful, relevant, viable, or however we want to call the positive end of the scale of evaluation, if it stands up to experience and enables us to make predictions and to bring about or avoid, as the case may be, certain phenomena (i.e., appearances, events, experiences). . . . Logically, that gives us no clue as to how the ‘objective’ world might be; it merely means that we know one viable way to a goal that we have chosen under specific circumstances in our experiential world. It tells us nothing . . . about how many other ways there might be. (Glasersfeld 1987, p. 199)
This supports the foregoing delineation and suggests a further thesis implicit in the former statement:
There is no preferred epistemic conceptual structure; constructivism is a relativist doctrine.
And finally, in a move that many idealists before him have made, von Glasersfeld proceeds from an epistemological position to an ontological one:
Radical constructivism, thus, is radical because it breaks with convention and develops a theory of knowledge in which knowledge does not reflect an ‘objective’ ontological reality, but exclusively an ordering and organization of a world constituted by our experience. The radical constructivist has relinquished ‘metaphysical realism’ once and for all. (Glasersfeld 1987, p. 199)
This claim suggests two further constitutive theses of VGP:
Knowledge is the appropriate ordering of an experiential reality.
There is no rationally accessible, extraexperiential reality.
In his 1989 paper, von Glasersfeld quotes approvingly Ludwik Fleck and Richard Rorty. From a 1929 paper of Fleck, he repeats: ‘The content of our knowledge must be considered the free creation of our culture. It resembles a traditional myth’ (p. 122). From Rorty’s 1982 book, he repeats that the pragmatist ‘drops the notion of truth as correspondence with reality altogether, and says that modern science does not enable us to cope because it corresponds, it just enables us to cope’ (p. 124). These endorsements strengthen the nine-part delineation of VGP proposed above.
It is easy to see the influence of VGP in scores, in not hundreds, of constructivist publications. Stephen Fleury, for instance, writes that:
Two philosophical principles characterize constructivism. … The first is that knowledge is actively built by a cognizing subject. … A second foundational principle … [is that] the function of cognition is to organize one’e experiential world, not to discover an ontological reality. (Fleury 1998, pp. 157, 158)
Earlier, Grayson Wheatley offered a nearly identical summary of the epistemological core of constructivism, saying:
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. (Wheatley 1991, p. 10)
The late Rosalind Driver, in many publications, repeated elements of VGP. For instance:
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. (Driver & Oldham 1986, p. 109)
Because of its enormous influence, von Glasersfeld’s elaboration of constructivism warrants detailed attention. And it has major problems, specifically: its empiricism, its confusion of real and theoretical objects of science, its individualism, its account of concept acquisition and its idealism. (10)
The basic problem with VGP is that it is a variant of the empiricist conception of knowledge which the scientific revolution discredited. All the root commitments of empiricism are preserved and endorsed in VGP: knowledge is something that individuals create and adjudicate; experience is the raw material of knowledge claims; thus there is no immediate, epistemic access to the external world; once individual cognitive activity is recognized, it is assumed that cognitive claims are compromised, and knowledge of an external reality becomes impossible. VGP (1-9) both embraces and elaborates the consequences of empiricist epistemology.
Any epistemology which formulates the problem of knowledge in terms of a subject looking at an object and asking how well his or her experience or sensations reflects the nature or essence of the object, is quintessentially Aristotelian, or more generally empiricist – even if the conclusion is that sensory experience does not reflect properties of objects at all. Aristotelians were direct realists about perception; that is, the objects of perception were material bodies. Later empiricists were largely indirect realists; that is the objects of perception were sense impressions generated, it was supposed, by material objects. Locke, an avowed opponent of Aristotle, puts the matter this way in his Essay: ‘The mind, in all its thoughts and reasonings, hath no other immediate object but its own ideas, which it alone does or can contemplate.’
Variations of this Lockean problematic recur in modern constructivist formulations. Experience, rather than a means to knowledge, becomes the object of knowledge. This substitution is fatal. As is well known, Locke’s formulation of the problem of knowledge was used by Berkeley to support idealism and relativism. Berkeley’s argument in his Treatise was simple but devastating: ‘As for our senses, by them we have the knowledge only of our sensations, ideas, or those things that are immediately perceived by sense, call them what you will: but they do not inform us that things exist without the mind, or unperceived.’ It is not coincidental that modern constructivists, once having formulated the epistemological problem in Aristotelian-Lockean terms (VGP 4, 8), then endorse versions of Berkeley’s savage critique of it and end up with relativism (VGP 7) and, for the more consistent, idealism (VGP 9).
George Bodner, an American constructivist, provides a pleasingly frank endorsement of instrumentalism, saying: ‘The constructivist model is an instrumentalist view of knowledge. Knowledge is good if and when it works, if and when it allows us to achieve our goals (Bodner 1986, p. 874). To his credit, at least for consistency, he went on to align himself with the sixteenth century theologian Osiander, the instrumentalist champion in one of the great showdowns between instrumentalism and realism in the history of science. Bodner admits, but seemingly without embarrassment, that:
A similar view was taken by Osiander, who suggested in the preface of Copernicus’ De Revolutionibus [that] ‘There is no need for these hypotheses to be true, or even to be at all like the truth; rather, one thing is sufficient for them – that they yield calculations which agree with the observations’. (Bodner, 1986, p. 874)
Within the Aristotelian-empiricist tradition the possibility of knowledge was weakened once it was pointed out that the mind is active in cognition. The possibility of knowledge evaporated once it was claimed that the immediate objects of the intellectual faculty were sense impressions rather than nature itself. Nature, or in Kant's terms, the thing-in-itself, became unknowable, because we only ever see it through a distorting lens, and there is no privileged position from which to check the correspondence of thought to reality.
Following Kant, Piaget, and the host of postpositivist philosophers such as Toulmin, Kuhn, Feyerabend, Rorty and others, modern constructivism asserts that, because individuals are active in knowledge acquisition, knowledge of an external reality is impossible. The argument sets up the epistemological situation as an observer facing reality, and then argues that, in as much as the observer contributes to the resulting knowledge, it cannot be undiluted knowledge of reality.
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’; when Confrey speaks of ‘cognitive lens’; when 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. The empiricist assumptions of constructivism are also revealed by the frequent use of the Kuhn/Hanson ambiguous or hidden figures examples 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 the lens clearly or darkly, it is the metaphor of seeing through a lens which signals commitment to an empiricist theory of knowledge.
The one-step argument from the psychological premise (1) ‘the mind is active in knowledge acquisition,’ to the epistemological conclusion (2) ‘we cannot know reality,’ is endemic in constructivist writing. Lerman speaks for many when he says, of these two theses, that ‘the connections between hypothesis (1) and (2) seem to be quite strong’ (Lerman 1989, p. 212).
However, this conclusion only follows on the assumption that the empiricist tradition has correctly delineated the problem of knowledge. If one rejects the assumption that the problem of knowledge arises when a subject looks at an object and wonders whether his or her mental representation corresponds to the object, then none of the sceptical conclusions of radical constructivism follow. Non-empiricist theories of knowledge are not subject to this sceptical argument.
A number of these matters were developed by Wallis Suchting, who concluded a long and detailed analysis of Ernst von Glasersfeld’s radical constructivism with the opinion that: (11)
First, much of the doctrine known as ‘constructivism’ ... is simply unintelligible. Second, to the extent that it is intelligible ... it is simply confused. Third, there is a complete absence of any argument for whatever positions can be made out. ... In general, far from being what it is claimed to be, namely, the New Age in philosophy of science, an even slightly perceptive ear can detect the familiar voice of a really quite primitive, traditional subjectivistic empiricism with some overtones of diverse provenance like Piaget and Kuhn. (Suchting, 1992, p. 247)
THE NEW ZEALAND EXAMPLE
Unfortunately matters of deep philosophical import over which there have been centuries of debate, too frequently appear almost as throw-away lines in science education writing. It is in everyone’s interest that these epistemological and ontological claims be better scrutinised. New Zealand, where constructivism has had great influence across the curricula, and from top to bottom of the educational system, illustrates this matter.
For example the very influential and much-reprinted book of Roger Osborne and Peter Freyberg – Learning in Science: The Implications of Children's Science (Osborne & Freyberg, 1985) opens with the statement that:
Young children and scientists have much in common. Both are interested in a wide variety of objects and events in the world around them. Both are interested in, and attempt to make sense of, how and why things behave as they do. (Osborne & Freyberg 1985, p.1)
This idea – that science is about making sense of the world, rather than finding out about the world – has been much debated in the history of philosophy. But the book does not elaborate the debate or defend its position. The book concludes with a statement of the sine qua non of constructivism – the non-transferability of knowledge thesis:
Knowledge is acquired not by the internalisation of some outside given but is constructed from within. (Osborne & Freyberg 1985, p. 82)
Again there is no elaboration or defense of this, to put it mildly, contentious position. The alternative position in learning theory, for which there is a great deal of evidence, is one that maintains:
if you want somebody to know something, you teach it to them ... if you want somebody to know something and retain it for a long period of time, then you have them practice it. (Geary 1995, p. 33)
These casual, almost throw-away epistemological positions have cast a long shadow in New Zealand. For instance, the New Zealand National Curriculum in Science labels the chief learning areas: ‘Making Sense of the Living World’ (instead of Biology, or Finding Out About the Living World), and ‘Making Sense of Planet Earth and Beyond’ (instead of Astronomy, or Finding Out About the Solar System). And a 1990 draft syllabus identifies the ‘Role of the Teacher’ as being: ‘Helping students learn how to learn; being a learner too; ensuring equity for all students; creating a friendly, supportive learning enviornment; providing learning opportunities; listening to students; using the students' ideas, experiences, and interests; challenging sensitively the ideas of students; providing resources to help students learn; ensuring students communicate in a variety of modes; identifying and nurturing the scientific talent and interests of all students – provided that teachers are aware of the effectiveness of an open science programme which allows students to realise their own potential at their own pace; and finally, contributing to the planning of the school science programme’. This list has everything except knowing the subject matter to be taught, and being able to teach it in a clear, engaging and understandable manner.
There is a not-too-subtle difference between the constructivist formulation ‘making sense’, and the realist formulation ‘finding out’. The former has no epistemological or referential bite; the latter has both. Things can make perfect sense without being true; and making still more sense does not imply any increase in truth content.
It is notorious that people have for centuries thought that the grossest injustices, and the greatest evils, have all made sense. The subjection of women to men has, and still does, make perfectly good sense to millions of people and to scores of societies; explaining illness in terms of possession by evil spirits makes perfectly good sense to countless millions; the intellectual inferiority of particular races is perfectly sensible to millions of people including some of the most advanced thinkers. The list of atrocities and stupidities that made perfect sense at some time or other, or in some place or other, goes on and on. It seems clear that the appeal to sense is not going to be sufficient to refute such views, the appeal to truth which is independent of human desires or power, may be able, perhaps, to overturn such opinions. Certainly the interests of the less powerful and marginalised are not advanced by championing the view that power is truth; minority rights have always been better advanced by holding on to the view that truth is power.
CONSTRUCTIVIST TEACHING OF THE CONTENT OF SCIENCE
One response to criticism of constructivist theory is to say that constructivist pedagogy is valuable and should be encouraged, even if the theory is debatable. This position is understandable, but it rests on a moot point: namely, How efficacious is constructivist pedagogy in teaching science?
One prominent constructivist, Richard White, has said ‘although the research on alternative conceptions has sparked interest in content, it has not yielded clear advice about how to teach different topics’ (Fensham, Gunstone and White, 1994, p. 255). Given the necessity for any science programme to teach the content of science this is a serious failure.
The difficulty for constructivism posed by teaching the content of science is not just a practical one, it is a difficulty that exposes a fundamental theoretical problem for constructivism – if knowledge cannot be imparted, and if knowledge must be a matter of personal construction, then how can children come to knowledge of complex conceptual schemes that have taken the best minds hundreds of years to build up?
Many science educators are interested in finding out how, on constructivist principles, one teaches a body of scientific knowledge that is in large part abstract (depending on notions such as velocity, acceleration, force, gene), that is removed from experience (propositions about atomic structure, cellular processes, astronomic events), that has no connection with prior conceptions (ideas of viruses, antibodies, molten core, evolution, electromagnetic radiation), and that is alien to common-sense, and in conflict with everyday experience, expectations and concepts? Teaching a body of knowledge involves not just teaching the concepts, but also the method, and something of the methodology or theory of method. How all of this is to be taught, without teachers actually conveying something to pupils, is a moot point.
Joan Solomon, a prominent British science educator, well articulates the problem:
Constructivism has always skirted round the actual learning of an established body of knowledge ... students will find that words are used in new and standardised ways: problems which were never even seen as being problems, are solved in a sense which needs to be learned and rehearsed. For a time all pupils may feel that they are on foreign land and no amount of recollection of their own remembered territory with shut eyes will help them to acclimatise. (Solomon, 1994, p. 16)
The constructivist research of the late Rosalind Driver and scholars at Leeds University illustrates the ‘skirting around’ to which Solomon draws attention. In a recent book the Leeds group reasonably enough maintain that:
learning science involves being initiated into the culture of science. If learners are to be given access to the knowledge systems of science, the process of knowledge construction must go beyond personal empirical enquiry. Learners need to be given access not only to physical experiences but also to the concepts and models of conventional science. (Driver et al., 1994, p. 6)
There is near unanimity on this claim – conservatives and progressivists all agree, with perhaps just discovery-learners dissenting. The claim echoes the Leeds group’s oft-repeated assertion that constructivism is different from discovery learning (on this, see Miller & Driver 1987). But having made the above claim, the Leeds group go on to say that:
The challenge for teachers lies in helping learners to construct these models for themselves, to appreciate their domains of applicability and, within such domains, to use them.
One might reasonably ask whether, at this point, learning theory, or ideology, is simply getting in the way of good teaching. Why must learners construct for themselves the ideas of potential energy, mutation, linear inertia, photosynthesis, valency, and so on? Why not explain these ideas to students, and do it in such a way that they understand them? This process may or may not be didactic: it all depends on the classroom circumstance. There are many ways to explain science: didacticism is just one of them. Certainly a challenge for constructivist teachers lies in helping learners construct these ideas without violating constructivist learning principles. The Leeds group recognise this, and go on to say:
If teaching is to lead pupils towards conventional science ideas, then the teacher’s intervention is essential, both through providing appropriate experiential evidence and making the theoretical ideas and conventions available to pupils. (Driver et al. 1994b, p. 6)
This is perhaps the precise point where Joan Solomon’s ‘skirting around’ is evidenced. How can a teacher make ‘the theoretical ideas and conventions available to pupils’ without explaining them, without illustrating them, without showing their interconnections: in brief, without teaching them to pupils?
Constructivists addressed the problem of the teaching of the content of science at an international seminar held at Monash University in 1992. Its published proceedings were titled The Content of Science: A Constructivist Approach to its Teaching and Learning (Fensham, Gunstone and White, 1994). Rosalind Driver and colleagues made a contribution to the seminar on ‘Planning and Teaching a Chemistry Topic from a Constructivist Perspective’. They had children put nails in different places and observe the rate at which they rusted. They remarked that:
The theory that rusting is a chemical reaction between iron, oxygen and water, resulting in the formation of a new substance, is not one that students are likely to generate for themselves. (Scott et al. 1994, p. 206)
Indeed. After ten pages describing how the teacher tries to ‘keep faith with students’ reasoning ... yet lead them to the intended learning goals’ (p. 207), we are told that ‘The process of investigating personal ideas and theories may lead students to reflect upon and question them. At the same time, it is unlikely to lead to the scientific view’ (p. 218).
Quite so. But where does this leave constructivism as a putatively useful theory for science teachers?
Most science teachers realise this difficulty. They try their best to explain things clearly, to make use of metaphors, to use demonstrations and practical work to flesh out abstractions, to utilise projects and discussions for involving students in the subject matter, and so on. They realise that many, if not most, things in science are beyond the experience of students and the capabilities of school laboratories to demonstrate. The cellular, molecular and atomic realms are out of reach of school laboratories, as is most of the astronomical realm. Most of the time even things that are within reach do not work. It is a rare school experiment that is successful. For children, a great deal of science has to be taken on faith. Good teachers do their best in the situation, and try to point out why faith in science is warranted. They may refer to texts or studies that have better controlled for experimental conditions than is possible in school settings. They may get students to appreciate the general directions in which school laboratory results are heading. They may do various other things to get pupils to see that their particular experience of a situation falls short of the experience that scientific investigation requires.
Some would say that the constructivist/anti-constructivist argument reduces to a mere verbal preference: constructivist teachers (of the Leeds variety) perhaps do make the concepts available in the sense of teaching the concepts, but they prefer to talk of student construction, while traditionalists prefer to talk of transmission. Where there is a failure of match between the pupil’s idea and the scientific idea, constructivists prefer to talk of imperfect construction, and traditionalists prefer to talk of failure of attention, imperfect comprehension, inadequate preparation. Certainly translations can be made from constructivist discourse to traditional discourse. For instance: ‘perturbation = ‘anomaly’, ‘viability’ = ‘confirmation’, ‘construction of knowledge’ = ‘learning’, ‘facilitation’ = ‘teaching’, ‘scheme’ = ‘theory’, ‘accommodation’ = ‘theory change’. Provided both groups of teachers are doing the same thing, and judging the outcome by the degree to which the pupil understands the current scientific concept, then the argument could be seen as merely a verbal one over the name of a label.
But it is not just a verbal matter. A practical, but not insignificant, consideration is that science teachers are overwhelmed by challenges – pupils’ lack of interest in science, teachers’ inadequate knowledge of science, schools’ lack of resources, society’s lack of interest in education – they do not need to be further weighed down by illusory challenges, if indeed this is what the constructivist challenge amounts to. A theoretical consideration is the very justification of science in the curriculum. If Western science is truly just one among many equally warranted ways of making sense of experience, and it truly does not tell us anything about the world in which we live, then traditional arguments for compulsory school science, and ‘Science for All’, need to be re-thought.
Constructivism has done a service to science and mathematics education: by alerting teachers to the function of prior learning and extant concepts in the process of learning new material, by stressing the importance of understanding as a goal of science instruction, by fostering pupil engagement in lessons, and other such progressive matters. But liberal educationalists can rightly say that these are pedagogical commonplaces, the recognition of which goes back at least to Socrates. It is clear that the best of constructivist pedagogy can be had without constructivist epistemology – Socrates, Montaigne, Locke, Mill, and Russell are just some who have conjoined engaging, constructivist-like, pedagogy with non-constructivist epistemology.
Constructivism has also done a service by making educators aware of the human dimension of science: its fallibility, its connection to culture and interests, the place of convention in scientific theory, the historicity of concepts, the complex procedures of theory appraisal, and much else. But again realist philosophers can rightly maintain that constructivism does not have a monopoly on these insights. They can be found in the work of thinkers as diverse as Mach, Duhem, Bachelard, Popper, and Polanyi.
Constructivism, in all its varieties, has been the subject of heated debate. The debate is not simply about the adequacy of a particular learning theory, or the cogency of a epistemological position. Something more is at stake. Karl Popper recognised it when he wrote:
The belief of a liberal – the belief in the possibility of a rule of law, of equal justice, of fundamental rights, and a free society – can easily survive the recognition that judges are not omniscient and may make mistakes about facts ... But the belief in the possibility of a rule of law, of justice, and of freedom, can hardly survive the acceptance of an epistemology which teaches that there are no objective facts; not merely in this particular case, but in any other case. (Popper, 1963, p. 5)
The debate over constructivism in education is a component of the more general ‘Science Wars’ that have been raging in the final decades of the twentieth century. (13) Michael Devitt has written that:
I have a candidate for the most dangerous contemporary intellectual tendency, it is ... constructivism. Constructivism is a combination of two Kantian ideas with twentieth-century relativism. The two Kantian ideas are, first, that we make the known world by imposing concepts, and, second, that the independent world is (at most) a mere 'thing-in-itself' forever beyond our ken. ...[considering] its role in France, in the social sciences, in literature departments, and in some largely well-meaning, but confused, political movements [it] has led to a veritable epidemic of 'worldmaking'. Constructivism attacks the immune system that saves us from silliness. (Devitt 1991, p.ix).
Given the influence of constructivism on education reform, teacher education, curriculum development and pedagogy, it is important to be clear about just what are, and are not, the epistemological commitments of constructivism. And what relationship these commitments have, if any, to classroom practice. The history of education is littered with ‘ideas that seemed good at the time’, but whose enactment caused educational and cultural havoc. Constructivism has all the earmarks of being such an idea.
1. On this, see Matthews (1994, chap. 9) and Siegel (1997).
2. The following are some of the perhaps better known and more cited: Tobin (1993), Glasersfeld (1991), Fosnot (1996), Ernest (1994, 1998), Steffe (1991, 1994), Steffe & Gale (1995), Fensham, Gunstone & White (1994), Davis, Maher & Noddings (1990), Mintzes, Wandersee & Novak (1998) and Larochelle, Bednarz & Garrison (1998).
3. Fosnot also observed that: ‘In literacy, much in-service work is going on under the rubic of whole language/writing process. The psychological theory behind all of these reforms is constructivism.’ (Fosnot 1996, p. x).
4. Gerald Holton has documented efforts made to counteract constructivist interpretations of the history and philosophy of science in the Standards (Holton 1996).
5. On the relationship between constructivism and classic empiricism, see Matthews (1993) and Suchting (1992).
6. See my discussion of the parallels between certain modern constructivisms and classical 17th century empiricism in Matthews (1992).
7. For criticism of the strong programme in the sociology of scientific knowledge, and especially of its educational implications, see Slezak (1994a, b), Nola (1997) and Kraghe (1998). Suchting (1997) provides a most informed discussion of the strengths and weaknesses of the strong programme.
8. See for instance Good et al. (1993), Phillips (1995) and Geelan (1997).
9. See especially von Glasersfeld (1987, 1989, 1991, 1992, 1995).
10. These problems are elaborated in Matthews (1994, pp. 148-158).
11. Suchting’s article, and von Glasersfeld’s response, are reproduced in Matthews (1998).
12. The example is elaborated in Matthews (1995).
13. For contributions to the ‘Science Wars’ see Passmore (1978), Holton (1993), Gross and Levitt (1994), Ross (1996), Gross, Levitt and Lewis (1996), Sokal & Bricmont (1998), and Koertge (1998).
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Published as: Matthews, M.R.: 2000, 'Constructivism in Science and Mathematics Education'. In D.C. Phillips (ed.), National Society for the Study of Education, 99th Yearbook, Chicago, University of Chicago Press, pp. 161-192.