Abstract
This article sketches a framework of ideas developed in the context of decades of physics teacher-education that was entitled the "perceptional approach". Individual learning and the scientific enterprise are interpreted as different manifestations of the same process aimed at understanding the natural and social worlds. The process is understood to possess the basic nature of perception, where empirical meanings are first born and then conceptualised. The accumulation of perceived gestalts in the “structure of the mind” leads to structural perception and the generation of conceptual hierarchies, which form a general principle for the expansion of our understanding. The process undergoes hierarchical development from early sensory perception to individual learning and finally to science. The process is discussed in terms of a three-process dynamic. Scientific and technological processes are driven by the interaction of the mind and nature. They are embedded in the social process due to the interaction of individual minds. These sub-processes are defined by their aims: The scientific process affects the mind and aims at understanding; the technological process affects nature and aims at human well-being; and the social process aims at mutual agreement and cooperation. In hierarchical development the interaction of nature and the mind gets structured into a “methodical cycle” by procedures involving conscious activities. Its intuitive nature is preserved due to subordination of the procedures to empirical meanings. In physics, two dimensions of hierarchical development are distinguished: Unification development gives rise to a generalisation hierarchy of concepts; Quantification development transfers the empirical meanings to quantities, laws and theories representing successive hierarchical levels of quantitative concepts. Consequences for physics teaching are discussed in principle, and in the light of examples and experiences from physics teacher education.
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Notes
Such problems are widely described in literature. Feynman (1985) gives (pp. 191–195) an account of his experience of Brazilian physics teaching. He concludes that ‘no science is being taught in Brazil’. There are very illuminating pages dealing with the example of polarization of light on pp. 211–212. Of his physics class he says (p. 213): “…they could pass the examinations, and “learn” all this stuff, and not know anything at all, except what they had memorized”. Also, on pp. 217–218 Feynman discusses how detrimental it is to discuss physics without reference to the experiments. In similar tone, Arons (1997) notes “we are merely cultivating blind memorization without comprehension … crushing our students into the flatness of equation-grinding automats. …We do not even give them a chance to begin to understand what “understanding” means”. As a result “a great majority of university students of science and technology have no more understanding of the ideas involved than the seven-year-old…. They are unable to discriminate, what of knowledge they possess is based on evidence and understanding, and what consists of memorized, unsupported assertions”, and continues to note that “This undermines their capacity to distinguish between jargon and knowledge….This condition is destructive of any understanding of nature, power and limitations of science.”
In the beginning of twentieth century, gestalt psychologists endeavored to identify the principles through which sensory information is interpreted. These gestalt psychologists claimed that coherent perceptual experience is more than the sum of its parts and that objects are perceived as organised wholes, configurations or patterns—as Gestalten. To recognise an object, one must distinguish it from its ground. Gestalt laws of perception describe how elements tend to be perceived together: (1) proximity (elements occur closely in space or time), (2) similarity, (3) continuity, (4) closure (closed figures are perceived more easily), (5) part-whole relationship (the whole is greater than its parts), (6) common fate (elements seen moving together are perceived as belonging together (Gross 2005). Gestalts are related to the idea of schema and similar such constructs. Some researchers (e.g. Rowlands et al. 1999; diSessa and Sherin 1998) have studied learning by using the concept of schema, which they define as a mental representation of a set of related categories. With a somewhat similar purpose diSessa introduced the concept of “phenomenological primitives” (or “p-prims”), which are based on intuition and which must be appropriately organised and activated under various circumstances. These constructs share many similarities with the concept of gestalt introduced here.
Hadamard (1945, p. 103) notes: “Between the work of the student who tries to solve a problem … and a work of invention (of a mathematician),… there is only … a difference of level, both works being of a similar nature.”
Hadamard (1945, chap. VI) discusses, in a passage titled Words and Wordless Thought, the relation of language and thinking. He opposes Müller’s statement that “The idea cannot be conceived otherwise than through the word and only exists by the word.” and agrees with Hamilton, who says that the “… Idea must necessarily precede the word.” He also refers to sensations as a primary source of meanings, stating that “… if I remember lightning, I see in my mind the flash of light… and I should need an instant of reflection… if I should wish the corresponding word to recur to me.” In Appendix II, Einstein describes his own thinking as follows: “The words or the language … do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be ‘voluntarily’ reproduced and combined … Conventional words or other signs have to be sought for laboriously only in a secondary stage.”
Arons (1997) principle (p. 27) of “idea first and name afterwards” corresponds to the declaration “Meanings first” of the perceptional approach; he simply uses the term “percept” as a synonym for “gestalt”.
Einstein (1970) writes in his Autobiographical notes in p. 13: “The concepts…get “meaning,” viz. “content,” only through their connection with sense-experiences”.
Karvonen (1995) concludes in her linguistic thesis that “Textbooks take knowledge as given… a typical textual pattern is one that begins with a definition … the texts are deductive, they begin with finished presuppositions…. The texts do not make possible a process for the reader, let alone require it.”
James (1909) wrote: “Intellectualism in the vicious sense began when Socrates and Plato taught that what a thing really is, is told us by its definition. Ever since Socrates we have been taught that … the essences of things are known whenever we know their definitions. … The misuse of the concepts begins with the habit of … using them not merely to assign properties to things, but to deny the very properties with which the things sensibly present themselves. Logic can extract all the possible consequences from any definition, and the logician … is often tempted, when he cannot extract a certain property from a definition, to deny that the concrete object to which the definition applies can possibly possess that property.”
The constructivist learning theory discusses negotiations over meanings in a manner very similar to that of a dialectical process between the individual mind and socially agreed conceptions (see e.g. Tobin 1993).
This remark can be compared with Polykarp Kusch’s notion in his Nobel lecture in 1955, where he remarks that: “Our early predecessors observed Nature as she displayed herself to them. As knowledge of the world increased, however, it was not sufficient to observe only the most apparent aspects of Nature to discover her more subtle properties; rather, it was necessary to interrogate Nature and often to compel Nature, by various devices, to yield an answer as to her functioning. It is precisely the role of the experimental physicist to arrange devices and procedures that will compel Nature to make a quantitative statement of her properties and behavior” (Kusch 1955).
Einstein (1970) writes in his Autobiographical notes in p. 7: “What, precisely, is “thinking”? When, at the reception of sense-impressions, memory-pictures emerge, this is not yet “thinking.” And when such pictures form series, each member of which calls forth another, this too is not yet “thinking”. When however, a certain picture turns up in many such series, then—precisely through such return—it becomes an ordering element for such series, in that it connects series which themselves are unconnected. Such an element becomes an instrument, concepts.”
This is related to Hadamard’s (1945) description of a mainly unconscious “incubation stage” and the preceding “preparation stage” of conscious attempts to “solve a problem”.
In his book The Process of Learning, Jerome Bruner (1960) hypothesises that “any subject can be taught effectively in some intellectually honest form to any child at any stage of development” (p. 33). He argues the hypothesis with the notion of a spiral curriculum: “A curriculum as it develops should revisit this basic idea repeatedly, building upon it until the student has grasped the full formal apparatus that goes with it” (p. 13). The perceptional approach to teaching physics can be viewed as a roadmap to a spiral curriculum that systematically takes into consideration the hypothesis of an intellectually honest form of teaching a subject at any level.
The notion of the permanence of gestalts owes to their origins in intuitive understanding. As is well known, understanding obtained by intuition or intuitively considered right and correct is a very stable mental construct. The results of studies concerning students’ conceptions have convincingly shown that such constructs are persistent and resistant to changes, and are very difficult to change through instruction (e.g., Chi et al. 1994). Intuitive common-sense conceptions are persistent because they adequately explain everyday observations of the physical world (see e.g. Posner et al. 1982).
Arons (1997) writes (p. 354) that “… scientific terms go through an evolutionary sequence of redefinition, sharpening, and refinement as one starts at a crude, initial, intuitive level, ….”
This formulation emphasises the exclusion of hypotheses, fictitious conceptual constructs, and theoretical ad hoc suggestions for interpretation without a perceptional foundation, often called “theories”.
Neglecting the initial empirical meanings of quantities as perceivable properties of entities and phenomena seems to be a general problem in physics teaching. For instance, force, energy and work are often introduced on the basis of theoretical considerations only. Force is regarded as a theoretical concept which cannot be learned until the Piaget level of formal operations is reached. According to Feynman et al. (1963, chap. 4.1), energy is a mathematical concept: “There is a law governing all natural phenomena … called the conservation of energy …. That is a most abstract idea, because it is a mathematical principle;… it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same…. However, there are formulas for calculating some numerical quantity, and when we add it all together it gives … always the same number. It is an abstract thing in that it does not tell us the… reasons for the various formulas.” In addition, the never-ending discussion about the nature of mass, force and energy is based largely on highly theoretical considerations without reference to the initial empirical meanings.
Note the double meaning of “theory” in the context of concept formation. Firstly, it refers generally to the theoretical nature of all concepts regardless of their hierarchical position. All concepts are “theory” as the opposite of “empiry”. Secondly, in its specific meaning, “theory” refers to a coherent conceptual structure formed by certain basic laws so extensive that a “theory” is understood to constitute a common explanatory basic model of a whole class of phenomena. For instance, Newtonian mechanics and Maxwellian electrodynamics are theories in this sense.
The basic form and direction of progress in the conceptualisation process as outlined here is very common and has its roots in 19th century conceptions of the structure of science. Similar conceptions are also recognisable in many more recent logical reconstructions of science (e.g. in logical empiricism). These roots are discussed in more detail by Koponen and Mäntylä (2006) in their study as well as in references therein.
This is one aspect of the first assumption of Sect. 2.1 and has often been expressed more or less explicitly in the literature. According to T. H. Huxley, “science is nothing but well organized layman reason”. Einstein has said that “scientific reasoning is nothing but more accurate natural thinking”. Referring to E. Kaila, R. Nevanlinna states that “scientific thinking is nothing but refined everyday thinking”.
It is often necessary to ignore the strict constructs of formal logic and analytical philosophy if such ideas as “induction”, “deduction” and “inference” are used for practical purposes, in the same sense as Arons (1997) is speaking of “inductive and deductive reasoning”. These expressions have their more casual meanings, and the fact that they have been targets of logical analyses does not invalidate or render useless their original casual meanings. This point has been very cogently discussed by Toulmin (1958/2003), who in fact sees strict logic rather as a dead weight and burden than as an advantage.
Nearly all researchers and thinkers who have paid attention to the process of knowledge generation and discovery of knowledge, recognise such a repeated cycle. Chang (2004), for example, describes a similar type of cycle, and Helmholtz’s conception of the progress of conceptualisation also includes such cyclical development (Jurkowitz 2002). The idea of the methodical cycle has also been applied in descriptions of the learning and teaching of physics, in a form closely related to that introduced here (see the references given by Koponen and Mäntylä 2006).
In mathematics, however, the so called complete induction is a logically binding method of generalising proof.
Nevanlinna discusses this process of reduction and idealisation of observations as the basis of concept formation in several articles (see e.g. Nevanlinna 1950).
This “miracle” of models fitting the reality has recently been discussed by several authors (cf. Morgan and Morrison 1999 and references therein), who have also recognised the sequential fitting between the models and experimental results. A discussion of such models appears in Koponen (2007) from the perspective of their use in teaching. Sensevy et al. (2008) is also a similarly oriented study.
Hadamard (1945) writes (p. 106) “Some mathematicians are ‘intuitive’ and others ‘logical’”, but later adds (p. 112) that “…every mental work and especially the work of discovery implies the cooperation of the unconscious … there is hardly any completely logical discovery. Some intervention of intuition … is necessary at least to initiate the logical work.” In a letter to Hadamard (1945) (Appendix II), Einstein writes: “the desire to arrive finally at logically connected concepts is the emotional basis of this rather vague play with the above-mentioned elements …. this combinatory play seems to be the essential feature in productive thought—before there is any connection with logical construction…”.
Hadamard (1945) (footnote 7 of Ch. VII) writes: “… almost every mathematician would be a logician according to his own judgment”, and gives an example of the hidden intuition (p. 113): “I should think this to be the case with Hermite, who certainly did not omit anything strictly essential in the results of his reflections, so that his methods were quite correct and rigorous, but without letting any trace remain of the way in which he had been led to them.”
This is intended as a physical metaphor referring to the formation of new particles from their constituents.
In the literature, the theory-ladenness of observations is often emphasised (Hanson 1958), whereas the empiry-ladenness of theory seems to be largely ignored.
Interestingly, Duhem also describes theory as a “living organism”, that is always open to further developments whose concepts are never final or complete, and which is always open to redefinitions and reorganisation (Duhem 1914/1954). In Duhem’s case, this is closely related to his “underdetermination” principle, which means that no concepts or laws can be verified in isolation, thus leading to the conclusion that theories are always beyond final justification or verification.
Tala (2009) has recently provided a very thorough discussion from the point of view of techno-science, which advocates a similar inseparability of technology and science. Although Tala’s starting point is somewhat different, the general picture parallels what is discussed here.
The word “object” is avoided; rather, entities are regarded as subjects of nature. Entities, material bodies or particles and immaterial fields “exist” in some position or area of space, at some distance from other entities. Phenomena are events or processes, ways in which entities behave or anything that happens to them. They take place at some instant in time or over some time interval before, after or simultaneously with other phenomena.
This scheme was designed for teaching purposes. While combining different areas of physics into a whole, it ties the contents of the courses to the historical development.
The unification development introduced here is in many respects similar to William Whewell’s conception of how science progresses through unification. According to Whewell (1847) the natural sciences show a unification development driven by the logic of induction typical of all natural sciences, but of physics in particular. Also in Whewell’s model different branches are united through discoveries of common explanatory bases and common methodology. This model is often referred as Whewell’s tributary river model.
That students propose senseless values for quantities as answers to problems is a common problem. One conventional problem in an entrance examination for studying physics at the University of Helsinki dealt with the shot put. The suggestions for the initial velocity asked varied from 3 mm/s to three times the velocity of sound. Obviously, the aspect of magnitude was not properly linked to the gestalt of velocity.
This characterisation of theory as a collection of models is common in many views of the structure of science. In the semantic view of theories, for example, the theory is considered a collection of different levels of models, the highest level of which is called the theory (Giere 1988).
ISO (1993): “Quantity is a property which can be identified as to its quality and measured as to its amount.” ISO (2008): “A quantity is a property of a substance or a phenomenon that can be measured or calculated from other measured quantities.” ISO (2009): “quantity: property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference.” The earliest one of these is most explicitly related to perceptional concept formation.
Niiniluoto (1984) speaks of “comparative concepts”.
Quantification is in the core of so-called operationalism, introduced by Nobel prize-winning physicist Percy Williams Bridgman. “We evidently know what we mean by length if we can tell what the length of any and every object is, and for the physicist nothing more is required. To find the length of an object, we have to perform certain physical operations. The concept of length is therefore fixed when the operations by which length is measured are fixed: that is, the concept of length involves as much as and nothing more than the set of operations by which length is determined. In general, we mean by any concept nothing more than a set of operations; the concept is synonymous with the corresponding set of operations.” (Bridgman 1927).
This notion of empirical core meanings of quantities solves the problematic statement of operationalism that every experiment defines a different concept.
The idea of quantitative measurements as the basis of theory formation was the dominant view of nineteenth century continental empiricism. For example, according to Johann Christian Poggendorf, one of the champions of German empiricism, the advantage lay with the theory that was then developed regarding “measure and number, the true foundation of exact scientific research” (Jungnickel and McCormmach 1986). This conception of physics became dominant in the latter half of nineteenth century continental physics, which aimed to produce through “measure and number” the foundations of physics.
Bradley (1975) writes “… with good intentions, we have said to Robert: What matters is the atom, or the molecule or the equation. Poor Robert … resembles a child aged six given logarithms to multiply three by two ….”
Arons (1997) presents a “list of processes” (Sec I: 13.2) in excellent agreement with the perceptional approach. In the terminology of this article these “processes” can be characterised as procedural instructions. Most of them derive naturally from the processual dynamics of the learning process as suggested by the “practical teaching philosophy” presented. For points of agreement with and differences from Arons’ views the book review, Kurki-Suonio (1998) can be consulted.
Mach (1866) writes “It is a prevalent but wrong opinion that children are not able to form precise concepts and come to the right conclusions. The child is often more sensible than the teacher. The child is very well able to comprehend, if one does not offer too much new at a time, but properly connects the new to the old.”
The phenomenon of “rotation” was discussed as follows: Where in our surroundings might rotation occur? Long silence—a shy suggestion: “merry-go-round”—another silence—“spinning top”—silence—pointing to the window: “Does the thing on top of that tower rotate?” The participants were advanced physics students. Diagnosis: all preceding studies of physics, in the school as well as in the university, had no connection to the real world of phenomena. To find empirical meanings, one had to return to one’s memories of childhood.
The situations suggested for analysis were drawn from children’s everyday environment, such as “my morning from bed to departure for school”, “garden”, “sauna”, “playground” or “a normal non-science classroom”. One set was taken from titles of the primary school science curriculum and textbooks: “safely on my way to school”, “animal species”, “children and health”, and “appropriate clothing”.
The linguistic use of terms reflects the ontological position of their referents and the modes of causal thinking, as Lakoff and Johnson (1980), for instance, have discussed at length. Taking care that terms are used in linguistically proper form helps students to form an appropriate understanding of the referents of the terms, while incorrect use may cause unnecessary problems.
The suggested category of “models” was an intentional trap intended to help the participants to realise that, in fact, all concepts are models (cf. 4.2).
R. Kurki-Suonio (1999) reports about a course on perceptional empiry held as a part of the first complementary education course for in-service physics teachers in 1996–1997 with 150 participants: “After the course the participants were asked to do a personal self-evaluation of their progress in different respects, for instance in the planning of empirical wholes and in planning of single experiments. This yielded a large amount of surprisingly positive feedback. In a number of self-evaluations it was told that the participants felt that,
– they were no more tied to the textbook as they had been,
– they have learned to analyse and organize there teaching and got rid of ‘separate’ experiments,
– they have got new ideas and courage to plan own experiments on the basis of the conceptual aims,
– they have learned a lot of new experiments suitable for school,
– they have learned to use the “old experiments” in a purposeful way,
– they have learned to use the equipment of their own schools in new ways and,
– their way of teaching chemistry and mathematics has also changed.
It was told that the complementary education program “had developed and widened the knowledge and understanding of physics enormously”, “gave confidence in adopting new working methods” and “gave a completely new view on the teaching.””
This term was adopted to indicate that these theses were written within the programme of physics teacher education of the Department of Physics, while the theses in “didactics of physics” are done in the Department of Education.
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Acknowledgments
Many people have encouraged and supported the development of these ideas and their applications. First of all, without the continual confidence and co-operation of my late wife, Riitta, nothing here would have been possible. The contributions of Professor Maija Ahtee, Dr Ari Hämäläinen, Professor Heimo Saarikko and Professor Jari Lavonen have had an essential role in the work reported here. Of course, I can never forget the encouragement of the students in my courses. Finally, I thank Drs Hayo Siemsen, Karl-Hayo Siemsen, Ismo Koponen and Kalle Juuti for their help and for their insistent persuasion to write the present study.
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Kurki-Suonio, K. Principles Supporting the Perceptional Teaching of Physics: A “Practical Teaching Philosophy”. Sci & Educ 20, 211–243 (2011). https://doi.org/10.1007/s11191-010-9288-1
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DOI: https://doi.org/10.1007/s11191-010-9288-1