9. Growth, in Biology and in Education

9 Growth, in Biology and in Education RALPH W. LEWIS The purpose of this paper is to examine briefly the bodies of knowledge in biology and in education which are concerned with the phenomena generally known as "growth." The kinds of facts and the few laws and theories present in these segments of biology and education will be discussed. Attention will be given to the internal structure of the laws and theories that give or ganization within these bodies of knowledge and to some of the limitations of these laws and theories. Predictions made from the laws and theories will be scrutinized as a means of determining the worth of the concepts. >II: With the discussion on growth as a background, plus a few statements about other concepts that have been applied to the detriment of education, a set of criteria will be presented by which one can decide if concepts are worthy of being used as a basis for making decisions about human affairs.

1. Biological Growth Biological growth consists basically of increase in the amount of protoplasm usually accompanied by differentiation of the protoplasm. Because of the great complexity of the problem, biol• I use the word "concept" loosely in this paper to mean idea, law, or theory. 181 182 Scientism and Values ogists have conceptually and experimentally separated the two aspects of growth, increase and differentiation, even though in the growth of organisms they are not separate activities. Since there is no general theory of growth that deals with growth in toto by subsuming the two huge categories of facts concerning the two aspects of growth, one must examine each separately. Even a quick look at the quantitative aspects of growth in biological writings soon leads one to the Verhulst-Pearl law of growth (19) or some modification of this law. This law says that under the right conditions an individual or a population starting anew in a favorable environment will grow through the following phases (9): 1. Lag phase: growth rate null.

2. Acceleration phase: growth rate increases. 3. Exponential phase: growth rate constant. 4. Retardation phase: growth rate decreases. 5. Stationary phase: growth rate null. 6. Decline phas,e: growth rate negative. The usual method of determining quantitative growth is to measure the amount of protoplasm present at intervals of time. Measurement of the amount of protoplasm is never a direct process. Wet weight, dry weight, number of cells, linear measure ment, and the like are assumed to give a figure which is directly proportional to the amount of protoplasm in the organism. When the growth measurements are plotted against time, the growth curve will be the so-called S-shaped curve and will show the phases noted above. The curve is not really S-shaped. The lag phase starts parallel to the horizontal time coordinate. During the ac celeration phase the growth curve bends upward along the growth measurement coordinate until it reaches the exponential phase, which is represented by nearly a straight line sloping at an angle dependent upon growth rate. This maximum rate of growth begins to slow down as the retardation phase sets in. Gradually growth slows down until decline balances growth and the sta tionary phase is reached, the curve in this phase being again horizontal. Decline follows, and growth rate is negative.

This law of growth, despite its narrow limitations, has been very Growth}in Biology and, in Education 183 useful in biology. It forms the basis for the development of assay methods for vitamins and other biologically important substances; it permits comparisons of different diets; it forms the basis for recognizing and analyzing variability in populations; it is, useful in exploring the problem of enzymatic adaptation; and other problems such as the exploration of factors in. the environment that affect growth. One often finds that growth fails to follow the expected S curve. Deviations in the curve suggest that unexpected factors are at work. These factors may be in the external or in the internal environment. The work of Braun (2) describes a situation in which an internal genetic factor and external nutritional factors are at work simultaneously in modifying the typical growth curve.

Knowledge of the law of growth, plus much other knowledge, often makes it possible for scientists to explain apparent deviations from the law, and thus the law of growth forms the basis for advances in biological knowledge. The growth of populations, or of individuals in nature seldom follows the law of growth in detail. The smooth curves are based chiefly upon laboratory data. Varying factors in a natural environ ment, such as temperature, rainfall, food supply, disease, usually disturb the even growth curve that is so often found under labo ratory conditions. Inherent factors will cause pronounced deviations from the law of growth in many organisms, whether growing in nature or in the laboratory. In mammals the inherent characteristic of carrying the young internally through early stages of growth greatly affects the growth curve of each individual. The onset of activity in some endocrine glands may also affect growth to a considerable extent.

Both of these effects are pronounced in human growth. In this brief look at the law of growth we have already noted some of the applications and limitations of the concept. Even when we consider its application to quantitative growth alone, the law has stringent limitations. As a descriptive tool the law serves fairly well under carefully controlled conditions, but even here difficulties exist. A statement by Sholl (17) points out some of these difficulties when considering the growth of an animal.

184 Scientism and Values To illustrate this discussion it is convenient to consider the array of points resulting from plotting the weight of an organism against its age; the principles will apply to any other measure of size while the extremely difficult problem of shape (Medawar, 1945) will not be considered. In general, this array of points will lie scattered about some line which is a picture of the general trend of growth of the animal, and our first problem is the description of this line. Such a line can give no information about fine details, but is rather like the line depicting the track of a railway on a continental map; the general direction of the railway is shown, but small variations do not appear. There was a time when many workers thought it possible to find the fonnulation of such a line by a priori methods, by thinking of chemi cal metabolism, surface absorption, and similar notions. There have been numerous examples of this kind, and perhaps the best known is Robertson's autocatalytic theory and the resulting curve. We are now more fully aware of our inability to specify the many factors that may be responsible for growth in terms of a few parameters, let alone finding a mathematical statement about their relationships; in any case, such a relationship would be of such a complexity that it would not be expressible in terms of simple mathematical functions. Further it must be remembered that if any such function were fitted to the data, no demonstration of closeness of fit can ever prove the curve to be that one which is in any sense the unique "true" curve.

At the other methodological extreme we should be tempted to use the purely mathematical approach and use a polynomial of such a degree that the fit was adequate. This would be statistically highly satisfactory, but it would be very difficult to interpret the resulting curve and to assign a biological interpretation to the parameters in volved. Consequently, we must consider a more empirical approach, and the two criteria for choosing a curve would seem to be that it must provide a good statistical fit and also have a reasonably simple func tional expression involving the number of interpretable parameters. . . . Naturally, we shall draw on our biological experience where possible and choose curves whose parameters have a biological sig nificance . . . . As is often the case in the application of mathematics to biology, we see that we are well advised to combine our intuitive approach with suitable mathematical methods ....

Growth}in Biology and in Education 185 Because of the large number of significant variables that can affect growth, the growth law has rather limited predictive powers. For example, I have determined the growth of a fungus on a simple medium under carefully controlled conditions. I have determined growth curves when different amino acids or vitamins were included in the medium. From these data I would like to predict what will happen when I use other vitamins or amino acids singly or in combinations. But from the growth data which I have accumulated I cannot predict new situations. Of course, I can say that if growth occurs at all, its plot will be an S curve. Also, if I have controlled the amount of energy food, I can usually predict the level of the stationary phase; but that is all. As a predictive tool, the growth law has not yet proved very fertile. Von Bertalanffy (21) has related, in many animal species, the metabolic rate of an organism to the type of growth curve pro duced by the organism. He says that there are three classes of animals as determined by plotting their growth curves and that the class to which an animal belongs can be predicted from a determination of the "metabolic type" of the organism. Thus, this work, "aimed at establishing connections between metabolism arid growth," has greatly extended the importance of growth studies and, the author says, forms the basis for a gener.al growth theory.

Studies on the relative quantitative growth of different parts of a single organism, called "allometric growth," have produced a law of fairly wide applicability among both animals and plants. This law can be stated simply by saying that if the logarithm of the measurement of one organ is, plotted against the logarithm of the measurement of another organ of the same animal, and if this is repeated several times during growth, the points will fall on a straight line. Bonner (I) considers this law of allometric growth to be descriptive only and without the capacity to reveal hidden biological secrets. Because the law of allometric growth compares two organs of one organism, it can be expected to be free from many fluctua tions due to internal or external environmental factors; thus, in the future it may have great value when eventually it is related 186 Scientism and Values by new concepts to other biological laws. At present the limita tions of the law are apparent in the facts it interrelates, and the few predictions it permits.

The study of differentiation has produced all. enormous collec tion of facts. These facts deal with changes that occur in organisms as they grow and mature. Most of the facts have come from ob servations of gross and microscopic structures as they change during the development of an adult from a zygote. The observa tions have revealed structures and activities that are so complex that no theory has yet been produced which is even partially ade quate in providing a general explanatory system with fruitful predictive powers. Several broad and important generalizations arrived at by simple enumeration are present, but there is as yet no general theory comparable to the theory of evolution or the gene theory which are so fruitful in other areas of biology. 2. Educational Growth Educational growth is a much confused concept. A goodly portion of the confusion arises from the willingness of many in dividuals to accept weak, tentative hypotheses as truth or as a good approximation of truth. Additional confusion arises from an extrapolation (sometimes willfully, but more often unwittingly) of a small understanding of biological growth into the area of educational growth. Some basis for analogy between the two exists, but it remains analogy, and good scientists would not use knowledge of the biological growth of babies as an argument to support an idea concerning the educational growth of children.

Examples of this kind of argument are noted below under Resist ance to Displacement and Convergence and under Developmental Theory in Education. The term "growth" as used in its fullest sense in the science of education subsumes both the biological growth of human beings and all other aspects of human growth such as intellectual, artistic, personality, social, moral, emotional, and perceptual growth (3, 8, 12). Physical growth in humans is determined by the same kinds of methods that can be used on almost any higher Growth) in Biology and in Education 187 animal. In addition to height and weight measurements, other criteria such as strength of grip, carpal development as determined from X-ray photographs, and dental development are often used for determining physical growth. Growth of mental attributes is measured by a number of different kinds of psychological tests and by verbal descriptions.

Some of the tests used and the attributes they are presumed to measure are: Kuhlmann-Binet, mental age; Gates and Stanford, reading age; Stanford, educational age; Doll, social age; Furfey and Sullivan, developmental age. The scores on these tests and the biological measurements are not used directly in the studies considered below, but are con.. verted to "growth ages." Norms have been established for each test and for each biological characteristic by determining the aver .. age of representative groups of children of different chronological ages for each of the biological and mental attributes. The meas.. urement or score of the testee is compared to the set of norms, and his "growth age" is that of the norm equaled by his measure ment or score. Thus, if a seven-year-old receives, a score on a Kuhl mann-Binet test equal to the norm for nine-year-olds, he will be given a mental age rating of nine. If his height measurement equals the norm for eight-year-olds, his height age will be eight.

Collectively mental age, height age, weight, reading age, etc., are called growth ages. Although most of the following discussion will be concerned with growth ages for both biological and mental attributes, a word about intelligence quotient, I.Q., will explain the virtual omission of the term. An I.Q. score is the mental age, as deter .. mined above, divided by the testee's chronological age multiplied by one hundred. This kind of score does not permit a ready com parison with the age units as determined for the other attributes and so is not used for studies of "total" growth discussed below. The most comprehensive and the most scientific studies on the growth of the "whole" child are those of Olson (12). He and his colleagues have determined growth ages of many children, usually from age five to age twelve. 'The growth ages for each child are determined several times during the seven-year span. The pub188 Scientism and Values lished data resulting from the tests and measurements are usually presented on graphs with the chronological age on the horizontal axis and the growth age on the vertical axis. The height ages for a child are plotted above the corresponding chronological ages, and the points. are joined successively by straight lines. All the other growth ages are plotted in like manner on the same graph.

Since all the attributes usually increase in time, the graph of a child's growth consists of a series of lines ascending across the graph to the right. Olson and Hughes (15) thought "it would be of interest in testing hypotheses of children as wholes [sic!] to study the center of gravity of growth systems and the relation of separate aspects of growth to the whole." In order to do this they plotted an "organ ismic age" curve for each child so studied. The organismic age for anyone chronological age was computed by averaging all the growth ages for that chronological age. After an organismic age was computed for each chronological age, the points were plotted and connected in sequence, thus producing the organismic age curve. After studying many children by means of growth age curves, Olson has arrived at some conclusions and definitions, a theory of growth, and a number of applications of his views to the prob lems of education. In the remainder of this essay I shall describe and criticize several of these ideas. I am omitting for the sake of brevity any critical examination of the raw "facts," the bases upon which they rest, and their statistical manipulation. In the present discussion I shall assume that growth curves are a "true"

representation of the attribute for which they stand. Pattern. A pattern of growth refers to the relationship of various measured characteristics within an individual at a given point in time, or to a succession of changes with time. Thus a child who at the age ten has a high mental age, a high reading age, and a somewhat lower height age, weight age, carpal age, and dental age, differs from one who has high physical ages and relatively low mental and achievement ages.

Growth) in Biology and in Education 189 One might also speak of a given child's pattern of growth in reading as showing a period of plateau from ages six to nine with a rapid increase or spurt in the period from ages nine to twelve.(ll) A study of the patterns of growth of large numbers of children has led Olson (12, 16) to rather definite ideas about the growth of children. Some of these ideas are "unfolding design," "going togetherness," "variation," "stability of the center of gravity," "resistance to displacement," "convergence," and "deprivation." Unfolding Design. Everyday experience supplies us with the in formation that, as children grow physically, some kind of "un folding" of mental attributes occurs and that this unfolding roughly parallels physical development. No one doubts this. Nor does anyone doubt that children are as different in mental at tributes as they are in physical attributes. But as a person goes from an examination of biological gro,vth to an examination of early and late mental development of children, he will recognize the stringent limitations of "unfolding design" as a scientific con cept.

Olson (12) states "... that a child has a design for growing, that optimum nurture fulfills this design." What does he mean by "design"? Does he mean that "design" and "optimum nurture" are singular and fixed for a developing child? In this quotation it seems that he does consider them singular and fixed, yet in his discussions of nature and nurture he seems not to take such a limited view of the potentialities of human development. Once the data are in and the growth curves are plotted, a single, limited design for a child certainly is present on the graph. Con sider, however, a child of five. Is there a single design to be followed by this child in his grovvth? As a biologist I cannot con ceive of the design as fixed except within very wide and, at present, very indefinite limits. Several years ago I became aware that the biological concept of optimum nutrition was of little use. Innumerable combinations of nutrients produce maximum growth in weight, while some of these combinations and perhaps still others unidentified produce optimum qualitative character190 Scientism and Values istics. The same can be said for other environmental factors. Thus, at the biological level the "design" present at the start of growth has before it in time a huge number of possible designs. There is no such thing as an optimum nurture. Dozens, possibly thousands, of different combinations of environmental factors may supply the conditions for achieving a single kind of optimum or a number of different optima simultaneously. Many kinds of optima are known, and probably many are yet to be discovered. Therefore, for an individual of any species, I hesitate to speak of "optimum nurture" and of "design" for growth without a careful qualific.a tion of "optimum" and of "nurture."

Since mental growth stems from, but greatly supersedes, the complexities of biological growth, the term "design" should be discarded in talking of the growth of children, especially when presented against a background of growth curves. So presented, it may be even more readily misused than were I.Q. scores in their day (18, 20). Som.e term which conveys the idea of the plural potentialities of children should be coined before the textbooks of education take up such statements as the following: "Every child progresses toward a specific maximum." "Each child is ap parently born with potentialities for growing according to a speci fic design" (8). The "design" as seen in growth graphs is ex post facto and should never be taken to represent what was fixed there before the design was recorded. Going Togetherness) Variation) Center of Gravity of Growth) and Readiness. The literature at hand (6, 7, 8, 12, 13, 16) contains graphs of sets of growth age curves for a total of twenty children.

Each child's record is a pattern unto himself. In one paper (16) four graphs are chosen to illustrate a "going togetherness" of all growth attributes in each child. These four graphs do illustrate this, and the author says that based upon other graphs of fifty-six boys and girls (which he does not show) "... one secures a most dramatic picture of the generalization that growth tends towards unified patterns." But among the twenty growth graphs shown in the six publica tions, only eleven show "trends toward unified patterns"; nine Growth) in Biology and in Education 191 do not. From these data, therefore, I find it difficult to see that the ideas of "going togetherness" and "variations" are much refined beyond the common-sense understanding of these that an experienced teacher possesses without any special study of growth. Hughes (5) has examined variability among and within a hun dred boys, ages four to twelve. Instead of plotting all growth ages for one boy on a graph, he has used a single growth age, such as height age, on the vertical axis and the chronological age on the horizontal. The curves for the one hundred boys are plotted on one graph. Ten graphs for ten biological and mental attributes are thus presented. Concerning these graphs he says: "The evi dence is clear in showing that there are great differences in the distribution of measures (ordinate values) when the chronological age is held constant. In addition it should be noted that the varia tion of age (abscissa values) is almost equally great when the value of the measure is constant."

Some idea of the differences in distribution is secured by ex amining the height age and the mental age curves. At height age ten about ninety percent of the curves spread over a horizontal distance of three chronological years. At mental age ten about ninety percent of the curves spread over a horizontal distance of three and a half chronological years. The other sets of curves are quite similar in spread to the mental age curves. Hughes' paper develops a new view of organismic growth. Instead of being satisfied with the organismic growth curve of an individual as the measure of the "center of gravity" of growth, he plots a narrow band and wider band over the organismic curve by specified mathematical techniques. The organismic curve is approximately at the center of these two bands. The inner band is about half the width of the wider band. Concerning these graphs Hughes says: The central dense band has been labeled the organismic area and has been presented to suggest that for management and educational pur poses the child is generally "mature" within the limits of the band on an ordinate and generally "ready" to fit a level on any abscissa. Also 192 Scientism and Values the organismic area is shown to illustrate more clearly the fact that both maturity and readiness are distributed as necessary consequences of variation within the individual rather than narrowly fixed as the organismic age line would imply.

The peripheral lighter band has been added to the pattern to insure recognition of another fact of within variability [sid]; namely, that for about 20 to 25 percent of growth items, maturity and readiness are, indeed, very broadly distributed. Within some individual graphs and from graph to graph, there is in the organismic area a variation in "readiness" from one half to three chronological years and a variation in "maturity" of about the same number of growth years. For the peripheral band, that is, for about twenty percent of the growth items, readiness and maturity extend twice as far-from one to six chronological years. Most teachers will agree that Hughes' treatment of "readiness" and "maturity" expresses these concepts in a manner much closer to reality as determined by observations of growing children. The concepts in this form appear to agree with Olson's (12) observa tion that "one of the striking abilities of the human organism is the power to take on new modifications throughout its lifetime."

With these views of variability in mind, one wonders if possibly "readiness" in most students may not be more a matter of being ready for persistent work at studies rather than being some innate developmental factor which cannot be overcome by insistence upon reasonable standards of accomplishment. Resistance to Displacement and Convergence. Under the head ing "Resistance to Displacement" Olson (12) says: A useful principle growing out of hundreds of studies of growth is that if an experimental factor capable of producing a difference in growth is introduced, either artificially or naturally, a child tends to resume his own normal rate of growth as soon as the factor disappears or is removed. To support this view Olson cites a study on head sizes of pre mature and mature infants. Is this kind of extrapolation, which Growth) in Biology and in Education 193 I have found often in the literature of child development, sensible when considering the mental growth of children?

The resumption of the normal rate of growth after "depriva tion" or "extra stimulation" is "convergence." Olson cites ex amples of convergence from endocrine therapy and from at~ tempts to stimulate progress in arithmetic and reading. Progress is made during "treatment," but when special attention is stopped, the children resume their previous pattern. Millard (6) presents a striking example of convergence. A girl was given special tutoring in spelling and made phenomenal gains. After the tutoring stopped, she drifted back to the level of her ascending spelling curve. The convergence notion is evidently not widely held. Thomp son (20) cites considerable evidence which appears not to agree. Olson (12) goes to considerable pains to refute the work which presumably showed that special tutoring helped slow readers to become better readers. He says: "Many studies (on remedial reading) of the foregoing types have been reported, but they fail to randomize or control persistence and industry." Herein lie two of the most crucial aspects in the development of mental at tributes. Can they be "randomized"? Are they not often deter mined by the complexities of the teacher-pupil relationship to such an extent that they defy measurement?' Those who have been taught by at least one teacher with the power to engender persist ence and industry acquire the knowledge that displacement is real and that convergence can be overcome.

Developmental Theory in Education. Although I disagree strongly with many of Olson's views on education, I favor his con.. tinuous application to studies of growth through the last two decades. I also favor his recent attempt at presentation of .a de velopmental theory (14) in such a complex field of knowledge. Unfortunately, I do not understand his. type of theory, and I question if it is really a theory. The pattern presented by Werk meister (22) as exemplifying physical theory is not present. Nor is the pattern-facts A, B; deduction 1; fact C; deduction 2; fact D; deduction 3-such as is found in the theory of evolution (4) present.

194 Scientism and Values This absence of a clear pattern may be a sign of developments to follow. Confusion at the beginning seems to be a normal step in the growth of theories. For examples of this see the Harvard Case Histories in Experimental Science) especially the one by Nash (10) on The Atomic-Molecular Theory in which Dalton's early difficulties are discussed. Olson (14) first defines growth, maturation, and development. He then presents five "developmental equations" as follows: 1. Maturation X Nurture = Development He says that equation I is too simple if thought of only as a factor system. 2. Maturation X Zero nurture = Zero achievement 3. Variable maturation X Constant supply nurture = Variable achievement 4. Constant maturation X Variable supply nurture = Variable achievement Equations 1 through 4 are clearly too simple an answer, for there appears to be evidence for "differential uptake." This results in an enhancement effect, because the differentials, once established in achievement, in turn so modify the organism as to make it more selective, permitting more rapid uptake in some and less rapid in others. In effect, then, the constant supply is surely a myth, since children seek a larger or smaller supply from what is available, as in the following equation: 5. Variable maturation X Differential uptake of nurture = En hanced variable achievement Next Olson presents "The Nature of the Evidence." He says: "There is much evidence to support the general theory back of the writing of such equations as those preceding." What can he mean by this? I had presumed that the equations were possibly the postulates of the theory. Does the theory lie behind these, or is the evidence what lies behind them?

Growth} in Biology and' in Education 195 He next describes growth ages briefly and then presents a graph in which the organismic .age curves of three groups of boys are compared to their reading curves. The boys were s,eparated into three groups on the basis of their reading scores at age eleven: fast, intermediate, and slow readers. The organismic age curve and the reading age curve of the fast readers are above the other curves from age six to eleven. Except for ages seven to eight the two curves for the intermediate readers are between the curves for slow readers and fast readers. Both curves for the slow readers are below the others except at age six, where the slow readers are slightly better ,at reading than the intermediate. On the basis of the graph Olson argues in support of equation 5 above. From this he moves to a model which consists of three approxi mately parallel lines extending diagonally across a growth age chronological age plot. The curves represent rapid, average, and slow growth "according to the equation Maturation X Nur ture = Development." Concerning this model Olson says: We can now set up a series of concepts involving known facts sur rounding the model. These are of varying degrees of generalization, and each should be preceded by the qualification "other things being equal." The model is based on the assumption that the growth repre sented by the curves represents a composite according to the equation Maturation X Nurture = Development. Viewed alone it appears as a relatively static model with much stability and continuity. Injected into a social field, however, the children represented become dynamic in the sense of relationship to other individuals and to meeting the requirements of each situation.

What general theory can be built around the model in the illustra tion? Principles of Human Development Concepts that will stand the test of universality, of experiment, and of prediction are hard to come by in afield governed by multiple causation. When stated, such concepts are limited in the sense that other postulates may in part account for the phenomenon. There is always something of an indeterminant character when variable indi viduals experience variable nurture.

196 Scientism and Values The following postulate comes close to having generality: "For all achievements which increase with chronological age, the rapidly growing child will yield the achievement earlier, and the slowly growing child will achieve the status later than the average child of a given age." From such a postulate one can predict in advance the individual differences that will exist, the factors that must be observed in an adequate experimental design, and the constant errors which must be allowed for or adjusted. We can predict in advance the results of many types of experiment. With such a postulate a person can predict, as an average trend at least, many of the types, of data that can be secured in a classroom group or even in physiological experiments. The basic evidence needed for the predictions is a fairly accurate account of age change. For example, knowing that emotional out bursts decrease in number and severity with age, we can predict that a child showing such outbursts will have many characteristics of the slowly gro'wing child. Some of the objective findings on associations with the model furnish a basis for more general theory.

Associations with the Model Here are some operational associations and deductions from the model. It should be noted that the effects are not only in the model as constructed, but also in the matrix of all the associated factors that go into the loading of the model. The differ,ences shown have important associations with socioeconomic status, social acceptability, responsibility, levels of interests, reaction to frustration, age of accom plishment of developmental tasks, and many valued traits of character and personality. The differences also run in families and are remark ably resistant to planned change, although reflecting changes in design over the years. More specifically, A [the top curve] as contrasted with C [the bottom curve] will be higher in social age, will be advanced in interests, and will be superior in social status in the group. C, contrasted with A, will have more behavior problems, whether checked by self, teacher, parent, or associates. Child A as contrasted with Child C will be characterized by more active, seeking behavior in general, including motivation for achievement. His appetite and interest in food will be greater, although calories per unit of body weight will be less in accord with the age trend. .

Growth} in Biology and in Education 197 The associates of A will be more like A than they are like C, and similarly, the associates of C will be more like C than like A. The rationalization of the association may be in terms of social status, in~ terest, values, levels of development, or comparable skills of achieving or performing. Some examples of the significance of the associations for other systematic approaches can be illustrated. The headings of the sections. that follow are: The Model and Psychoanalytic Theory, The Model and Frustration-Aggression Theory, The Model and Theories of Intelligence, Reconciliation of Explanatory Theories, Individual Predictions. versus Explana tory Principles, The Task of Education, and Seeking, Self-Selec tion, and Pacing. What I find in Olson's theory is not what I understand as theory in science, but rather a number of generalizations by simple enu meration, some tentative hypotheses, some vague ideas, and some discussions on related topics,. Some of the generalizations seem to me to be those that the percipient and thoughtful teacher would arrive at after two or three years of teaching.

Nowhere is my study of growth age patterns or of this theory do I find a good discussion of the large middle group of average students. The slow and the fast can be recognized, but the only mention of the middle group is the paper by Hughes (5). On the basis of understanding derived from growth. theory and from other "concepts of values and directions," Olson makes many recommendations about pedagogy. One of these is that "absolute standards" are not good. Possibly this is a good decision when considering the children at the high and low levels, but what about the large group in the center? Were not the so-called absolute standards arrived at by the te.achers who had had long experience with children? Are not the so-called absolute standards the standards that were found to be achievable by this large central group of children? Seeking, self-selection, and pacing are also recommended by Olson on the basis of his theory of growth. These recommenda tions are made on the ground that "The idea that there exists a 198 Scientism and Values 'wisdom of the body' that enables children to make wise choices in matters educational has led to direct demonstrations and a whole theory of curriculum and method in education." The paper (23) cited in Olson's book as a demonstration of the working of this idea showed the self-selection group to be a little better in a few attributes than the group taught in the traditional manner.

The differences were not so great that I would be convinced until I saw the results of many more experiments. In support of his views on seeking and self-selection Olson (14) resorts once to a biological analogy, twice to infant growth, and once to the activities of preschool children. Are these a sound basis for making decisions about the management of schools?' Why does he not present growth age curves which would permit me to comp.are children schooled in a traditional way with those schooled under the "wisdom of the body" idea? Ample evidence of this sort would do much to convert the "wisdom of the body" idea from a weak analogy with a biological concept into an educa tional hypothesis. Olson says that in order to be sure the seeking activity of the student is satisfied to the full, the teacher must be sure to provide the materials at the right time. This activity of the teacher is called pacing. Pacing also "refers to the attitude which expects from the child only that which he can yield at his stage of maturity."

Some students of child development appear not to be impressed by what they have seen of the permissive treatment of children in schools which presumably gains support from the above ideas. Their views contrast strongly with the ideas of "wisdom of the body" and of seeking and pacing. Breckenridge and Vincent (3) say: It is in order to build a secure sense of being needed and useful that children should learn to work. Our recent emphasis upon pro tecting children from child labor, our urgent planning to fill chil dren's time with happiness and play, our progressive education em phasis upon making learning quick and easy through proje,cts and Growth) in Biology and in Education 199 easily motivated activities-all this has resulted in depriving children of the opportunity to learn to work for the sheer sake of fulfilling necessary obligations and responsibilities. 3. Criteria for the Application of Scientific Concepts to Humans The headlong rush to apply new facts and new concepts in the field of education has brought disrepute to professional educa tion in the eyes of most scholars and in the eyes of many· citizens.

During the last few decades we have seen, for example, the theory of identical elements and a strongly narrowed concept of utility used as the bases for discarding the classics, foreign language, mathematics, and science from the school curricula and from the curriculum of individual students. We have seen the loose and unstudied concept of life adjustment used as a basis for inserting trivia into the regular school hours. Possibly the concept of de velopment is destined to be used as a basis for the support of more trivia. I hope not, because it may develop into a con cept of real worth if treated with scholarly rigor, criticism, and imagination. We have seen the concept of interest in relation to learning perverted into a concept of whim and caprice to such an extent that lack of interest is constantly used by students as a "reason" for not studying. We have seen a concept of integration of knowl edge used as the basis for disrupting pedagogical and learning ef ficiency. This has been done by creating core courses, activity programs, practical courses, community studies, and the like in lieu of the study of traditional bodies of knowledge. The tradi tional bodies of knowledge exist because there are inherent in them patterns of multiple reasoned relationships that give the best order and greatest simplicity so far achieved. They exist also because they are the most economical way of learning something of the real breadth and depth of human experience. To disrupt this order at the teaching level is to take from the teacher variety, order, and simplicity in presentation; and to take from the stu dent a wealth of opportunities to explore and rediscover the rea200 Scientism and Values soned pathways which were the great achievements of the master minds.

Since man, even though mistaken in his views, will always strive to apply concepts to better the lot of man, how can he avoid the misapplication of concepts? In those areas whose concepts de rive from science, this question can be answered in part. Before a concept is applied we should know well the internal struc ture of the concept and the facts it interrelates·. The concept should have withstood the buffetings of scholarly criticism by virtue of its intellectual integrity. And the concept should have been explored long enough and thoroughly enough so that we are aware of several of its major limitations. If the concept is to be taught to prospective teachers who will be expected to apply it, . then the limitations should be well enough worked out so they can be taught with efficiency and clarity. These criteria for the application of concepts to humans are severe for persons who seem to prefer immediate utility to understanding; yet, in the long run, the criteria will contribute much to both utility and under standing.

NOTES 1. J. T. Bonner, Morphogenesis, An Essay on Development (Princeton: Princeton University Press, 1952). 2. W. Braun, "Studies on Population Changes in Bacteria and Their Relation to Some General Biological Problems," American Naturalist, LXXXVI (1952), 355-371. 3. M. E. Breckenridge, and E. L. Vincent, Child Development, Physical and Psychological Growth Through the School Years (3rd ed.; Phila dephia: W. B. Saunders Company, 1955). 4. G. de Beer, "The Darwin-Wallace Centenary," Endeavour, XVII (1958), 61-76. 5. B. O. Hughes, "Variability Among and Within Individuals in Relation to Education," Merrill-Palmer Quarterly, I (1957), 167-187. 6. W. A. Ketcham, "Growth Patterns for Gifted Chidren," Merrill-Palmer Quarterly, I (1957), 188-197. 7. E. Mechem, "Affectivity and Growth in Children," Child Development, XIV (1943), 91-115. 8. C. V. Millard, Child Growth and Development (Boston: D. C. Heath and Company, 1951).

Growth) in Biology and in Education 201 9. J. Monod, "The Growth of Bacterial Cultures," Annual Review of Microbiology~ III (1949), 371-394. 10. L. K. Nash, "The Atomic-Molecular Theory," Case 4, Harvard Case Histories in Experimental Science (Cambridge: Harvard University Press, 1950). II. W. C. Olson, "l\1eaning of Growth," in C. V. Millard, ed., Child Growth in an Era of Conflict, Fifteenth Yearbook, Michigan Education Associa tion and Department of Elementary School Principals (Lansing, 1944). 12. W. C. Olson, Child Development (Boston: D. C. Heath and Company, 1949). 13. W. C. Olson, "Achievement as Development," International Review of Education~ III (1957), 135-142. 14. W. C. Olson, "Developmental Theory in Education," in D. B. Harris, ed., The Concept of Development (Minneapolis: University of Min nesota Press, 1957). 15. W. C. Olson, and B. O. Hughes, "The Concept of Organismic Age,"

Journal of Educational Research~ XXXV (1942), 525-527. 16. W. C. Olson, and B. O. Hughes, "Growth of the Child as a Whole," in R. G. Barker, J. S. Kounin, and H. F. Wright, Child Behavior and Development (New York: McGraw-Hill Book Company, 1943). 17. D. A. Sholl, "Regularities in Growth Curves, Including Rhythms and Allometry," in E. J. Boell, ed., Dynamics of Growth Processes~ Soc. for the Study of Development and Growth (Princeton: Princeton University Press, 1954). 18. J. C. Sullivan, "Effect of Teacher Pressure," in C. V. Millard, ed., Child Growth and Development in an Era of Conflict~ Fifteenth Yearbook, Michigan Education Association and Department of Elementary School Principals (Lansing, 1944). 19. D'Arcy W. Thompsbn, On Growth and Form (Cambridge: Cambridge University Press, 1948). 20. G. G. Thompson, Child Psychology (Boston: Houghton MifHin Com pany, 1952). 21. L. von Bertalanffy, "Quantitative Laws in Metabolism and Growth,"

Quarterly Review of Biology, XXXII (1957), 217-231. 22. W. H. Werkmeister, The Basis and Structure of Knowledge (New York: Harper and Brothers, 1948). 23. J. W. Wrightstone, "Evaluation of the Experiment with the Activity Program in the New York City Elementary Schools," Journal of Edu cational Research, XXXVIII (1944), 252-257.