Stuffing is the process of accumulating course content - subjects, themes, names, or what not - instead of restricting content to the course essentials. The main form of stuffing is indeed adding more and more topics, in that way loosing sight of what the course originally might have been meant for. Other forms of deviating from the original goals of a course are possible, however, such as making it more and more rigorous - especially in mathematics as well as by mathematizing non-mathematic content (in economics) - or in an indirect way by designing test questions about minor details of the course content instead of about the major insights the course should offer students.

“In training a child to activity of thought, above all things we must beware of what I will call ‘inert ideas’ -- that is to say, ideas that are merely received into the mind without being utilised, or tested, or thrown into fresh combinations.

In the history of education, the most striking phenomenon is that schools of learning, which at one epoch are alive with a ferment of genius, in a succeeding generation exhibit merely pedantry and routine. The reason is, that they are overladen with inert ideas. Education with inert ideas is not only useless: it is, above all things, harmful — *Corruptio optimi, pessima.* Except at rare intervals of intellectual ferment, education in the past has been radically infected with inert ideas. That is the reason why uneducated clever women, who have seen much of the world, are in middle life so much the most cultured part of the community. They have been saved from this horrible burden of inert ideas. Every intellectual revolution which has ever stirred humanity into greatness has been a passionate protest against inert ideas. Then, alas, with pathetic ignorance of human psychology, it has proceeded by some educational scheme to bind humanity afresh with inert ideas of its own fashioning.

Let us now ask how in our system of education we are to guard against this mental dryrot. We recur to our two educational commandments, ‘Do not teach too many subjects,’ and again, ‘What you teach, teach thoroughly.’ ”

Alfred North Whitehead (1917).** The Organization of Thought: Educational and Scientific.** London: William and Norgate. Reprinted partially in his 1929 ‘Aims of education.’ html chapter 1

A. N. Whitehead (1911). **An introduction to mathematics** Het Spectrum, Aula 226. http://www.archive.org/details/anintroductiont01whitgoog

The reason for this failure of the science to live up to its reputation is that its funda- mental ideas are not explained to the student disentangled from the technical procedure which has been invented to facilitate their exact presentation in particular instances. Accordingly, the unfortunate learner finds himself struggling to acquire a knowledge of a mass of details which are not illuminated by any general conception. Without a doubt, technical facility is a first requisite for valuable mental activity: we shall fail to appreciate the rhythm of Milton, or the passion of Shelley, so long as we find it necessary to spell the words and are not quite certain of the forms of the individual letters. In this sense there is no royal road to learn- ing. But it is equally an error to confine attention to technical processes, excluding consideration of general ideas. Here lies the road to pedantry.

The object of the following chapters is not to teach mathematics, but to enable students from the very beginning of their course to know what the science is about, and why it is necessarily the foundation of exact thought as applied to natural phenomena. All allusion in what follows to detailed deductions in any part of the science will be inserted merely for the purpose of example, and care will be taken to make the general argument comprehensible, even if here and there some technical process or symbol which the reader does not understand is cited for the purpose of illustration.

"One way that the mathematics education community has attempted to answer questions about the nature of foundation level mathematics has been through consensus-building activities aimed at the development of standards for curriculum and assessment. Typically, these efforts enlist 'stakeholders' who mainly included practitioners representing schools and school teachers, or mathematics professors representing traditional university departments. Little input tends to be sought from people who represent hyphenated fields lying at the intersections of traditional disciplines—or future-oriented fields that are heavy users of mathematics in the 21st century. Consequently, results from these consensus-building efforts tend to focus on making incremental improvements in traditional curriculum materials—rather than on taking a fresh look at foundations for the future."

Richard Lesh, Eric Hamilton and Jim Kaput (2007). Directions for future research. In Richard A. Lesh, Eric Hamilton and James J. Kaput (Eds) (2007). **Foundations for the future in mathematics education** (449-453). Erlbaum.

Drew H. Gitomer (1993). Performance assessment and educational measurement. In Randy Elliot Bennett and William C. Ward: **Construction versus choice in cognitive measurement: Issues in Constructed Response, Performance Testing, and Portfolio Assessment.** Erlbaum.

- p. 244: "Schoenfeld (1985) [Mathematical problem solving], for example, noted that the algorithmic focus of mathematics education has little to do with genuine mathematical problem solving."

Jeremy Kilpatrick and Jane Swafford (Eds) (2002). Helping children learn mathematics. piecewise html.

- p. 3-4: "Textbooks are typically packed with an assortment of topics. so that the treatment of any one topic is often both shallow and repetitive. Key ideas can be difficult to pick up from among the many incidental details. This scattered and superficial curriculum means that students learn much less than they might. They then take standardized tests that often measure low-level skills rather than the kind of problem-solving abilities needed in modern life. All too often, mathematics instruction serves to alienate students rather than to reveal to them the beauty and usefulness of mathematics."

But let me tell you how I feel about the teaching of calculus. I think it has completely diverged from the way in which calculus is thought about and used by professionals. What is taught under the name of calculus has become a ritual, that's all. There is a long essay on education by Alfred North Whitehead which he starts by saying that the biggest problem is how to stop teaching inert matter. Most of what we teach in calculus is inert.

Peter D. Lax, in Donald J. Albers, Gerald L. Alexanderson and Constance Reid (Eds) (1990). **More mathematical people. Contemporary conversations** (p. 148). New York: Harcourt Brace Jovanovich.

NCTM (****). **Curriculum focal points for prekinderkarten through grade 8 mathematics**. National Council of Teachers of Mathematics. downloads page (The full document is 18.9 Mb)

- "The Curriculum Focal Points are the most important mathematical topics for each grade level. They comprise related ideas, concepts, skills, and procedures that form the foundation for understanding and lasting learning."
- This is an attempt to
*prevent*stuffing the mathematics curriculum. - “An approach that focuses on a small number of significant mathematical ‘targets’ for each grade level offers a way of thinking about what is important in school mathematics that is different from commonly accepted notions of goals, standards, objectives, or learning expectations. These more conventional structures tend to result in lists of very specific items grouped under general headings. By contrast,
*Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics*offers more than headings for long lists, providing instead descriptions of the most significant mathematical concepts and skills at each grade level. Organizing a curriculum around these described focal points, with a clear emphasis on the processes that*Principles and Standards*addresses in the Process Standardsâ€”communication, reasoning, representation, connections, and, particularly, problem solvingâ€”can provide students with a connected, coherent, ever expanding body of mathematical knowledge and ways of thinking. Such a comprehensive mathematics experience can prepare students for whatever career or professional path they may choose as well as equip them to solve many problems that they will face in the future.”

The trend towards more rigorous treatment of course material is very conspicuous in mathematics, at alle educational levels as well. This trend has been heavily criticized by Hans Freudenthal (for example his 1973), see the references in matheducation.htm. What is especially problematic about more rigorous courses is what Freudenthal calls the 'didactic inversion,' in fact preventing students to discover for themselves how better/best to organize the mathematical material they have acquainted themselves with. Another very problematic aspect of the trend towards more rigor in mathematics is the downplaying of applications of the very same mathematics.

A. Leen (1961). **De ontwikkeling van het rekenonderwijs op de lagere school in de 19e en het begin van de 20ste eeuw.** Groningen: Wolters. Proefschrift Vrije Universiteit Amsterdam.

Bezemer, C. H. Bezemer (1987). **Les répétitions de Jacques de Révigny. Recherches sur la répétition comme forme d'enseignement juridique et comme genre littéraire, suivies d'un inventaire des textes.** Brill. Proefschrift Leiden. Ook verschenen als deel 13 van de serie Rechtshistorische Studies.

- [About the
*repetitio*, a special lecture outside the regular curriculum, to comment on one particular law only] L’origine de la répétition est brumeuse, les témoignages les plus anciens datent du milieu du 13e siècle et s’orientent vers Bologne. L’assertion de Meijers selon laquelle on ne trouve pas de répétitions provenant de Bologne avant 1300 s’ révélée incorrecte. La naissance de cette forme d’enseignement semble être en rapport avec l’augmentation des matières enseignées pendant les cours normaux. Depuis les premiers Glossateurs, autour de certains passages du*Corpus iuris*qui servaient de prétexte s’étaient accumulées des matières entières, surtout à propos de sujets compliqués et controversés.**Pour ces matières de plus en plus nombreuses, le temps disponibles lors des cours normaux se révélait insuffisant.**[my emphasis, b.w.] Cela avait pour conséquence que certains*volumina*du*Corpus iuris*n’étaient pas nalysés intégralement ou dans les délais voulus. Ce phénomène, en combinaison avec la menace des faiblesses humaines toujours présentes (de la part des professeurs: absentéisme, écarts au sujet, marottes; de la part des étudiants: passion excessive pour le débat), fut probablement le motif des premi``eres*punctationes*ou*taxationes punctorum*. Par elles, on fixa d’un moment à l’autre le nombre de matières que l’on devait obligatoirement étudier (..). Cette méthode ne tenait pas compte du besoin de faire des digressions lors de l’analyse de certaines lois. Cette lacune pouvait alors être comblée par la répétition. On réservait du temps, à côté des cours normaux, pour un examen approfondi d’une certaine matière qui n’était pas ou insuffisament abordée lors des cours normaux. On laissait de plus place au débat qui était exclu durant les cours normaux. Cette explication nous paraît être l’hypothèse le plus plausible concernant l’origine de la répétition. (p. 18-20)

Brown, Joanne (19??). **The definition of a profession. The authority of metaphor in the history of intelligence testing, 1890-1930.** Princeton UP.

Arthur Engel (1974). The emerging concept of the academic profession at Oxford 1800-1854. In Lawrence Stone: **The university in society. Vol. I Oxford and Cambridge from the 14th to the early 19th century. Vol. II Europe, Scotland, and the United States from the 16th to the 20th century** (p. 305-352). Princeton: Princeton University Press.

Robert L. Church (1974). Economists as experts: the rise of an academic profession in America 1870-1917. In Lawrence Stone: **The university in society. Vol. I Oxford and Cambridge from the 14th to the early 19th century. Vol. II Europe, Scotland, and the United States from the 16th to the 20th century** (p. 571-610). Princeton: Princeton University Press.

McClelland (1985). Zur Professionalisierung der akademischen Berufe in Deutschland. In W. Conze und J. Kocka: **Bildungsbürgertum im 19. Jahrhundert. Teil I. Bildungssystem und Professionalisierung in internationalen Vergleichen.** Stuttgart: Klett-Cotta.

Hilde de Ridder-Symoens (1996). Training and professionalization. In W. Reinhard: **Power elites and state building** (p. 149-171). Oxford: Clarendon Press.

Kees Gispen (1990). Engineers in Wilhelmian Germany: Professionalization, deprofessionalization, and the development of nonacademic technical education. In Geoffrey Cocks and Konrad H. Jarausch: **German professions 1800-1950.** Oxford: Oxford University Press.

R. MacLeod and R. Moseley (1980). The 'Naturals' and Victorian Cambridge: Reflections on the anatomy of an elite, 1851-1914. *Oxford Review of Education, 6*, 177-195.

- "provides a study of the intellectual and social effects of the Cambridge Natural Sciences Tripos." (NST for short)
- p. 179: "For all its obvious importance, the relation between the introduction of examinations and the production of elites has been little studied [refers Keith Hoskin's contribution in Macleod (1980):
**Days of Judgement**]. On the one hand, the rate of progress within scientific knowledge is rarely considered a function of the examination system obtaining at a given time; on the other hand, any possible relationships existing between early education and later eminence have been much less interesting to historians of science than to social or educational historians." - p. 180: "The examination structure was the mechanism by which intellectual and eventually professional disctinctions between men were made and maintained. In introduing the NST, a new set of elites was produced, which, in the fullness of time, began to reproduce itself, much as the Anglican clergy had done since the Reformation."

V. L. Bullough (1978). Achievement, professionalization, and the university. In J. IJsewijn and J. Paquet: **The universities in the late middle ages** (p. 497-510). Leuven, at the University Press.

B. Kimball (1992). **The 'true professional ideal' in America. A history.** Oxford: Blackwell.

M. Ramsey. The politics of profssional monopoly in nineteenth-century medicine: The French model and its rivals. In Gerald L. Geison: **Professions and the French state, 1700-1900** (p. 225-306). Philadelphia: University of Pennsylvania Press.

Monte A. Calvert (1967). **The mechanical engineer in America, 1830-1910. Professional cultures in conflict.** Philadelphia: Johns Hopkins.

Berelson, B. (1960). **Graduate education in the United States.** New York: McGraw-Hill.

- Berelson unintentionally reveals much about the mechanisms of building professions here. [I must check this again]
- " In working up this study, the author reviewed the available literature and talked with graduate deans, presidents, deans, departmental chairmen, and faculty members in many colleges and universities. Questionnaires were sent to graduate deans in 92 universities, the graduate faculty in the same universities, a sample of the 1957 recipients of the doctorate, the presidents of all liberal arts and teachers colleges, and all industrial firms employing over 100 professional and technical personnel. "
- "The book deals with the sources and supply of college teachers, the demand for top-ranking educators, the professionalization of graduate students, and the meanings and functions of graduate degrees."

A. M. Carr-Saunders and P. A. Wilson (1933). **The professions**. Oxford: Clarendon Press.

Constantijn Huygens (2003). **Mijn leven verteld aan mijn kinderen.** Ingeleid, bezorgd, vertaald en van commentaar voorzien door Frans R. E. Blom. Amsterdam: Prometheus.

- Blom, vol II p. 45, citeert Constantijn Huygens' (vader van Christiaan Huygens) eerdere autobiografie 'Mijn jeugd' p. 50, over het gebruik van Latijn in onderwijs en de wetenschap: "Wat is dat toch voor waanzin om ruimschoots de middelen in huis te hebben waarmee je de wetenschappen een stuk makkelijker aanleert, en dan toch deze schatten van eigen bodem onbenut te laten liggen en er zelfs de neus voor op te halen, en dat alles alleen maar om het leren extra moeilijk te maken?"
- Blom p. 32: "Dat de landstaal evengoed voor wetenschappelijk werk gebruikt kon worden, toonden geleerden als hugo de Groot met zijn
*Inleydinghe tot de Hollandsche rechts-geleertheydt*, Johan van Beverwijck met zijn medische standaardwerken*Schat der ongesontheyt*en*Schat der gesontheyt*en P. C. Hooft met zijn*Nederlandsche Historiën*." - Blom p. 31: "Huygens veroordeelt de blinde verering van de taal van Rome en de daaruit voorvloeiende gewoonte om het Latijn tot het alles-overheersende onderdeel van de opvoeding te maken." "Huygens beschrijft hier in
*Mijn leven*zijn onderwijs in grammatica, retorica en logica, maar steekt eerst een vlammend betoog af tegen het Latijn." (regels 70-102). - Blom, p. 33: "In de jeugdbiografie valt te lezen dat Huygens met het grootste welbehagen terugdenkt aan de tijden dat hij Latijn ging leren. (...) Die plezierige lessen waren te danken aan Christiaan Huygens. Omdat hij de gangbare schoolgrammatica's nodeloos ingewikkeld vond en al te zeer uitgebreid met weetjes die in de praktijk van de lectuur wel aangeleerd konden worden, had hij uit verscheidene leerboekjes de grammatica voor zijn twee zoons in een efficiënte synopsis bijeengebracht en vermakelijk omgesmeed tot verzen. In een volgend stadium werd datzelfde gedaan voor de regels van de prosodie. De methode was zo succesvol dat Huygens de compendia van zijn vader dertig jaar later ook door zijn eigen kinderen heeft laten gebruiken. [In de collectie van de Leidse universiteitsbibliotheek bevindt zich nog het grammaticacompendium van Constantijn Huygesn jr, onder de titel
*Grammatica Latina, Rudimenta*(sign. Hug. F 49).]"

June 1, 2010 \ contact ben at at at benwilbrink.nl

http://www.benwilbrink.nl/stuffing/stuffing.htm