Stuffing course content

An inventory

Ben Wilbrink

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.

About the mechanism of more and more topics getting stuffed in existing courses, thus preventing any focusing on essential insights.

inert ideas—inert matter—mental dryrot

“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.

The study of mathematics is apt to commence in disappointment. The important applications of the science, the theoretical interest of its ideas, and the logical rigour of its methods, all generate the expectation of a speedy introduction to processes of interest. We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it — '"Tis here, 'tis there, 'tis gone" — and what we do see does not suggest the same excuse for illusiveness as sufficed for the ghost, that it is too noble for our gross methods. "A show of violence," if ever excusable, may surely be " offered " to the trivial results which occupy the pages of some elementary mathematical treatises.
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.

concensus building mechanism

"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.

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


ritualistic calculus

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)

About the mechanism of course content becoming more and more rigorous instead of anything else.

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 mechanism of a profession or a discipline becoming more and more mysterious to outsiders, thus gaining respect and/or protecting the profession's market share.

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.

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.

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.

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