Part I. Experimental Studies: 2. Experiment in psychology 3. Experiments on perceiving III Experiments on imaging 4-8. Experiments on remembering: (a) The method of description (b) The method of repeated reproduction (c) The method of picture writing (d) The method of serial reproduction (e) The method of serial reproduction picture material 9. Perceiving, recognizing, remembering 10. A theory of remembering 11. Images and their functions 12. Meaning Part II. Remembering as a Study in Social Psychology: 13. Social psychology 14. Social psychology and the matter of recall 15. Social psychology and the manner of recall 16. Conventionalism 17. The notion of a collective unconscious 18. The basis of social recall 19. A summary and some conclusions.

Remembering. A Study in Experimental and Social Psychology, Cambridge (University Press) 1964.

Running head: WHY MINIMALLY GUIDED INSTRUCTION DOES NOT WORK Why Minimal Guidance during Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching

Evidence for the superiority of guided instruction is explained in the context of our knowledge of human cognitive architecture, expert–novice differences, and cognitive load. Although unguided or minimally guided instructional approaches are very popular and intuitively appealing, the point is made that these approaches ignore both the structures that constitute human cognitive architecture and evidence from empirical studies over the past half-century that consistently indicate that minimally guided instruction is less effective and less efficient than instructional approaches that place a strong emphasis on guidance of the student learning process. The advantage of guidance begins to recede only when learners have sufficiently high prior knowledge to provide "internal" guidance. Recent developments in instructional research and instructional design models that support guidance during instruction are briefly described.

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Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching

This article reports the authors' efforts to develop a practice-based theory of content knowledge for teaching built on Shulman's (1986) notion of pedagogical content knowledge. As the concept of p...

https://harringtonmath.com/wp-content/uploads/2013/11/Content-knowledge-for-teachers.pdf

Content Knowledge for Teaching: What Makes It Special?

Pedagosko i psiholosko testiranje i procjenjivanje spadaju među najvažnije doprinose znanosti o ponasanju nasem drustvu i pružaju temeljna i znacajna poboljsanja u odnosu na ranije postupke. Iako se ne može ustvrditi da su svi testovi dovoljno usavrseni niti da su sva testiranja razborita i korisna, postoji velika kolicina informacija koje ukazuju na ucinkovitost kvalitetnih instrumenata u onim situacijama u kojima je njihovo koristenje potkrijepljeno validacijskim podacima. Pravilna upotreba testova može dovesti do boljih odluka o pojedincima i programima nego sto bi to bio slucaj bez njihovog koristenja, a također i ukazati na put za siri i pravedniji pristup obrazovanju i zaposljavanju. Međutim, losa upotreba testova može dovesti do zamjetne stete nanesene ispitanicima i drugim sudionicima u procesu donosenja odluka na temelju testovnih podataka. Cilj Standarda je promoviranje kvalitetne i eticne upotrebe testova te uspostavljanje osnovice za ocjenu kvalitete postupaka testiranja. Svrha objavljivanja Standarda je uspostavljanje kriterija za evaluaciju testova, provedbe testiranja i posljedica upotrebe testova. Iako bi evaluacija prikladnosti testa ili njegove primjene trebala ovisiti prvenstveno o strucnim misljenjima, Standardi pružaju okvir koji osigurava obuhvacanje svih relevantnih pitanja. Bilo bi poželjno da svi autori, sponzori, nakladnici i korisnici profesionalnih testova usvoje Standarde te da poticu druge da ih također prihvate.

Standards for educational and psychological testing

During the last half century, school mathematics in North America has undergone two major waves of attempted reform: the new math movement of the 1950s through the early 1970s and the standards-based movement of the past two decades or so. Although differing sharply in their approach to curriculum content, these reform efforts have shared the aim of making mathematics learning more substantial and engaging for students. The rhetoric surrounding the more recent movement, however, has been much more shrill, the policy differences more sharply drawn, the participants more diverse. The so-called math wars of the 1960s (DeMott, 1962, ch. 9) were largely civil wars. They pitted advocates of rigor and axiomatics against those promoting applied, genetic approaches and were conducted primarily in journal articles and at professional meetings. Today’s warfare ranges outside the profession and has a more strident tone; it is much less civil in both senses of the word. Debates about the new math never became directly implicated in national politics in North America (although they did at times elsewhere in the world). The controversy over recent reform proposals, however, has irresistibly drawn U.S. politicians into the fray—from President Reagan’s plug for one of John Saxon’s mathematics textbooks at a White House reception for school principals in July 1983, to Congress’s 1994 mandate that the Office of Educational Research and Improvement establish expert panels that would identify exemplary and promising educational programs, to Secretary Riley’s 1998 call for a cease-fire in the “math wars,” to last year’s U.S. House Committee on Education and the Workforce’s hearing on the federal role in Grades K‐12 mathematics reform. This high-profile involvement of politicians has helped inflame an atmosphere already heated by melodramatic discourse in the press. In the Wall Street Journal, Lynne Cheney (1997) recounts horror stories of students failing to learn basic skills in the nation’s mathematics classrooms:

Where's the Evidence?

Didactic transposition: an epistemological model Almost no one today believes that knowing is passively receiving everything ready-made from one's environment. The rejection of this belief is a fundamental assumption of the constructivism that is a major influence on the thinking of educators and cognitive scientists. Constructivists are not in accord, however, on the old quarrel between the ontological view that accepts the objectivity of knowledge and the phenomenological view that denies it. That is, radical constructivists take the drastic step of replacing objectivity with the intersubjectivity of knowledge, and thus set themselves free from the traditional epistemological paradox posed by the skeptics, whereas trivial constructivists consider only the process of cognitive construction and do not take the paradox seriously [von Glasersfeld, 1985]. In fact, the paradox itself is already a trap to both ontology and phenomenology. There is no way out of the dilemma without some cost. The solution given by radical constructivism is one way out at the cost of confining knowledge to a specific kind. That is, the negation of the objectivity of knowledge by the radical constructivists can be persuasive only when one says about knowledge that, apart from faith and dogma, it fits observations [von Glasersfeld, 1987, p. 5]. That negation is a consequence of considering the binary relation between knowledge and the knower. The ordinary usage of the word teach, however, assumes the ternary relation of the teacher, the student, and the knowledge taught. Furthermore, knowledge to be taught in school has many aspects other than that it fits one's observations. We may need an alternative epistemology if we admit that most of the knowledge in school mathematics is a compound of knowledge that fits observations together with our values, instructional purposes, mathematical skills, and so on. "Constructivists need to clarify and develop their ontological commitments.... We need an epistemology that takes ontology into account" [Kilpatrick, 1987, p. 19]. Can we construct an epistemology that allows us to treat knowledge at least "as if it existed independently outside of the knower without violating much of the constructivist position? One epistemological model that gives a positive answer can be found in the didactic transposition theory of Chevallard [1985, 1988; see also Balacheff, 1990]. Didactic transposition theory is based on an assertion that bodies of knowledge are, with a few exceptions, designed not to be taught but to be used. The didactic transposition of knowledge is the transposition from knowledge regarded as a tool to be put to use to knowledge as something to be taught and learned [Chevallard, 1988, p. 5]. Thus any modification of knowledge under instructional purposes can be called a didactic transposition. The difference between knowledge used and knowledge taught is that as long as you only use knowledge in doing something, you need not justify nor even take note of that knowledge to endow your activity with social meaning. In contrast, teaching requires the social acknowledgement and legitimation of the knowledge taught [Chevallard, op, cit., p. 9]. The first step in establishing some body of knowledge as teachable knowledge consists in making it into an organized and more or less integrated whole [Chevallard, op, cit., p. 8]. As a way of achieving this goal, taught bodies of knowledge have been derived from corresponding scholarly bodies of knowledge. A scholarly body of knowledge is nothing other than knowledge used both to produce new knowledge and to organize the knowledge newly produced into a coherent theoretical assemblage [Chevallard, op. cit., p. 10]. In teaching, however, the mechanism of knowledge production and assembly is hidden. It is the task of didactic transposition theory to illuminate that mechanism so that we can produce didactic transpositions that will be to our society's best advantage [Chevallard, op. cit., p. 12].

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Didactic Transposition in Mathematics Textbooks.

Mathematics education as a research domain : a search for identity : an ICMI study

Each age defines education in terms of the meanings it gives to teaching and learning, and those meanings arise in part from the metaphors used to characterise teachers and learners. In the ancient world, one of the defining technologies (Bolter, 1984) was the potter’s wheel. The student’s mind became clay in the hands of the teacher. In the time of Descartes and Leibniz, the defining technology was the mechanical clock. The human being became a sort of clockwork mechanism whose mind either was an immaterial substance separate from the body (Descartes) or was itself a preprogrammed mechanism (Leibniz). The mind has also, at various times, been modelled as a wax tablet, a steam engine and a telephone switchboard.

Jeremy Kilpatrick

Papers

Where's the Evidence?

Didactic Transposition in Mathematics Textbooks.

Mathematics education as a research domain : a search for identity : an ICMI study

Reflection and Recursion

A history of school mathematics