Knowledge structure in curriculum and pedagogy: continuity or dichotomy?

Jeanne Gamble University of Cape Town

Paper presented at theKnowledge and Curriculum in Higher Education

Symposium7 – 8 November 2012

Abstract

In the concluding section of Basil Bernstein’s early seminal paper ‘On the Classification and Framing of Educational Knowledge’, he explains that the paper explored the concept of ‘boundary’ and that the analysis focussed upon the structuring of transmitted educational knowledge (1975, 110).

Though his last work shifted the focus from classification and framing to knowledge structure, as related to the formalisation and growth of disciplines, the Durkheimian emphasis on boundary was maintained through all phases of his work.

This paper considers why it is important to both curriculum and pedagogy to retain Bernstein’s emphasis on boundary.

“Aren’t we all progressivists at heart?”

(Joe Muller, in a class many years ago)

The nature of modern science

Zilsel (2000) traces the birth of modern science to the period 1300 to 1600 and the emergence of early capitalism in Europe. Zilsel distinguishes three strata of intellectual activity. Logical training was reserved for upper-class scholars (professors and humanistic literati as two distinctive strata) while experimentation, causal interest and quantitative method were the domain of lower-class artisans. Science was born, he argues, when the progress of technology weakened social prejudice against manual labour and the experimental method was adopted by rationally trained scholars to position deductive and inductive methods of investigation in a collateral relationship

Neither Durkheim nor Bernstein considers boundaries to be immutable. Durkheim argues that the placing in a relationship of orders sacred and profane is a delicate operation which requires a complex initiation (Durkheim, 1912/1995, 38). .

• Atkinson (1985, 143) argues that, like Mary Douglas, Bernstein’s constructs are ‘continuous rather than dichotomous’.• Although Bernstein differentiated strongly between restricted and elaborated codes, ‘he was well aware that a number of different dimensions of meaning were involved and that the overall pattern was one of gradience, not discrete categories’ (Halliday, 1995, 140).•More recently, Karl Maton has used legitimation codes and the constructs of semantic gravity/semantic density to argue for ‘reconceptualising forms of discourse, knowledge structure, curriculum structure and learning on a continuum rather than as dichotomous ideal types’ (Maton, 2009, 55)

So, why are we wanting to making the move from dichotomy (or boundary) to continuum?

I want to argue that it is because we are trying to work with the notion of knowledge structure in curriculum terms. In order to do so, we need to transpose the language of hierarchy and generalisation to curriculumLet us just remind ourselves that in ‘vertical discourse’ BB creates a language to describe growth in disciplinary knowledge•Hierarchy is established though attempts to create very general propositions and theories, which integrate knowledge at lower levels and in this way shows underlying uniformities across an expanding range of apparently different phenomena (verticality - Muller 2007)•Hierarchy and generalisation are deemed constitutive features of knowledge structure (Shalem & Slonimsky, 2010).

What language does BB make available for talking about curriculum?

• In his early language of description, the basic structure of curriculum was given by the strength of the classificatory relation: collection code & integrated code (1975, 90).

• In the ‘pedagogic device’ the formulation of pedagogic discourse (ID/RD) at the level of recontextualising rule raises the language of framing to the level of curriculum – i.e. selection, sequencing pacing, criteria for evaluation as well as hierarchical rules or teacher-pupil relations now operate at the level of curriculum as well as at the level of pedagogic practice.

Distinction between macro- framing at the level of curriculum and micro- framing at the level of classroom practice (Reeves 2010).

This language for describing curriculum structure is similar to the language emanating from the ‘opportunity to learn’ (OTL) literature which identifies curriculum structure with concepts such as content coverage by cognitive demand, content exposure, curriculum pacing, curriculum coherence (Reeves & Muller 2005; Schmidt, Hsing Chi Wang & McKnight, 2008; Reeves 2010). It is the prescription for levels of cognitive demand that is important here as this carries a notion of hierarchy, which brings brings Bloom’s Taxonomy of Educational Objectives (1956) and what is called the Revised Taxonomy (2001) into play.

A taxonomy creates a hierarchical classification system with subsumption of lower levels into higher levels

Kratwohl describes the logic of the taxonomy as follows: The original Taxonomy provided carefully developed definitions

for each of the six major categories in the cognitive domain.

The categories were ordered from simple to complex and from concrete to abstract. Further, it was assumed that the original Taxonomy represented a cumulative hierarchy; that is, mastery of each simpler category was prerequisite to mastery of the next more complex one (Kratwohl, 2002, 212-213).

Structure of the Original Bloom’s Taxonomy(Bloom, Engelhart, Furst, Hill & Krathwohl, 1956)

1.0 Knowledge 2.0 Comprehension1.10 Knowledge of specifics 2.1 Translation

1.11 Knowledge of terminology 2.2 Interpretation

1.12 Knowledge of specific facts 2.3 Extrapolation

1.20 Knowledge of ways and means of dealing with specifics

3.0 Application4.0 Analysis

1.21 Knowledge of conventions 4.1 Analysis of elements

1.22 Knowledge of trends and sequences 4.2 Analysis of relationships

1.23 Knowledge of classifications and categories

4.3 Analysis of organizational principles

1.24 Knowledge of criteria 5.0 Synthesis

1.25 Knowledge of methodology 5.1 Production of a unique communication

1.30 Knowledge of universals and abstractions in a

Field

5.2 Production of a plan, or proposed set of operations

5.3 Derivation of a set of abstract relations

1.31 Knowledge of principles and generalizations

6.0 Evaluation

1.32 Knowledge of theories and structures 6.1 Evaluation in terms of internal evidence

6.2 Judgments in terms of external criteria

REVISED TAXONOMY OF EDUCATIONAL OBJECTIVES

(Anderson, Krathwohl (Eds.), 2001)Structure of the Knowledge Dimension Structure of the Cognitive Process Dim.

A. Factual Knowledge – The basic elements that students must know to be acquainted with a discipline or solve problems in it.

1.0 Remember – Retrieving relevant knowledge from long-term memory.

B. Conceptual Knowledge – The interrelationshipsamong the basic elements within a larger structurethat enable them to function together

2.0 Understand – Determining the meaning of instructional messages, including oral, written, and graphic communication.

C. Procedural Knowledge – How to do something; methods of inquiry, and criteria for using skills, algorithms, techniques, and methods.

3.0 Apply – Carrying out or using a procedure in a given situation.

4.0 Analyze – Breaking material into its constituent parts and detecting how the parts relate to one another and to an overall structure or purpose.D. Metacognitive Knowledge – Knowledge of

cognition in general as well as awareness and knowledge of one’s own cognition.

5.0 Evaluate – Making judgments based on criteria and standards.

6.0 Create – Putting elements together to form a novel, coherent whole or make an original product.

In one fell swoop this allows for the transposition of hierarchy in knowledge-building to hierarchy in curriculum structure.

Even though Reeves (2012) has shown that there are different levels of difficulty between questions which align to a particular type of cognitive demand’ and that a question that tests specific knowledge can actually be more difficult than a multi-step, multiple-concept question, the idea of a continuum of cognitive complexity is seductive in terms of its implicit assumption of logical continuity and/or cumulative links between the various categories or types. 2 Dangers:• genericism (general cognitive attributes)•A way of ranking assessment items becomes a general theory of pedagogy

In order to find another solution we turn to Halliday’s language-based theory or learning and the post-Vygotskian work of Vasili Davydov..

A model of human semiotic development (Halliday, 1993, 111). (protolanguage) - generalisation - abstractness - metaphor (8) (18)

• Synoptic/dynamic complementarity(21)

… the underlying assumption is that they do not follow in a direct sequence. Abstraction does not develop out of generalisation as they are fundamentally different processes.

What then is the teaching process towards symbolic abstraction?.

For this we move to post-Vygotskian research related to Vygotsky’s distinction between ‘spontaneous‘ or everyday concepts and

‘scientific’ or theoretical concepts. Both are concepts, in the sense of being an idea about a class of objects at a general level, but they have

different ontogenetic or developmental pathways.

Daniels (2008, 18) relates the instructional approach of theorists such as Davydov to Bernstein’s distinction between horizontal and vertical discourse.

Davydov and his colleagues are critical of both traditional and guided discovery forms of classroom practice (more commonly known as constructivism).

At the core of this argument we find a strong distinction between empirical and theoretical generalisation as entirely independent processes.

‘Ascent from the abstract to the concrete’ ‘Discovery and mastery of the abstract and universal precedes

mastery of the concrete and particular, and the concept itself as a certain method of activity serves as a means of ascending from the abstract to the concrete’ (Davidov, 1990 174).

The assertion is that empirical generalisation is accomplished as a result of comparison and singling out the general (similar) properties of the phenomena being compared. This is an important form of generalisation, but Davydov argues that ‘numerous facts testify that the initial generalisations obtained by the students according to the scheme “from the bottom up” in themselves often do not provide for movement “from the top down,” from the general to the particular’ (Davydov, 1990, 11; emphasis added).

This is so because the transition from general concepts to particular operations functions as ‘an entirely independent process’ (12). For Davydov a scientific concept reflects what is ‘essentially general’.

‘Such a theoretical derivation is accomplished by a two-way movement from the general to the particular and from the particular to the general - generalization and theoretical cognition are interrelated. Here one must make a clear-cut distinction between the process of empirically “suggesting” the externally general and the process of theoretically deriving certain theses on the basis of the essentially general’ (Dayvydov, 1990, 91, emphasis added).

Drawing such a distinction does not mean that concrete objects are discarded. On the contrary, he argues that ‘genuine mastery of abstract knowledge occurs in proportion to its enrichment with concrete-sensory content’ (12). With regard to students’ life-worlds, he argues:‘Of course, this experience should be used in instruction, but only through a substantial reconstruction within a form of scientific knowledge that is qualitatively special and new for the student, which in no way corresponds, and cannot correspond, to simple life experience’ (Davydov, 1990. 40; original emphasis).

In the teaching of academic subjects, the key task for students is to identify the ‘primary general relationship’ and to make the discovery ‘that this relationship is manifest in many other particular relationships found in the given material’ (cited in Engeström, 2005, 164-165).

‘To make such a generalisation means to discover a principle, a necessary connection of the individual phenomena within a certain whole, the law of formation of that whole’ (as cited in Tuomi-Gröhn & Engeström, 2007, 29). Here is the defining feature of knowledge structure - the necessary connection between ‘parts and the whole’

N apples were in a bowl on the table. R people entered the room and each took an apple. How many apples remained? Children first analyze the structure of the problem, identifying it as a part-whole structure, with N as the whole and R as a part. They schematize the quantitative relations expressed in the problem as follows:

N

R ?

Since they know the whole and are trying to find a part, they know the missing part must be the difference between the whole and the known part, i.e. N – R (Schmittau, 2005, 19).

Continued:

Schmittau goes on to show that later, when these students are confronted with numerical designations instead of symbols, they apply the same symbolic logic. For example:

‘There were seven books on the shelf. Nine children entered the library and each placed a book on the shelf. How many books are now on the shelf?’

In this problem the students are able to recognise that both numbers are now parts and that the whole must be greater than the parts in order for this problem to have a solution.

Schmittau argues that ‘because they have a theoretical orientation to the problem structure, they can analyze the relationships between the quantities … without any numerical designations to provide them with cues’ (2005, 19).

So what does this say about pedagogy related to the transmission of knowledge structure?

To have the recognition rule for a given problem or case is to be able to recognise the relational whole of which the problem or case is a part. The teacher’s task is to model, in some form, the relational whole or its proxy. Whatever there is of conceptuality in terms of low or high verticality must be put up front – so to speak. Not to do so may give students access to the capacity to reason empirically but not to the capacity to reason theoretically. Once principles or rules are stated, students can often apply these to given problems but, what they cannot do, is to recognise the general principle inherent in a particular case or problem. Misrecognition of this kind keeps students trapped in the world of particular orders of meaning.

Logically, the interpretation that follows is that whatever the level of verticality, it is theoretical generalisation that constitutes the boundary between horizontal and vertical discourse.

If this is so and if we take the point that abstractedness (for Halliday) and theoretical generalisation (for Davydov) are separate from and different to empirical generalisation, then we can see why it is so crucial to recognise the directionality of pedagogies that privilege knowledge structure to give access to ‘powerful knowledge’.

And that is why the argument has been that we need to retain a strong notion of boundary in our framing of our educational work, even as we work towards a stronger understanding of continua

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