Vocabulary

The origins of the hierarchical complexity construct, as it is defined here, are in the work of Jean Piaget, whose model of mental representation delineates five developmental stages (and a varying number of sub-stages), These have been represented as the (1) reflexive, (2) sensorimotor, (3) symbolic or preoperational, (4) concrete, and (5) formal stages (Piaget & Inhelder, 1969). Each of these developmental stages is defined by a set of formal properties. In the Piagetian model, development from one form of thought to the subsequent form involves a process of hierarchical integration, in the sense that the actions of the earlier form become the content of the actions of the latter (Piaget, 1985).

A number of researchers have described general developmental sequences that elaborate this notion of hierarchical integration (Baldwin, 1894; Case, 1991; Demetriou & Valanides, 1998; Fischer, 1980; Pascual-Leone & Goodman, 1979; Werner, 1948). Recently, for example, Noelting and Rousseau (2000) employed the notion of hierarchical integration to demonstrate that each Piagetian stage is composed of three levels — two substages and one consolidated stage — to form a hierarchy of 12 levels covering the period from early childhood to adulthood. The concept of hierarchical integration is also fundamental to several neo-Piagetian models of cognitive development, including those of Fischer (1980), who emphasizes the development of skill hierarchies in particular contexts; Pascual-Leone and Goodman (1979), who focus on the growth of mental attention and memory capacity; Case (1991), who describes the development of memory capacity and associated processing structures; and Demetriou & Valanides (1998), who describe hierarchical development in terms of processing functions.

Hierarchical integration is observable in performance in the form of hierarchical complexity (Commons et al., 1998; Fischer, 1980; Piaget, 2000), but few efforts have been made to establish a general method that can be employed to measure this property across domains. Instead of identifying the general attributes of different orders of hierarchical complexity and establishing a scoring system based on those attributes, most researchers have employed the notion of hierarchical integration to develop domain-based scoring systems whose scoring criteria are specific to a particular knowledge domain (Armon, 1984b; Colby & Kohlberg, 1987a; Kitchener & King, 1990). In other words, even though the theoretical construct, hierarchical integration, is a considered to be a global phenomenon, we have constructed a separate ruler for every knowledge domain in which it is assessed. If developmental level could be readily assessed in terms of its more general features (hierarchical complexity) rather than its contextual features (domain specific content/structures), it would not only become possible to conduct empirical comparisons of development across domains, but we could meaningfully examine the relation between developmental levels and the conceptual content of a domain, allowing for cross-context comparisons of conceptual development.

Level	Conceptual structure	Logical structure
6 Single representations 26-40 mos	Concepts are 1st order representational sets These coordinate symbolic systems. In responses to the Joe dilemma, for example, the concept of camping coordinates activities like swimming, sleeping in a tent, and painting, and the concept of a paper route coordinates activities like riding a bike, delivering papers, and receiving money.	The logical structure is definitional It identifies one aspect of a single representation—as in "Camping is fun," in which fun is an "aspect" of camp.
7 Representational mappings 4-5 years	Concepts are 2nd order representational sets These coordinate or modify representational sets (the concepts constructed at the single representations level). The very popular representational mappings Lectical™ level concept of having favorites, for example, can be employed to rank camping and fishing. "Camping is my favorite, and fishing is my next favorite." Concepts like being mean, keeping a promise, changing one’s mind, and sharing also become common at this Lectical™ level. "[Joe’s father] is just being mean; he is taking the money away from his kids."	The logical structure is linear It coordinates one aspect of two or more representations—as in, "If you do not do what your father tells you to do, he will get really mad at you," in which doing what your father says and not doing what your father says are coordinated by his anticipated reaction.
8 Representational systems 6-7 years	Concepts are 3rd order representational sets These coordinate elements of representational systems. For example, the concept of trust, articulated for the first time at this Lectical™ level, can be used to describe the system of interactions between Joe and his father. "Joe trusted [his Dad] that he could go to the camp if he saved enough money, and then his father just breaks it, and the promise is very important." Concepts like to turn against, to blame, to believe, and being fair are also infrequently observed before this level. "[If you break a promise] they will not like you anymore, and your friends will turn against you."	The logical structure is multivariate It coordinates multiple aspects of two or more representations—as in, "If Joe’s Dad says Joe can go to camp, then he says he can’t go to camp, that’s not fair because Joe worked hard and then his Dad changed his mind," in which two conflicting representations of Dad’s authority are evaluated in terms of his changed mind and Joe’s hard work.
9 Single abstractions 9-11 years	Concepts are 1st order abstractions These coordinate representational systems. For example, the concept of trustworthiness, articulated for the first time at this Lectical™ level, defines those qualities that make a person trustworthy rather than describing a particular situation in which trust is felt or not felt. It is composed of qualities that produce trust, such as telling the truth, keeping secrets, and keeping promises. "It's always nice…to be trustworthy. Because, then, if [someone has] a secret, they can come and talk to you." Concepts like kindness, keeping your word, respect, and guilt are also rare before the this level. "If you don't do something you promise, you'll feel really guilty."	The logical structure is definitional It identifies one aspect of a single abstraction—as in, "Making a promise is giving your word," in which giving one's word is an "aspect" of a promise.
10 Abstract mappings	Concepts are 2nd order abstractions These coordinate or modify abstractions. For example, the abstract mappings level concept basis can be employed to coordinate the elements essential to a good relationship. "To me, [trust and respect are] the basis of a relationship, and without them you really don't have one." Concepts like coming to an agreement, making a commitment, building trust, and compromise are also rare before this Lectical™ level. "I think [Joe and his father] could come to an agreement or compromise that they are both comfortable with."	The logical structure is linear The most complex logical structure of this Lectical™ level coordinates one aspect of two or more abstractions—as in, "Joe has a right to go to camp because his father said he could go if he saved up the money, and Joe lived up to his commitment." Here, Joe's fulfillment of his father's conditions determines whether Joe has a right or does not have a right to go to camp.
11 Abstract systems	Concepts are 3rd order abstractions These coordinate elements of abstract systems. For example, the concept of personal integrity–which is rare before the abstract systems level–refers to the coordination of and adherence to notions of fairness, trustworthiness, honesty, preservation of the golden rule, etc., in one’s actions. "[You should keep your word] for your own integrity. For your own self-worth, really. Just to always be the kind of person that you would want to be dealing with." Concepts like verbal contract, moral commitment, functional, development, social structure, and foundation are also uncommon before the abstract systems level. "A promise is the verbal contract, the moral commitment that the father made to his son. It is the only way for the child to…develop his moral thinking—from watching his parent's moral attitude."	The logical structure is multivariate The most complex logical structure of this level coordinates multiple aspects of two or more abstractions. "Following through with his commitment and actually experiencing camp combine to promote Joe’s growth and development, not just physically but psychologically, emotionally, and spiritually." Here, multiple facets of Joe’s personal development are promoted when he both keeps his commitment and accomplishes his goal.
12 Single axioms/ principles	Concepts are 1st order axioms/ principles These coordinate abstract systems. The notion of the social contract, for example, results from the coordination of human interests (where individual human beings are treated as systems). "Everybody wants to be treated equally and have a sense of fair play. Because this is so, we have an obligation to one another to enter into a social contract that optimizes equality and fairness." Concepts like autonomy, fair play, heteronomy, higher order principle, and philosophical principle are rare before the single axioms/ principles level. "The only time we’re justified in breaking the social contract is when a higher principle, such as the right to life, intervenes."	The logical structure is definitional It identifies one aspect of a principle or axiom coordinating systems—as in, "Contracts are articulations of a unique human quality, mutual trust, which coordinates human relations." Here, contracts are seen as the instantiation of a broader principle coordinating human interactions.

In scoring text performances, hierarchical order of abstraction must be taken into account, because new concepts are formed at each complexity order as the operations of the previous complexity order are “summarized” into single constructs (Fischer, 1980). Burtis (1982) and Halford (1999) suggest that this summarizing or “chunking” makes more complex thought possible by reducing the number of elements that must be simultaneously coordinated, freeing up processing space and making it possible to produce an argument or conceptualization at a higher complexity order. Fischer identifies three distinct conceptual forms in the portion of the developmental scale examined with the LAS—representations, abstractions, and principles. At the single representations (6), single abstractions (9), and single principles (12) levels, the new concepts not only coordinate or modify constructions from the previous level, they are qualitatively distinct conceptual forms (Fischer, 1980). The appearance of each of these conceptual forms ushers in three repeating logical forms—single elements, mappings or relations, and systems (Fischer, 1980). Because these three logical forms are repeated several times throughout the course of development, it is only by pairing a logical form with a hierarchical order of abstraction that a rater can make an accurate assessment of the complexity order of a performance. Other researchers have observed and described similar conceptual forms and repeating logical structures (Case, Okamoto, Henderson, & McKeough, 1993; Fischer & Bidell, 1998; Piaget & Garcia, 1989).

The figure below shows the progress of hierarchical integration in the representations and abstractions tiers.

Structures, as conceived by Piaget, are open systems of transformations, composed of elements and the relations between them. These elements can include operations, and substructures such as schemas, concepts, perceptions, and memories, all of which are interconnected through spatial-temporal, causal, implicative, and other relations (Piaget, 1970). Elements, although they constitute the content of more global structures, have a structure of their own. For example, a proposition such as, “A good education is one in which you learn what you need to make a living,” has structural features. One of these is the connection established between two concepts, learning and making a living. However, the proposition is also content with respect to the overarching structure of the larger argument of which it is a part. In other words, there may be many layers of structure present in a given performance, and this can be an obstacle to differentiating between structure and content, making it difficult to determine where one ought to look for evidence of the overall level of reasoning employed by an individual.

Despite these problems, Piaget’s distinction between levels of structure, in which he defines substructures as content with respect to global structures (stages), points to one way to operationalize the content/structure distinction. Stages can be defined as global orders of hierarchical complexity, and their presence can be inferred from the over-arching organization of arguments. The particular propositions constituting these arguments can then be treated as content. In this way, the most formal and (arguably) universal features of performance are differentiated from the more context dependent features. In other words, one can distinguish between what Piaget calls operations or global reasoning structures and the particular elements that are operated on with these structures. Global reasoning structures are conceptualized here as orders of hierarchical complexity. The elements of these structures are propositions constructed within informational, contextual, and complexity order boundaries. Though the elements have their own structure, in the present context they are treated as content. This classification is referential. Concepts and propositions are content with respect to the larger structures in which they are embedded.

The possibility of distinguishing structure from content in this way cannot be taken for granted. In fact, even the wisdom of making such an attempt has been challenged in the literature. The debate is characterized by at least three distinct positions: The first of these asserts that form and content are part of a dynamic whole that is irreducible (Colby & Kohlberg, 1987a; Vuyk, 1981a, 1981b). Universal processes may exist, but these cannot be studied independently of their content. A second position is that developmental differences in both structural and content features of behavior are an artifact of social transmission, rather than the result of internal processes (Bandura, 1986; Shweder, Mahapatra, & Miller, 1987). In this view, there is no basis for distinguishing between them, because they both emerge from the same source. A third position, and the one we take, is that structure and content, though they are part of a dynamic whole, have distinct features. Structures, at the level of operations, undergo a series of universally observable hierarchical integrations. It is the content of these operational structures that varies. Structure and content, looked at in this way, can be identified and isolated for the purpose of understanding both their distinct qualities and their interrelations.

Hierarchical Complexity Theory posits a three-layer model of conceptual structure. In this model, the surface layer represents conceptual content, the middle layer represents domain-level structure, and the central layer represents "core" structure.

The Lectical™ Assessment System (LAS) targets core structures. These are hierarchical order of abstraction and logical structure. Most domain-based scoring systems target domain-level structures such as sociomoral perspective. Many of these scoring systems also target conceptual content.

LAS analysts assign a score based on hierarchical order of abstraction and logical structure. To do this, they must be able to observe how these manifest in a given performance. This means that scoring is an iterative process—one in which the rater moves back and forth from one layer of structure to the next, finally converging on an interpretation of the core structure of a performance.

For example, a rater was asked to score the following interview segment:

[COULD YOU HAVE A GOOD LIFE WITHOUT HAVING HAD A GOOD EDUCATION?]
Yeah, probably so, I would say. I wouldn’t...it would be richer with education, but it wouldn’t...
[WHY DO YOU THINK IT WOULD BE RICHER WITH EDUCATION?]
Well, you just, your mind would be open to a lot more things. (Good Education 0212)

The rater's response illustrates how each layer of structure plays a role in the scoring process:

"Well, this isn’t a very sophisticated notion of the role of education in the good life. Especially because, at first, I thought that he was saying that you’d be richer, money-wise (laughter), with an education. That would make 'richer' a representational notion, but I see that it’s actually at least abstract, because it’s related to this idea of open-mindedness. It seems there are two variables [richer life, open mind] that are in a logical relation to one another…as in, "If you get a good education, your mind will be more open, and therefore you will have a richer life." This is at least an abstract mapping, but could it be higher than that? Well, richer life could be higher than abstract, and so could open mind, so I’m looking for evidence that they are…but the perspective here is of the individual person and his life, without bringing in anyone else’s perspective, or a social perspective, so you can’t say, really. Abstract mappings; I’ll stick with abstract mappings."

In this example, the rater appeals to all three levels of structure. The content level is referenced in her initial attempt to understand the argument, and again when she double checks her understanding at the end. The domain structure level is briefly included when she examines the social perspective of the respondent to see if there are grounds for considering the possibility that the statement is higher than abstract mappings. The core structure is reflected in her analysis of the hierarchical order of abstraction and logical structure of the argument (abstract variables, logical relation).

It is easy to see from this example how central meaning is to the scoring process. Without a correct interpretation of the meaning of a statement, the rater cannot even begin the process of scoring. For example, knowing which sense of richer is intended by the respondent is essential to a correct interpretation of the hierarchical order of abstraction of the concept.