Model of hierarchical complexity - AbsoluteAstronomy.com

The model of hierarchical complexity is a framework for scoring how complex a behavior

Behavior

Behavior or behaviour refers to the actions and mannerisms made by organisms, systems, or artificial entities in conjunction with its environment, which includes the other systems or organisms around as well as the physical environment...

is. It quantifies the order of hierarchical complexity of a task based on mathematical principles of how the information is organized and of information science

Information science

-Introduction:Information science is an interdisciplinary science primarily concerned with the analysis, collection, classification, manipulation, storage, retrieval and dissemination of information...

. This model has been developed by Michael Commons

Michael Commons

Michael Lamport Commons is a theoretical behavioral scientist and a complex systems scientist. He developed the Model of Hierarchical Complexity...

and others since the 1980s.

Overview

The model of hierarchical complexity (MHC), which has been presented as a formal theory, is a framework for scoring how complex a behavior is. Developed by Michael Lamport Commons

Michael Commons

Michael Lamport Commons is a theoretical behavioral scientist and a complex systems scientist. He developed the Model of Hierarchical Complexity...

, it quantifies the order of hierarchical complexity of a task based on mathematical principles of how the information is organized, and of information science

Information science

. Its forerunner was the General Stage Model. It is a model in mathematical psychology

Mathematical psychology

Mathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior...

.

Behaviors that may be scored include those of individual humans or their social groupings (e.g., organizations, governments, societies), animals, or machines. It enables scoring the hierarchical complexity of task accomplishment in any domain. It is based on the very simple notions that higher order task actions are a) defined in terms the next lower ones (creating hierarchy), b) they organize those actions c) in a non-arbitrary way (differentiating them from simple chains of behavior insuring a match between the model-designated orders and the real world orders). It is cross-cultural

Cross-cultural

cross-cultural may refer to*cross-cultural studies, a comparative tendency in various fields of cultural analysis*cross-cultural communication, a field of study that looks at how people from differing cultural backgrounds communicate...

ly and cross-species valid. The reason it applies cross-culturally is that the scoring is based on the mathematical complexity of the hierarchical organization of information. Scoring does not depend upon the content of the information (e.g., what is done, said, written, or analyzed) but upon how the information is organized.

The MHC is a non-mentalistic model of developmental stages. It specifies 15 orders of hierarchical complexity and their corresponding stages. It is different from previous proposals about developmental stage applied to humans. Instead of attributing behavioral changes across a person's age to the development of mental structures or schema

Schema (psychology)

A schema , in psychology and cognitive science, describes any of several concepts including:* An organized pattern of thought or behavior.* A structured cluster of pre-conceived ideas....

, this model posits that task sequences of task behaviors form hierarchies that become increasingly complex. Because less complex tasks must be completed and practiced before more complex tasks can be acquired, this accounts for the developmental changes seen, for example, in individual persons' performance of complex tasks. (For example, a person cannot perform arithmetic

Arithmetic

Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers...

until the numeral representations of numbers are learned. A person cannot operationally multiply the sums of numbers until addition is learned). Furthermore, previous theories of stage have confounded the stimulus and response in assessing stage by simply scoring responses and ignoring the task or stimulus.

The model of hierarchical complexity separates the task or stimulus from the performance. The participant's performance on a task of a given complexity represents the stage of developmental complexity.

Vertical complexity of tasks performed

One major basis for this developmental theory is task analysis

Task analysis

Task analysis is the analysis of how a task is accomplished, including a detailed description of both manual and mental activities, task and element durations, task frequency, task allocation, task complexity, environmental conditions, necessary clothing and equipment, and any other unique factors...

. The study of ideal tasks, including their instantiation in the real world, has been the basis of the branch of stimulus control called psychophysics

Psychophysics

Psychophysics quantitatively investigates the relationship between physical stimuli and the sensations and perceptions they effect. Psychophysics has been described as "the scientific study of the relation between stimulus and sensation" or, more completely, as "the analysis of perceptual...

. Tasks are defined as sequences of contingencies, each presenting stimuli and each requiring a behavior or a sequence of behaviors that must occur in some non-arbitrary fashion. The complexity of behaviors necessary to complete a task can be specified using the horizontal complexity and vertical complexity definitions described below. Behavior is examined with respect to the analytically-known complexity of the task.

Tasks are quantal

Quantum

In physics, a quantum is the minimum amount of any physical entity involved in an interaction. Behind this, one finds the fundamental notion that a physical property may be "quantized," referred to as "the hypothesis of quantization". This means that the magnitude can take on only certain discrete...

in nature. They are either completed correctly or not completed at all. There is no intermediate state (tertium non datur). For this reason, the Model characterizes all stages as P-hard and functionally distinct. The orders of hierarchical complexity are quantized

Quantum

like the electron

Electron

The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

atomic orbitals around the nucleus

Atomic nucleus

The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...

. Each task difficulty has an order of hierarchical complexity required to complete it correctly, corresponding to the atomic Slater

Slater

Slater is an occupational surname of English origin. A slater is a tradesman.-Surname:* Allana Slater , Australian artistic gymnast* Bert Slater , Scottish football player* Bill Slater , English footballer...

eigenstate. Since tasks of a given quantified order of hierarchical complexity require actions of a given order of hierarchical complexity to perform them, the stage of the participant's task performance is equivalent to the order of complexity of the successfully completed task. The quantal feature of tasks is thus particularly instrumental in stage assessment because the scores obtained for stages are likewise discrete.

Every task contains a multitude of subtasks (Overton, 1990). When the subtasks are carried out by the participant in a required order, the task in question is successfully completed. Therefore, the model asserts that all tasks fit in some configured sequence of tasks, making it possible to precisely determine the hierarchical order of task complexity. Tasks vary in complexity in two ways: either as horizontal (involving classical information); or as vertical (involving hierarchical information).

Horizontal complexity

Classical information describes the number of "yes–no" questions it takes to do a task. For example, if one asked a person across the room whether a penny came up heads when they flipped it, their saying "heads" would transmit 1 bit of "horizontal" information. If there were 2 pennies, one would have to ask at least two questions, one about each penny. Hence, each additional 1-bit question would add another bit. Let us say they had a four-faced top with the faces numbered 1, 2, 3, and 4. Instead of spinning it, they tossed it against a backboard as one does with dice in a game of craps

Craps

Craps is a dice game in which players place wagers on the outcome of the roll, or a series of rolls, of a pair of dice. Players may wager money against each other or a bank...

. Again, there would be 2 bits. One could ask them whether the face had an even number. If it did, one would then ask if it were a 2. Horizontal complexity, then, is the sum of bits required by just such tasks as these.

Vertical complexity

Hierarchical complexity refers to the number of recursion

Recursion

Recursion is the process of repeating items in a self-similar way. For instance, when the surfaces of two mirrors are exactly parallel with each other the nested images that occur are a form of infinite recursion. The term has a variety of meanings specific to a variety of disciplines ranging from...

s that the coordinating actions must perform on a set of primary elements. Actions at a higher order of hierarchical complexity: (a) are defined in terms of actions at the next lower order of hierarchical complexity; (b) organize and transform the lower-order actions (see Figure 2); (c) produce organizations of lower-order actions that are qualitatively new and not arbitrary, and cannot be accomplished by those lower-order actions alone. Once these conditions have been met, we say the higher-order action coordinates the actions of the next lower order.

To illustrate how lower actions get organized into more hierarchically complex actions, let us turn to a simple example. Completing the entire operation 3 × (4 + 1) constitutes a task requiring the distributive act. That act non-arbitrarily orders adding and multiplying to coordinate them. The distributive act is therefore one order more hierarchically complex than the acts of adding and multiplying alone; it indicates the singular proper sequence of the simpler actions. Although simply adding results in the same answer, people who can do both display a greater freedom of mental functioning. Additional layers of abstraction can be applied. Thus, the order of complexity of the task is determined through analyzing the demands of each task by breaking it down into its constituent parts.

The hierarchical complexity of a task refers to the number of concatenation operations it contains, that is, the number of recursions that the coordinating actions must perform. An order-three task has three concatenation operations. A task of order three operates on one or more tasks of vertical order two and a task of order two operates on one or more tasks of vertical order one (the simplest tasks).

Stages of development

The notion of stages or stagecraft

Stagecraft

Stagecraft is a generic term referring to the technical aspects of theatrical, film, and video production. It includes, but is not limited to, constructing and rigging scenery, hanging and focusing of lighting, design and procurement of costumes, makeup, procurement of props, stage management, and...

is fundamental in the description of human

Human evolution

Human evolution refers to the evolutionary history of the genus Homo, including the emergence of Homo sapiens as a distinct species and as a unique category of hominids and mammals...

, organism

Organism

In biology, an organism is any contiguous living system . In at least some form, all organisms are capable of response to stimuli, reproduction, growth and development, and maintenance of homoeostasis as a stable whole.An organism may either be unicellular or, as in the case of humans, comprise...

ic, and machine

Technological evolution

Technological evolution is the name of a science and technology studies theory describing technology development, developed by Czech philosopher Radovan Richta.-Theory of technological evolution:...

evolution

Evolution (term)

The English noun evolution refers to any kind of gradual change.It is used in biology, of biological evolution, in economics, historical linguistics, and many other technical fields where systems develop or change gradually over time, e.g...

. Previously it has been defined in some ad hoc ways. Here, it is described formally in terms of the Model of Hierarchical Complexity (MHC).

Formal definition of stage

Since actions are defined inductively, so is the function h, known as the order of the hierarchical complexity. To each action A, we wish to associate a notion of that action's hierarchical complexity, h(A). Given a collection of actions A and a participant S performing A, the stage of performance of S on A is the highest order of the actions in A completed successfully at least once, i.e., it is: stage (S, A) = max{h(A) | A ∈ A and A completed successfully by S}. Thus, the notion of stage is discontinuous

Classification of discontinuities

Continuous functions are of utmost importance in mathematics and applications. However, not all functions are continuous. If a function is not continuous at a point in its domain, one says that it has a discontinuity there...

, having the same transitional gaps as the orders of hierarchical complexity. This is in accordance with previous definitions.

Because MHC stages are conceptualized in terms of the hierarchical complexity of tasks rather than in terms of mental representations (as in Piaget's stages), the highest stage represents successful performances on the most hierarchically complex tasks rather than intellectual maturity. Table 1 gives descriptions of each stage.

Stages of hierarchical complexity

Table 1. Stages described in the Model of Hierarchical Complexity
Order or stage	What they do	How they do it	End result
0 – calculatory	Exact computation Computation Computation is defined as any type of calculation. Also defined as use of computer technology in Information processing.Computation is a process following a well-defined model understood and expressed in an algorithm, protocol, network topology, etc... only, no generalization Generalization A generalization of a concept is an extension of the concept to less-specific criteria. It is a foundational element of logic and human reasoning. Generalizations posit the existence of a domain or set of elements, as well as one or more common characteristics shared by those elements. As such, it...	Human-made programs manipulate 0, 1, not 2 or 3.	Minimal human result. Literal, unreasoning computer programs (at Turing's alpha layer) act in a way analogous to this stage.
1 – sensory or motor	Discriminate in a rote Rote learning Rote learning is a learning technique which focuses on memorization. The major practice involved in rote learning is learning by repetition by which students commit information to memory in a highly structured way. The idea is that one will be able to quickly recall the meaning of the material the... fashion, stimuli Stimulus (physiology) In physiology, a stimulus is a detectable change in the internal or external environment. The ability of an organism or organ to respond to external stimuli is called sensitivity.... generalization, move	Move limbs, lips, toes, eyes, elbows, head; view objects or move	Discriminative establishing and conditioned Classical conditioning Classical conditioning is a form of conditioning that was first demonstrated by Ivan Pavlov... reinforcing stimuli
2 – circular sensory-motor	Form open-ended proper classes Class (set theory) In set theory and its applications throughout mathematics, a class is a collection of sets which can be unambiguously defined by a property that all its members share. The precise definition of "class" depends on foundational context...	Reach, touch, grab, shake objects, circular babble	Open ended proper classes, phoneme Phoneme In a language or dialect, a phoneme is the smallest segmental unit of sound employed to form meaningful contrasts between utterances.... s, archiphonemes
3 – sensory-motor	Form concept Concept The word concept is used in ordinary language as well as in almost all academic disciplines. Particularly in philosophy, psychology and cognitive sciences the term is much used and much discussed. WordNet defines concept: "conception, construct ". However, the meaning of the term concept is much... s	Respond to stimuli in a class successfully and non-stochastically	Morpheme Morpheme In linguistics, a morpheme is the smallest semantically meaningful unit in a language. The field of study dedicated to morphemes is called morphology. A morpheme is not identical to a word, and the principal difference between the two is that a morpheme may or may not stand alone, whereas a word,... s, concepts
4 – nominal	Find relations among concepts; use names	Find relations among concepts; use names	Single words: ejaculatives & exclamations, verbs, nouns, number names, letter names
5 – sentential	Imitate and acquire sequences; follows short sequential acts	Generalize match-dependent task actions; chain words	Various forms of pronouns: subject (I), object (me), possessive adjective (my), possessive pronoun (mine), and reflexive (myself) for various persons (I, you, he, she, it, we, y'all, they)
6 – preoperational	Make simple deduction Deductive reasoning Deductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypothesis... s; follow lists of sequential acts; tell stories	Count event Phenomenon A phenomenon , plural phenomena, is any observable occurrence. Phenomena are often, but not always, understood as 'appearances' or 'experiences'... events and objects; connect the dots; combine numbers and simple proposition Proposition In logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence... s	Connectives: as, when, then, why, before; products of simple operations
7 – primary	Simple logic Logic In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science... al deduction and empirical Empirical The word empirical denotes information gained by means of observation or experimentation. Empirical data are data produced by an experiment or observation.... rules involving time sequence; simple arithmetic	Adds, subtracts, multiplies, divides, counts, proves, does series of tasks on own	Times, places, counts acts, actors, arithmetic outcome, sequence from calculation
8 – concrete	Carry out full arithmetic Arithmetic Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers... , form clique Clique A clique is an exclusive group of people who share common interests, views, purposes, patterns of behavior, or ethnicity. A clique as a reference group can be either normative or comparative. Membership in a clique is typically exclusive, and qualifications for membership may be social or... s, plan deals	Does long division Long division In arithmetic, long division is a standard procedure suitable for dividing simple or complex multidigit numbers. It breaks down a division problem into a series of easier steps. As in all division problems, one number, called the dividend, is divided by another, called the divisor, producing a... , short division, follows complex social rules Convention (norm) A convention is a set of agreed, stipulated or generally accepted standards, norms, social norms or criteria, often taking the form of a custom.... , ignores simple social rules, takes and coordinates perspective Perspective (cognitive) Perspective in theory of cognition is the choice of a context or a reference from which to sense, categorize, measure or codify experience, cohesively forming a coherent belief, typically for comparing with another... of other and self	Interrelations, social events, what happened among others, reasonable deals, history, geography
9 – abstract	Discriminate variables Variable (mathematics) In mathematics, a variable is a value that may change within the scope of a given problem or set of operations. In contrast, a constant is a value that remains unchanged, though often unknown or undetermined. The concepts of constants and variables are fundamental to many areas of mathematics and... such as stereotype Stereotype A stereotype is a popular belief about specific social groups or types of individuals. The concepts of "stereotype" and "prejudice" are often confused with many other different meanings... s; logical quantification Quantification Quantification has several distinct senses. In mathematics and empirical science, it is the act of counting and measuring that maps human sense observations and experiences into members of some set of numbers. Quantification in this sense is fundamental to the scientific method.In logic,... ; (none, some, all)	Form variables out of finite classes; make and quantify propositions	Variable time, place, act, actor, state, type; quantifiers (all, none, some); categorical assertions Categorical proposition A categorical proposition contains two categorical terms, the subject and the predicate, and affirms or denies the latter of the former. Categorical propositions occur in categorical syllogisms and both are discussed in Aristotle's Prior Analytics.... (e.g., "We all die")
10 – formal	Argue using empirical or logical evidence Evidence Evidence in its broadest sense includes everything that is used to determine or demonstrate the truth of an assertion. Giving or procuring evidence is the process of using those things that are either presumed to be true, or were themselves proven via evidence, to demonstrate an assertion's truth... ; Logic is linear, 1 dimensional	Solve problems with one unknown using algebra Algebra Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures... , logic Logic In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science... and empiricism Empiricism Empiricism is a theory of knowledge that asserts that knowledge comes only or primarily via sensory experience. One of several views of epistemology, the study of human knowledge, along with rationalism, idealism and historicism, empiricism emphasizes the role of experience and evidence,...	Relationships (for example: causality Causality Causality is the relationship between an event and a second event , where the second event is understood as a consequence of the first.... ) are formed out of variables; words: linear, logical, one-dimensional, if then, thus, therefore, because; correct scientific solutions
11 – systematic	Construct multivariate system System System is a set of interacting or interdependent components forming an integrated whole.... s and matrices Matrix (mathematics) In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...	Coordinates more than one variable as input; consider relationships in contexts.	Events Phenomenon A phenomenon , plural phenomena, is any observable occurrence. Phenomena are often, but not always, understood as 'appearances' or 'experiences'... and concepts situated in a multivariate context; systems are formed out of relations; systems: legal, societal, corporate, economic, nation Nation A nation may refer to a community of people who share a common language, culture, ethnicity, descent, and/or history. In this definition, a nation has no physical borders. However, it can also refer to people who share a common territory and government irrespective of their ethnic make-up... al
12 – metasystematic	Construct multi-systems and metasystems out of disparate systems	Create metasystems out of systems; compare systems and perspectives; name properties of systems: e.g. homomorphic, isomorphic, complete Completeness In general, an object is complete if nothing needs to be added to it. This notion is made more specific in various fields.-Logical completeness:In logic, semantic completeness is the converse of soundness for formal systems... , consistent (such as tested by consistency proof Consistency proof In logic, a consistent theory is one that does not contain a contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent if and only if it has a model, i.e. there exists an interpretation under which all... s), commensurable	Metasystems and supersystems are formed out of systems of relationships
13 – paradigmatic	Fit metasystems together to form new paradigm Paradigm The word paradigm has been used in science to describe distinct concepts. It comes from Greek "παράδειγμα" , "pattern, example, sample" from the verb "παραδείκνυμι" , "exhibit, represent, expose" and that from "παρά" , "beside, beyond" + "δείκνυμι" , "to show, to point out".The original Greek... s	Synthesize metasystems	Paradigms are formed out of multiple metasystems
14 – cross-paradigmatic	Fit paradigms together to form new fields	Form new fields by crossing paradigms	New fields are formed out of multiple paradigms

Relationship with Piaget's theory

There are some commonalities between the Piagetian

Theory of cognitive development

Piaget's theory of cognitive development is a comprehensive theory about the nature and development of human intelligence first developed by Jean Piaget. It is primarily known as a developmental stage theory, but in fact, it deals with the nature of knowledge itself and how humans come gradually to...

and Commons' notions of stage and many more things that are different. In both, one finds:

Higher-order actions defined in terms of lower-order actions. This forces the hierarchical nature of the relations and makes the higher-order tasks include the lower ones and requires that lower-order actions are hierarchically contained within the relative definitions of the higher-order tasks.

Higher-order of complexity actions organize those lower-order actions. This makes them more powerful. Lower-order actions are organized by the actions with a higher order of complexity, i.e., the more complex tasks.

What Commons et al. (1998) have added includes:

Higher order of complexity actions organize those lower-order actions in a non-arbitrary way.

This makes it possible for the Model's application to meet real world requirements, including the empirical and analytic. Arbitrary organization of lower order of complexity actions, possible in the Piagetian theory, despite the hierarchical definition structure, leaves the functional correlates of the interrelationships of tasks of differential complexity formulations ill-defined.

Moreover, the model is consistent with the neo-Piagetian theories of cognitive development

Neo-Piagetian theories of cognitive development

Jean Piaget's theory of cognitive development has been criticized on many grounds. One criticism is concerned with the very nature of development itself. It is suggested that Piaget's theory does not explain why development from stage to stage occurs. The theory is also criticized for ignoring...

. According to these theories, progression to higher stages or levels of cognitive development is caused by increases in processing efficiency and working memory

Working memory

Working memory has been defined as the system which actively holds information in the mind to do verbal and nonverbal tasks such as reasoning and comprehension, and to make it available for further information processing...

capacity. That is, higher-order stages place increasingly higher demands on these functions of information processing, so that their order of appearance reflects the information processing possibilities at successive ages (Demetriou, 1998).

The following dimensions are inherent in the application:

Task and performance are separated.
All tasks have an order of hierarchical complexity.
There is only one sequence of orders of hierarchical complexity.
Hence, there is structure of the whole for ideal tasks
Ideal tasks
Ideal tasks arise during task analysis. Ideal tasks are different from real tasks. They are ideals in the Platonic sense of a circle being an ideal where as a drawn circle is flawed and real...

and actions.
There are transitional gaps between the orders of hierarchical complexity.
Stage is defined as the most hierarchically complex task solved.
There are discrete gaps in Rasch
Rasch
Rasch is surname of:* Albertina Rasch , a Jewish Austrian-born naturalized American dancer and choreographer* Bent Peder Rasch , a Danish sprint canoer* Carl L...

Scaled Stage of Performance.
Performance stage is different task area to task area.
There is no structure of the whole—horizontal decaláge—for performance. It is not inconsistency in thinking within a developmental stage. Decaláge is the normal modal state of affairs.

Orders and corresponding stages

The MHC specifies 15 orders of hierarchical complexity and their corresponding stages, showing that each of Piaget's substages, in fact, are robustly hard stages. Commons also adds four postformal stages: Systematic stage 11, Metasystematic stage 12, Paradigmatic stage 13, and Crossparadigmatic stage 14. It may be the Piaget's consolidate formal stage is the same as the systematic stage. There is one other difference in the orders and stages. At the suggestion of Biggs and Biggs, the sentential stage 5 was added. The sequence is as follows: (0) computory, (1) sensory & motor, (2) circular sensory-motor, (3) sensory-motor, (4) nominal, the new (5) sentential, (6) preoperational, (7) primary, (8) concrete, (9) abstract, (10) formal, and the four postformal: (11) systematic, (12) metasystematic, (13) paradigmatic, and (14) cross-paradigmatic. The first four stages (0–3) correspond to Piaget's sensorimotor stage at which infants and very young children perform. The sentential stage was added at Fischer's suggestion (1981, personal communication) citing Biggs & Collis (1982). Adolescents and adults can perform at any of the subsequent stages. MHC stages 4 through 5 correspond to Piaget's pre-operational stage; 6 through 8 correspond to his concrete operational stage; and 9 through 11 correspond to his formal operational stage.

The three highest stages in the MHC are not represented in Piaget's model. These stages from the Model of Hierarchical Complexity have extensively influenced the field of Positive Adult Development

Positive Adult Development

Positive Adult Development is one of the four major forms of adult developmental study that can be identified. The other three forms are directionless change, stasis, and decline...

. Few individuals perform at stages above formal operations. More complex behaviors characterize multiple system models. Some adults are said to develop alternatives to, and perspectives on, formal operations. They use formal operations within a "higher" system of operations and transcend the limitations of formal operations. In any case, these are all ways in which these theories argue for and present converging evidence that some adults are using forms of reasoning that are more complex than formal operations with which Piaget's model ended.

Empirical research using the model

The MHC has a broad range of applicability. The mathematical foundation of the model makes it an excellent research tool to be used by anyone examining task performance that is organized into stages. It is designed to assess development based on the order of complexity which the individual utilizes to organize information. The MHC offers a singular mathematical method of measuring stages in any domain because the tasks presented can contain any kind of information. The model thus allows for a standard quantitative analysis of developmental complexity in any cultural setting. Other advantages of this model include its avoidance of mentalistic or contextual explanations, as well as its use of purely quantitative principles which are universally applicable in any context.

The following can use the Model of Hierarchical Complexity to quantitatively assess developmental stages:

Cross-cultural
Cross-cultural
cross-cultural may refer to*cross-cultural studies, a comparative tendency in various fields of cultural analysis*cross-cultural communication, a field of study that looks at how people from differing cultural backgrounds communicate...

developmentalists;
Animal developmentalists;
Evolutionary psychologists;
Organizational psychologists
Industrial and organizational psychology
Industrial and organizational psychology is the scientific study of employees, workplaces, and organizations. Industrial and organizational psychologists contribute to an organization's success by improving the performance and well-being of its people...

;
Developmental political psychologists;
Learning theorists;
Perception
Perception
Perception is the process of attaining awareness or understanding of the environment by organizing and interpreting sensory information. All perception involves signals in the nervous system, which in turn result from physical stimulation of the sense organs...

researchers;
History of science
History of science
The history of science is the study of the historical development of human understandings of the natural world and the domains of the social sciences....

historians;
Educators;
Therapists;
Anthropologists.

The following list shows the large range of domains to which the Model has been applied. In one representative study, Commons, Goodheart, and Dawson (1997) found, using Rasch (1980) analysis, that hierarchical complexity of a given task predicts stage of a performance, the correlation being r = 0.92. Correlations of similar magnitude have been found in a number of the studies.

List of examples

List of examples of tasks studied using the Model of Hierarchical Complexity or Fischer’s Skill Theory (1980):

Algebra (Commons, in preparation)
Animal stages (Commons & Miller, 2004)
Atheism (Commons-Miller, 2005)
Attachment and Loss (Commons, 1991; Miller & Lee, 2000)
Balance beam and pendulum (Commons, Goodheart, & Bresette, 1995; Commons, Pekker, et al., 2007)
Contingencies of reinforcement (Commons, in preparation)
Counselor stages (Lovell, 2004)
Empathy of Hominids (Commons & Wolfsont, 2002)
Epistemology (Kitchener & King, 1990; Kitchener & Fischer, 1990)
Evaluative reasoning (Dawson, 2000)
Four Story problem (Commons, Richards & Kuhn, 1982; Kallio & Helkama, 1991)
Good Education (Dawson-Tunik, 2004)
Good Interpersonal (Armon, 1989)
Good Work (Armon, 1993)
Honesty and Kindness (Lamborn, Fischer & Pipp, 1994)
Informed consent (Commons & Rodriguez, 1990, 1993; Commons, Goodheart, Rodriguez, & Gutheil, 2006; Commons, Rodriguez, Adams, Goodheart, Gutheil, & Cyr, 2007).
Language stages (Commons, et al., 2007)
Leadership before and after crises (Oliver, 2004)
Loevinger's Sentence Completion task (Cook-Greuter, 1990)
Moral Judgment (Armon & Dawson, 1997; Dawson, 2000)
Music (Beethoven) (Funk, 1989)
Orienteering (Commons, in preparation)
Physics tasks (Inhelder & Piaget, 1958)
Political development (Sonnert & Commons, 1994)
Relationships (Armon, 1984a, 1984b)
Report patient's prior crimes (Commons, Lee, Gutheil, et al., 1995)
Social perspective-taking (Commons & Rodriguez, 1990; 1993)
Spirituality (Miller & Cook-Greuter, 2000)
Tool Making of Hominids (Commons & Miller 2002)
Views of the Agood life@ (Armon, 1984c; Danaher, 1993; Dawson, 2000; Lam, 1995)
Workplace culture (Commons, Krause, Fayer, & Meaney, 1993)
Workplace organization (Bowman, 1996a, 1996b)
Writing (Commons & DeVos, 1985)

Literature

Armon, C. (1984a). Ideals of the good life and moral judgment: Ethical reasoning across the life span. In M.L. Commons, F.A. Richards, & C. Armon (Eds.), Beyond formal operations: Vol. 1. Late adolescent and adult cognitive development (pp. 357–380). New York: Praeger.
Armon, C. (1984c). Ideals of the good life and moral judgment: Evaluative reasoning in children and adults. Moral Education Forum, 9(2).
Armon, C. (1989). Individuality and autonomy in adult ethical reasoning. In M.L. Commons, J.D. Sinnott, F.A. Richards, & C. Armon (Eds.), Adult development, Vol. 1. Comparisons and applications of adolescent and adult developmental models, (pp. 179–196). New York: Praeger.
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