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A Comparison Post Piagetian Models Stages and Levels About thirty-five years ago, the first neo-Piagetian models began to appear Although Piaget opposed these models, they have persisted These new models have some similarities to Piaget’s theory and some differences Comparing a Number of Neo-Piagetian Models Which proposals have generating mechanisms? How many stages and levels are produced? What assumptions does each make? To what extent does each proposal account for all known stages and levels? How complete are they? To what extent are they content bound? What is the proposed mechanism of stage transition? Inhelder and Piaget Higher stages are defined in terms of lower ones Higher stages organize the actions from the lower stages Their theory did not separate tasks and performances Coded performances without examining task characteristics Posited schemas, operations and other inferred mental actions Notion of stage transition is not based on a learning theory Proposed four overall stages, with 2 to 3 substages in each (a total of 9 levels) Inhelder and Piaget Sensory Motor A (Circular Sensory Motor 2) Sensory Motor B (Sensory Motor 3) Preoperational A (Nominal 4) Preoperational B (Preoperations 6) Concrete Operations A (Primary 7) Concrete Operations B (Concrete 8) Formal Operational A (Abstract 9) Formal Operational B (Formal 10) Formal Operational C (Systemic 11) Pascual Leone Pascual Leone (1972) developed the first new theory that fit much of the data This began the Neo Piagetian era Pascual Leone was the first to divide each Inhelder and Piaget’s stages into two stages His was a psychological theory of levels of human development The generator mechanism was based on working memory and how that controls executive function One of his students was Robbie Case There are others who have followed in this tradition including but not limited to Frye and Zelazo? A generator theory has been proposed by Halford It does not map at all onto other Neo-Piagetian theories, including Pascual Leone’s, Fischer’s or Commons? Kurt Fischer’s Theory It is also a generator theory It uses mapping to generate the levels It is the second most complete It is only missing the Sentential stage, which Fischer suggested for the Model of Hierarchical Complexity It does not include postformal stages beyond the Metasystematic Stage It does not separate task characteristics from performance but that is acceptable to Fischer It includes support, making clear how to test better for levels The Model of Hierarchical Complexity It separates task characteristics (Orders of Hierarchical Complexity) from performance (Rasch Scaled Stage Scores) As in Piaget, higher order task actions defined in terms of lower order ones Also, their organization is non arbitrary Content, context less, and animal free It mathematically proves there is only one sequence of at least 15 orders It has a similar number of stages to Fischer’s but adds The Calculatory Stage 0 (Computers) Sentential Stage 5 (Sequences of Representations) It also adds two postformal stages Paradigmatic Stage 13 Cross-paradigmatic Stage 14 MHC Stage and Stage Numbers Computational 0 Sensory or Motor 1 Circular Sensory Motor 2 Sensory-Motor 3 Nominal 4 Sentential 5 Preoperational 6 Primary 7 Concrete 8 Abstract 9 Formal 10 Systematic 11 Metasystematic 12 Paradigmatic 13 Cross-Paradigmatic 14 Many other theories have many fewer stages Halford has only 4 major groupings Some have at least the postformal stages But they have too many assumptions making them content bound Kohlberg, Kegan, etc. are examples Others are perceptual? These include Feldman and Leeuwenberg Other models have used other metrics of complexity Simon’s theory is about horizontal complexity and not even implicitly stage-like But it does have chunking Many of the traditional stage theories have specialized in specific domains because they found differences in performances across domains Why would there be these differences? As Andrew Richards will show, when looking at just the physical and mathematical sciences, there appears to be only one domain Why would that be so? The reason is that the content in tasks from these domains come relatively well coded There is only a general specialized knowledge of the words used and in a few cases such as algebra and infinity, some education Content and Context Variability and Coding Difficulties We posit that almost all the content and context variability across domains is due to encoding difficulties In the Heinz dilemma, one has to figure out what the variables are. They do not jump out What is the system of rights to live made up of What are the relations and their underlying variables What is the system of duties made up of What are the relations and their underlying variables? Studying the Effects of Coding We need to find out what are the coding requirements for tasks (Problems, vignettes and dilemmas) Vignettes and dilemmas are written in narrative form There is no precoding of entities In mathematics problems, variables are precoded The effects of precoding versus no coding could be compared Vignettes could be given two ways One in which there are suggested codes to tasks The other without the precoding Are there more stages? Because this question always gets asked Are there stages beyond cross-paradigmatic. Yes.?We are not high stage enough to know them Are the stages universal There is only one order of hierarchical complexity which is universal Hence there can only be one correct stage theory Whether people obtain these stages is up to education and culture.