Two Concepts:Cognitive residue

and Emergent ModelsSandra HerbertMay 14, 2004

Cognitive residues

Computer Supported Collaborative Learning (CSCL)

• Many cite Salomon, Perkins & Globerson (1991) • For example

– “Effects with technology obtained during intellectual partnership with it and effects of it in terms of the transferable cognitive residue that this partnership leaves behind in the form of better mastery of skills and strategies” (Salomon, Perkins & Globerson, 1991 in Pea,1997)

– “changes in the learner’s understanding of the work domain (or the “cognitive residue”) after they have used the software” (Salomon et al. , 1991 in Quintana, Fretz, Krajcik & Soloway, 2000).

– “Salomon, Perkins, & Globerson, (1991) coined the term 'cognitive residue' a reference to a byproduct effect of learners interacting with media” (Agostino, 1999).

Salomon, Perkins & Globerson (1991)

• Doesn’t explain the term – just uses it.

• “subsequent changes in mastery of knowledge, skill or depth of understanding away from the computer”(p.3)

• “higher order thinking skills that are either activated during an activity with an intellectual tool or are explicitly modeled by it can develop and can be transferred to other dissimilar, or at least similar situations” (p.6)

Development of Salomon’s Use of “Cognitive Residue”

• Anderson(1983)is listed in references– “acquisition of cognitive skills”

• Perkins & Salomon (1988) and Salomon & Perkins (1987) – use the phrase “transfer of cognitive skills”

• Salomon, Globerson & Guterman (1989) and Salomon (1990) use the term “cognitive residue”– “improve learners' performance and to leave a

transferable cognitive residue in the form of improved competencies” (1989,p. 621)

– “stretching and internalization of cognitive operations and strategies” ( 1990, p.40)

Example – Symbolic Math Guide

• Free Flash application for TI CAS calculators• Takes users through the step-by-step algebraic

solution of problems • For example:

– the solution of equations – simplification of expressions involving algebraic

fractions• At each step SMG prompts the user to choose

from a finite list of items dedicated to the particular form of the algebra at that point in the solution.

Example – Symbolic Math Guide

• Screen dump???

Example – Symbolic Math Guide

• Cognitive residue of SMG might be:-

• A suite of strategies for tackling an algebraic problem.

• Competence in SMG favoured procedures.

• A habit of approaching an algebraic procedure in a step-by-step fashion.

• Greater algebraic expectation.

Other users of the term “cognitive residue”

• Rosenbaum, D. A. (1972). The theory of cognitive residues: A new view of fantasy. Psychological Review, Vol. 79(6), 471-486.

• Skinner, N. F., & Lynch, P. B. (1985). Cognitive residues revisited: A critical appraisal of Rosenbaum's "new view of fantasy." Imagination, Cognition & Personality, 5(4), 295-302.

Emergent models

Gravemeijer’s emergent models

• “[emergent] model evolves from a ‘model of’ the student’s [own] informal mathematical activity to a ‘model for’ more mathematical reasoning”

• “something is symbolized (model of) and the symbolization is used to reason with (model for)”– For example:

• the empty number line used to record measuring activities (model of) can be used for abstract addition or subtraction (model for)

• “ a shift from informal situated solution procedures [models of] to more formal mathematical reasoning [which is] connected with the creation of a new [for the student] mathematical reality [model for]”

(Gravemeijer & Stephan, 2002).

Gravemeijer’s emergent models

• “Modeling and symbolizing [are] an integral part of an organizing activity that aims at coming to grips with a problem situation” (Gravemeijer & Doorman, 1999, p.119)– For example: Calculus

• “problems about velocity and distance [are modeled by] graphs of discrete functions [which] later develop into models for formal mathematical reasoning about calculus” (Gravemeijer & Doorman, 1999, p.122)

• The model of-model for shift is a dynamic process • Not always one-way• Eventually “ the model becomes an entity in its own right

and serves more as a means of mathematical reasoning than as a way to symbolize mathematical activity grounded in particular settings” (Gravemeijer, 1999, p. 164)

Emergent Models: Four Levels of Activity

• Task setting– “models are initially tied to activity in specific settings and

involve situation-specific imagery”• Referent

– “models are grounded in students’ understandings of paradigmatic, experientially real settings”

• General – “emerge as students’ reasoning loses its dependency on

situation-specific imagery and the role of the models gradually change as they take on a life of their own”

• Formal– “no longer dependent on the support of models for to achieve

mathematical activity(Gravemeijer, 1999)

Example - Mathworlds

• Mathworlds is a animated simulation software developed by the SimCalc project under the direction of Prof. Jim Kaput.

• Powerful interconnectivity of multiple representations associated with simulation.

• Establishes a model of a situation which is experientially real for students.

Emergent ModelsDo students develop connected models of velocity, position and time resulting from experience with technology (e.g., a lift or a person ) ?

Emergent ModelsCan students use these models of to think and talk about the concepts related to velocity, position, and time in terms of lifts and people when technology is not present?

Emergent ModelsCan students use these models of velocity, position, and time to think and talk about velocity, position, and time in other contexts when technology is not present?

Emergent ModelsCan these models of velocity, position, and time be used as models for other rates of change (e. g., items per minute on a conveyor belt)?

Cognitive ResidueCan)?

s.herbert@ballarat.edu.au

References• Salomon, G., & Perkins, D. N. (1987). Transfer of

cognitive skills from programming: When and how? Journal of Educational Computing Research, 3(2), 149-169.

• Perkins, D. N., & Salomon, G. (1988). Teaching for transfer. Educational Leadership, 46(1), 22.

• Salomon, G., Globerson, T., & Guterman, E. (1989). The computer as a zone of proximal development: Internalizing reading-related metacognitions from a reading partner. Journal of Educational Psychology, 81(4), 620-627.

References

• Salomon, G. (1990). Cognitive effects with and of computer technology. Communication Research, 17(1), 26-44.

• Salomon, G., Perkins, D. N., & Globerson, T. (1991). Partners in cognition: Extending human intelligences with intelligent technologies. Educational Researcher(April), 2-9.

• Anderson, J. (1983). The architecture of cognition. Cambridge, MA: Harvard University Press

References• Pea, R. D. (1997). Practices of distributed intelligence

and designs for education. In G. Salomon (Ed.), Distributed cognitions: Psychological and educational considerations. (pp. 47-87). New York, NY, US: Cambridge University Press.

• Agostino, A. (1999). The relevance of media as artifact: Technology situated in context. Educational Technology & Society, 2(4).

• Quintana, C., Fretz, E., Krajcik, J., & Soloway, E. (2000). Assessment Strategies for Learner-Centered Software. In B. Fishman & S. O'Connor-Divelbiss (Eds.),Fourth International Conference of the Learning Sciences (pp. 254-255). Mahwah, NJ: Erlbaum.

References• Gravemeijer, K., & Doorman, M. (1999). Context problems in

realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39(1-3), 111-129.

• Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical Thinking & Learning, 1(2), 155.

• Gravemeijer, K. (2002). Preamble:From models to modeling. In K. Gravemeijer & R. Lehrer & B. v. Oers & L. Verschaffel (Eds.), Symbolizing, modeling and tool use in mathematics education (pp. 7-22). Netherlands: Kluuwer Academic Publishers.

• Gravemeijer, K., & Stephan, M. (2002). Emergent models as an instructional heuristic. In K. Gravemeijer & R. Lehrer & B. v. Oers & L. Verschaffel (Eds.), Symbolizing, modeling and tool use in mathematics education (pp. 145-169). Netherlands: Kluuwer Academic Publishers.

• Cognitive residues are “cognitive structures which remain ‘intact” in the mind after being displaced or absorbed by other structures” (p. 472)

• “stand as reminders of old abandoned beliefs that should now be avoided” (p. 477)

• Can be challenged through cognitive conflict causing – absorption, – modification or – intact preservation

• subordinate to the currently held structure of beliefs, constructs and schemas.

• May re-assert dominance or find expression in fantasy• Humanistic view

Rosenbaum1972

• Summarises Rosenbaum’s theory as – “ a description of hypothetical structural changes that

beliefs, constructs and schemas may undergo during an individual’s cognitive development” (p.296).

• Criticises humanistic view• Disagrees with Rosenbaum & asserts that all

residues are not preserved intact. • Comments that there have only been two

(passing) references to cognitive residues between 1972 and 1986

Skinner & Lynch1985