Tabachneck-Schijf, H. J., Leonardo, A. M., Simon, H. A. (1997). CaMeRa: Computational Model of Multiple Representations. Cognitive Science, 22 (3), 305-350.

@Article{TabachneckschijfLeonardoSimon1997,
  author = 	 {Tabachneck-Schijf, Hermina and Leonardo, Anthony
		  and Simon, Herbert},
  title = 	 {CaMeRa: A Computational Model of Multiple Representations},
  journal = 	 {Cognitive Science},
  year = 	 {1997},
  number = 	 {3},
  volume = 	 {21},
  pages = 	 {305--350}
}

Author of the summary: Michael A. Schildknecht, 2010, mschildk@connect.carleton.ca

Cite this paper for:

SYSTEM: CaMeRa (Computational model of Multiple Representations)
Experts are dependent on multiple representations. [p306]
Different representations that contain equivalent information often differ computationally (Glasgow 1993, Larkin & Simon 1987). [p306]
A representation has 2 components: a format for recording/presenting information and processes for using/modifying information. [p307]
Different modalities (visual vs. verbal) have different representations. [p309]
Mental images contained in the Mind’s Eye resemble visual stimuli closely but can differ in levels of detail (Kosslyn 1980, Anderson 1985). [p309]
All inferences are made on working memory contents. [p311]
Experts can use and integrate multiple representations; novices have difficulty (Tabachneck 1982). [p312]
Pictorial representations are often computationally advantageous (Larkin & Simon 1987). [p315]
External representations serve as supplemental memory (Koedinger & Anderson 1990, Kotovsky, Hayes & Simon 1985, Zhang and Norman 1994). [p315]
Different subrepresentations exist for spatial and object information (Farah 1990, Kosslyn 1994). [p316]
Perception separates object from ground. [p317]
Objects can be represented in at least 3 distinct reference frames. [p317]
Different sensory modes of a model may associate with one another (within a memory layer).
Modifications are initiated only by STM and only to memory systems of the same modality. [p323]

CaMeRa simulates expert problem solving using multiple data representations (economics example: finding equilibrium price on supply/demand graphs). Experts depend on computational differences between multiple representations but novices fail to successfully incorporate them. [p.312]

“A representation has two components:

A format for recording and presenting information.
Processes for using and modifying the information.

Neither a format nor a set of processes is sufficient by itself to define a representation” [p307]

Pictorial: parts of the CaMeRa model that “process graphs and drawings…” [p307]

Mind’s Eye Hypothesis (Glasgow 1993, Kosslyn 1980, Tabachneck & Simon 1996). [p309]
CaMeRa treats images from perception and memory in the same way (same operators/data structures). Perceived pictorial cues serve to initiate reasoning.

Structure of the model:

The CaMeRa model currently consists of an external pictorial display (‘blackboard’), as well as verbal and pictorial LTM and STM. Verbal and pictorial memory systems are separate modalities with modality-specific representations. Verbal memory is represented with a propositional list structure and pictorial memory with node-link structures. [p309]

Blackboard:
Graphs on the blackboard are read into the model via a tiered visual buffer that discriminates geometric features by means of Gestalt principles and pixel activation patterns. [p328]

Pictorial LTM:
Contains mathematical equations of lines and labels (as vectors of bits) composing a Supply/Demand graph. Contains functions to project these graphs onto the visual buffer. [p324]

Pictorial STM:
Contains object data structure and spatial structure to describe object features and location. [p326]

Verbal LTM:
Contains a template of a propositional relation to represent verbal knowledge:
“conceptC is the typeR relation between term1 and term2 ” [p325]

Verbal STM:
Represents propositions using the template found in verbal LTM. [330]

CaMeRa treats the modalities as parallel processes that can access but not modify each other as seen below.
 The following diagram (figure 7) is used to illustrate the structure of a Supply Line (Supply/Demand Graph) in CaMeRa.


         _______________________                 _______________________________________
        |                       |               |                                       |
        | Pictorial LTM         |               |       Verbal LTM                      |
        |                       | <---------->  |                                       |
        | prototype:    y = x   |               |       name:           Supply          |
        |_______ _______________|               |       relation:       proportional    |
                +                               |       between:        Price           |
                +                               |                       Quantity        |
                +                               |______________________ ________________|			
                +                                                      +
                +                                                      +
                +                                                      +
         _______+_______________________                 ______________+________________________
        |                               |               |                                       |
        | Pictorial STM (Mind’s Eye)    |               | Verbal STM (Mind’s Ear)               |
        |                               | ---------->   |                                       |
        | Object Form:                  |               | name:         Supply                  |
        | equation: y = x + 9.0         |               | relation:     Proportional            |
        | instance number: 1            |               | between:      Price                   |
        |                               |               |               Quantity                |
        | Spatial Location:             |               |                                       |
        | (x1, y1): (15, 135)           |               | instance number: 1                    |
        | (x2, y2): (135, 15)           |               |_______________________________________|
        |_______________________________|

--------> 	Indicates information can be accessed

  
+++++++++	Indicates that modifications 
		can take place between associated structures

Future additions to CaMeRa:

Differences in resolution of external images and images stored in pictorial STM.
Decay of visual buffer and pictorial STM requiring periodic ‘refreshing’ of images from the blackboard.
Corrections learned in LTM if STM inferences showed erroneous data.
Referents between modalities removed to simulate a novice problem solver.
Capabilities for converting between coordinate systems for object-, background- and self-oriented representations.
Capacity limits placed on both verbal and pictorial STM to simulate a novice problem solver.
Implementation of an auditory buffer to simulate the Mind’s Ear.
Verbal external memory used to input initial goal statement and to build up verbal LTM.