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External Mental Models

Barbara Bazzanella (University of Trento)
Paolo Bouquet (University of Trento)
Massimo Warglien (University of Venice)

This page describes an experiment which was designed to explore the experimental elicitation of external models of the premises as a tool to investigate how individuals build models of the premises and how they use them in reasoning.

Experimental design

The experiment was carried out in two phases: a baseline treatment and a control treatment.

Baseline Treatment

PARTICIPANTS


We tested 41 volunteers from VEGA Park in Venezia. The participants were 23 men and 18 women (aged from 25 to 65). For every trial, they were rewarded 1 Euro for the representation task and 1 Euro for the deductive task.

DESIGN

We asked participants to build all external models consistent with a set of premises and afterwards to draw a valid conclusion of six problems. The problems concerned features of human faces (e.g. the color of hair, or the presence of a beard).

MATERIALS

The six problems are reported below:

Task 1: If Laura has red hair, then she wears glasses
Laura doesn't wear glasses

Task 2: Either Stefano doesn't have black hair or else he wears a hat but not both
Stefano has black hair

Task 3: Antonio wears a hat or he has moustaches - or both.
Antonio doesn't wear a hat

Task 4: If Mary wears glasses then she has green eyes.
Mary wears glasses or else she has green eyes but not both

Task 5: Either Giorgio has blue eyes or else he smokes a cigar but not both
If Giorgio has brown hair then he has blue eyes.
Giorgio has blue eyes.

Task 6: Either Luigi has curled hair and he wears glasses or else Luigi has dark eyes and a beard but not both.
Luigi has curled hair

The experiment was carried out in Italian with Italian native speakers. The premises were printed on a sheet and were administrated one at time. The instructions for the task were briefly summarize at the top of each sheet. On the table used by participants to build models, there were scraps of paper reproducing the empty shape and features of a human face:
  • Eyes in 4 colours (black, blue, green and brown)
  • Beards and moustaches
  • Hair in 4 colours (black, brown, red and blonde)
  • Hats
  • Glasses
  • Cigars
Each element was provided in several instances to emphasize that the participants could build more than one model for each premise. Here you can find samples of experimental material. Models can be built by assembling objects from such a set.

PROCEDURE

The participants were tested individually in a quiet room. They were told that the experiment concerned reasoning about a series of deductive problems but that it was not a test of their intelligence. In addition they were told that they would be rewarded in proportion to their performance.

Each trial consisted of two phases:
  1. representation task
  2. deductive task
The experimenter explained that a video recording would be made so that there would an anonymous record of the sequences of models that the participants built up for each problem. The camera was placed in front of the subjects and was focused on the delimited area of a wide table on which the participants assembled their external model.

Representation task. For each problem the participants had to read carefully a first premise and then try to construct all possible models consistent with the premise. The experimenter showed a practice problem in order to familiarize the subjects with the experimental materials.
Since a premise is typically consistent with multiple models, subjects were explicitly told that they can built more than one model for each premise.

For example, given a premise (from task 1) like:

If Laura has red hair then she wears glasses

subjects are expected to build three models:
  • Laura with red hair and glasses

  • Laura with not red hair (brown, black or blonde) and not glasses

  • Laura with not red hair (brown, black or blonde) but with glasses

To represent that Laura hasn't red hair the participants could choose one of other three colours of hair or build three different models. We considered the set of models complete when all three representations are make explicit with at least one model for each. Afterward the experimenter presented a new premise, and asked to update the previously built set of models (or to build new models) to take into account the new premise(s). In the example reported above, the second premise was

Laura doesn't wear glasses

Subjects had to update the models eliminating the all faces which wear glasses.Consequently, three models were still available:

Five problems consisted of two premises and only one (task n°5) consisted of three. The participants could take as much time as they needed to carry out the task. The participants begun the proper experiment after he had asked any questions about the task and were certain that they understood it.

Control Treatment

PARTICIPANTS

We tested individually 44 volunteers ( 23 women and 21 men). They ranged in age from 19 and 65 years. Individuals didn't receive monetary reward.

MATERIALS and PROCEDURE

The participants were tested individually in a quite room. They were told that they were taking part in an experiment on deductive reasoning. Their task was to considers six problems and, for each of them to draw a conclusion (if they thought that there was one) that had to be true given that the premises were true. The subjects were presented the same six problems of baseline treatment and asked to draw a conclusion without having to construct any external representation. Each set of premises was printed on a separated page of paper and the participants wrote their answers beneath the premises. The experiment was carried out in Italian with native speakers of that language. The original materials are available here. Subjects were allowed to take as much time as they needed. On an average the task lasted 20 minutes.

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2001 - Università degli Studi di Trento