The Laundry Problem



Project Coordinator:
Eric Goodheart, Harvard University.
 
Project Participants:
Michael L. Commons, Harvard Medical School.
Eric Goodheart, Harvard University.
Theo L. Dawson, University of California at Berkeley.
Karen Draney, University of California at Berkeley.
Mark Wilson, University of California at Berkeley


Instrument

The Laundry Problem Task Series is a Piagetian Logical Task Series. It contains problems at the primary, concrete, abstract, formal, systematic, and metasystematic stages in the General Stage Model. The original Laundry problem had eight variants, each of which tested formal operations (Commons, Miller, and Kuhn, 1982). The problems presented the participants with a different kind of stain (D. Kuhn, personal communication, September, 1980). The task consisted of predicting which combination of ingredients would remove the stain. Although each configuration of variables was repeated once, this was not apparent until the problem had been solved. The solution of the laundry problem required the isolation of a causal variable and the rejection of the non-causal variables as having an effect on the outcome (clean or dirty). These problems were derived from Kuhn and Brannock's (1977) plant problem which, in turn, was derived from an earlier plant problem of Linn and Thier (1975; Linn, Chen, & Thier, 1976, 1977) and Inhelder and Piaget's (1958) pendulum problem. Two of the original eight variants of the formal-stage laundry problem were included in the instrument. Lower and higher stage versions of the laundry problem were constructed for this study. These have not been tested elsewhere.

Each laundry problem was comprised of informational episodes and prediction episodes. In each Informational Episode, a single combination of ingredients (values of the independent variables) is matched with an outcome (a value of the dependent variable). The ingredients were bleach (A or B), detergent (liquid or powder), water temperature (hot or cold), and booster (blue or pink). The outcome was either "clean" (the removal of the stain) or "dirty" (failure to remove the stain).

At the formal stage, only one out of the four independent variables predicts whether or not the stain would be removed. The informational episodes contain enough information so that the causal variable for the cloth outcome can be determined. In the Prediction Episodes, participants were asked to use the information from the Informational Episodes to determine whether the stain would be removed.

The Laundry Problem was chosen for a number of reasons.

  • Washing is a task that occurs in all cultures.
  • The variables are dichotomous and have discrete values (e.g., liquid or powdered soap).
  • The causal variable in the wash problem differed with each version, so the hypothetical nature of the problem is underscored, and no single variable is likely to become more pronounced than any other.
  • The stain and the causal variable for each trial did not usually match real world experience. The relationship between stain and causal agent was random.
  • Further, the outcomes associated with washing may have more relevance to members of other cultures than would a scientific chemical or physical task.
  • Additionally, due to the nature of the laundry problem itself, advancements towards performing at the formal operational stage lead to a higher percentage of correct answers for the participant. This feature is built into the problem to capitalize on the fact that when reinforcement is associated with correct answers, small advances may lead to more reinforcing situations.
  • The Laundry Problem task series includes problems of a range of difficulty, both hierarchically simpler and hierarchically more complex than the formal-stage problem described above. The most complex laundry problem on which a participant performs consistently indicates the developmental stage at which the participant is most likely to perform in this domain. The complete hierarchy of task complexity is described below.

    Primary Task
    20 Dichotymous Items

    At the primary stage, participants predict whether an ingredient cleans clothing. The informational episodes indicate whether an ingredient produces clean or a dirty cloth. The prediction episode stated what ingredient was used.

    Concrete Task
    18 Dichotymous Items

    At the concrete stage, the informational episodes state which combinations of four ingredients produce clean or dirty clothing. The prediction episodes state which combinations were used.

    Abstract Task
    16 Dichotymous Items

    At the abstract stage, the informational episodes state which combinations of two types of ingredient produce clean or dirty clothing. In the prediction episodes, the participants detect which of two types of ingredient predicts whether the cloth will come out clean or dirty. With only two variables, this task requires a minimal isolation of variables.

    Formal Task
    20 Dichotymous Items

    At the formal stage, the informational episodes state which combinations of four types of ingredient produce clean or dirty clothing. In the prediction episodes, participants isolate single variables whose value predicts whether or not particular combinations of ingredients will clean clothing. For example, in a particular problem, type of bleach determines the effectiveness of the combination. In another problem, water temperature is predictive. This conception of causality is univariate: If A, then B.

    The informational episodes of the formal stage problems are superficially similar to those of the concrete stage problems. However, at the concrete stage, the participants do not rely on isolating variables in making their predictions. Instead, they employ a simpler strategy, matching combinations of ingredients given in the prediction episodes whose effectiveness in cleaning is unknown with combinations given in the informational episodes whose outcome is known. In contrast, the informational episodes at the formal stage contain more information because there are more of them. This permits the isolation of the causal variable. Also, many of the combinations presented in the prediction episodes do not match combinations presented in the informational episodes. Thus there is no concrete-stage solution to the formal problems. Therefore proficiency at identifying univariate causal relations must be acquired in order to solve the more complex problems.

    Systematic Task
    34 Dichotymous Items

    At the systematic stage, the informational episodes state which combinations of four types of ingredient produce clean or dirty clothing. In the prediction episodes, participants identify the two variables whose values predicts whether or not particular combinations of ingredients will clean clothing. For example, in a particular problem, type of bleach AND water temperature determine the effectiveness of the combination. In another problem, type of detergent OR type of booster are predictive. This conception of causality is multivariate: If (A&B), then C, or if (A|B), then C. Either type of rule could govern causal relations at the systematic stage. Systematic-stage rules organize and coordinate formal-stage rules.

    Metasystematic Task
    10 polytomous Items

    At the metasystematic stage, the participants compare different systems of cleaning clothing in which different rules apply. These systems are provided in the informational episodes in the form of lists of combinations of ingredients whose effectiveness at cleaning is stated as a value of the outcome variable (clean or dirty). The participants must analyze each system in order to determine the rule that applies. In the prediction episodes, the participants rate pairs of systems with respect to their degree of similarity. Correct responses can be either high ratings of similar systems or low ratings of dissimilar systems. The metasystematic stage task requires the organization and coordination of lower stage tasks performed by the participants in the other parts of the instrument. There were ten metasystematic stage items.

    Abstracts

    A number of projects have been planned that use data gathered using the Laundry Problem Task Series. These projects listed below:

    1.  Goodheart, E. A., Dawson, T. L. (June 1996). "A Rasch Analysis of Developmental      Data from The Laundry Problem Task Series." Poster presented at the 11th Annual      Adult Development Symposium, Boston, MA.

    We perform a Rasch analysis of cross-sectional developmental data gathered from a group of adults to whom we presented the Laundry Problem Task Series. This analysis creates a probabilistic model that places both participants and problems along a single hierarchically ordered dimension. It is anticipated that both the participants and the problems will form a series of clusters along this dimension, the participants according to their developmental stage of performance and the problems according to their degree of hierarchical complexity. Questions of stage and hierarchical order will be examined.

    2.  Goodheart, E. A., Dawson, T. L., Draney, K., Commons, M. L. (March 1997). "A      Saltus Analysis of Developmental  Data from The Laundry Problem Task Series."      Poster to be presented at IOMW9, Chicago, IL.

    We perform a Saltus analysis of cross-sectional developmental data gathered from a group of 36 adults and 37children to whom we presented the Laundry Problem Task Series (Commons, Miller, and Kuhn, 1982). A Saltus analysis (Wilson, 1989; Wilson & Draney, 1995) is a thee-paramenter version of the Rasch model developed for the purpose of studying developmental data. Whereas a traditional Rasch analysis determines the probability of a given subject performing a given item in terms of item difficulty (delta) and subject ability (beta), a Saltus analysis introduces item stage as a third paramenter. This additional parameter can help to determine whether the gapiness and systematic shifts in item misfit present in an earlier two parameter Rasch analysis can be explained as stage change. Issues of fit and validity will be raised, and the results of the analysis will be discussed in terms of their general implications for developmental research as well as the more specific development of the Laundry Problem instrument.