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L R Novick

Publications and source records attributed to L R Novick.

10 recordsLinked to original sources
PubMed2001

To Matrix, Network, or Hierarchy: That Is the Question.

The authors present a structural analysis of three spatial diagrams-matrices, networks, and hierarchies-that specifies 10 properties on which these diagrammatic representations are hypothesized to differ: global structure, building block, number of sets, item/link constraints, item distinguishability, link type, absence of a relation, linking relations, path, and traversal. Each property has a "value" for each diagram, and these property values constitute the applicability conditions for the representations. Twenty-three college students (computer science majors and math educators) selected the type of diagram they thought would be most efficient for organizing the information in each of 18 short scenarios and verbally justified the reasons for their selections. The verbal protocols were coded with respect to the structural analysis. Both the representation selection and verbal justification data provided strong support for the structural analysis. Additionally, a factor analysis of students' justifications indicated that the organization of their knowledge is consistent with the structural analysis. Students' use of the structural properties to select appropriate representations and to justify those selections indicates that the structural analysis has psychological force.

Cognition↗
PubMed2000

Folding a fish, making a mushroom: the role of diagrams in executing assembly procedures.

Three experiments examined the role of step-by-step and final-state diagrams in supporting object assembly. A total of 180 college students made origami objects from instructions consisting of text only, text plus a final-state (completed-object) diagram, or text plus step-by-step and final-state diagrams. In Experiments 1 and 2, construction accuracy in the final-diagram condition was comparable to that in the step-by-step condition when the objects required few assembly steps, but it was comparable to that in the text-only condition when many steps were required. Experiment 3 independently manipulated the number of assembly steps and the ease of seeing the steps in, or inferring them from, the final diagram. The results indicated that the case of extracting the steps from the final diagram was the primary causal variable in the interaction with instructional condition. We interpret these results in terms of mental model construction and working memory load.

Adult↗
PubMed1999

Evidence for abstract, schematic knowledge of three spatial diagram representations.

Spatial diagram representations such as hierarchies, matrices, and networks are important tools for thinking. Our data suggest that college students possess abstract schemas for these representations that include at least rudimentary information about their applicability conditions. In Experiment 1, subjects were better able to select the appropriate spatial diagram representation for a problem when cued to use general category information in memory about those representations than when cued to use specific example problems given during the experiment. The results of Experiment 2 showed that the superior performance in the general category condition was not based on a comparison of the test problems with examples in memory. The results of Experiment 3 showed that the superior performance was not due to learning that occurred during the experiment or to transfer appropriate processing. The General Discussion section considers the nature of students' representation schemas and the question of why college students have only rudimentary schemas for common and widely applicable diagrammatic representations.

Female↗
PubMed1992

Covariation in natural causal induction.

The covariation component of everyday causal inference has been depicted, in both cognitive and social psychology as well as in philosophy, as heterogeneous and prone to biases. The models and biases discussed in these domains are analyzed with respect to focal sets: contextually determined sets of events over which covariation is computed. Moreover, these models are compared to our probabilistic contrast model, which specifies causes as first and higher order contrasts computed over events in a focal set. Contrary to the previous depiction of covariation computation, the present assessment indicates that a single normative mechanism--the computation of probabilistic contrasts--underlies this essential component of natural causal induction both in everyday and in scientific situations.

Cognition↗
PubMed1991

Causes versus enabling conditions.

People distinguish between a cause (e.g., a malfunctioning component in an airplane causing it to crash) and a condition (e.g., gravity) that merely enables the cause to yield its effect. This distinction cannot be explained by accounts of reasoning formulated purely in terms of necessity and sufficiency, because causes and enabling conditions hold the same logical relationship to the effect in those terms. Proposals to account for this apparent deviation from accounts based on necessity and sufficiency may be classified into three types. One approach explains the distinction in terms of an inferential rule based on the normality of the potential causal factors. Another approach explains the distinction in terms of the conversational principle of being informative to the inquirer given assumptions about his or her state of knowledge. The present paper evaluates variants of these two approaches, and presents our probabilistic contrast model, which takes a third approach. This approach explains the distinction between causes and enabling conditions by the covariation between potential causes and the effect in question over a focal set--a set of events implied by the context. Covariation is defined probabilistically, with necessity and sufficiency as extreme cases of the components defining contrasts. We report two experiments testing our model against variants of the normality and conversational views.

Adult↗
PubMed1991

Mathematical problem solving by analogy.

We report the results of 2 experiments and a verbal protocol study examining the component processes of solving mathematical word problems by analogy. College students first studied a problem and its solution, which provided a potential source for analogical transfer. Then they attempted to solve several analogous problems. For some problems, subjects received one of a variety of hints designed to reduce or eliminate the difficulty of some of the major processes hypothesized to be involved in analogical transfer. Our studies yielded 4 major findings. First, the process of mapping the features of the source and target problems and the process of adapting the source solution procedure for use in solving the target problem were clearly distinguished: (a) Successful mapping was found to be insufficient for successful transfer and (b) adaptation was found to be a major source of transfer difficulty. Second, we obtained direct evidence that schema induction is a natural consequence of analogical transfer. The schema was found to co-exist with the problems from which it was induced, and both the schema and the individual problems facilitated later transfer. Third, for our multiple-solution problems, the relation between analogical transfer and solution accuracy was mediated by the degree of time pressure exerted for the test problems. Finally, mathematical expertise was a significant predictor of analogical transfer, but general analogical reasoning ability was not. The implications of the results for models of analogical transfer and for instruction were considered.

Adult↗
PubMed1990

A probabilistic contrast model of causal induction.

Deviations from the predictions of covariational models of causal attribution have often been reported in the literature. These include a bias against using consensus information, a bias toward attributing effects to a person, and a tendency to make a variety of unpredicted conjunctive attributions. It is contended that these deviations, rather than representing irrational biases, could be due to (a) unspecified information over which causal inferences are computed and (b) the questionable normativeness of the models against which these deviations have been measured. A probabilistic extension of Kelley's analysis-of-variance analogy is proposed. An experiment was performed to assess the above biases and evaluate the proposed model against competing ones. The results indicate that the inference process is unbiased.

Adult↗
PubMed1988

Analogical transfer, problem similarity, and expertise.

When we encounter a new problem, we are often reminded of similar problems solved earlier and may use the solution procedure from an old problem to solve a new one. Such analogical transfer, however, has been difficult to demonstrate empirically, even within a single experimental session. This article proposes a framework for conceptualizing analogical problem solving that can account for the conflicting findings in the literature. In addition, the framework leads to two predictions concerning the transfer behavior of experts and novices. These predictions concern both positive and negative transfer and are based on the different types of features included in the problem representations of experts and novices. First, when two problems share structural features but not surface features, spontaneous positive transfer should be more likely in experts than in novices. Second, when two problems share surface but not structural features, spontaneous negative transfer should be stronger for novices than for experts. These predictions were supported by the results of three experiments involving college students solving a complex arithmetic word problem.

Achievement↗
PubMed1987

Cognitive constraints on ordering operations: the case of geometric analogies.

Many tasks (e.g., solving algebraic equations and running errands) require the execution of several component processes in an unconstrained order. The research reported here uses the geometric analogy task as a paradigm case for studying the ordering of component processes in this type of task. In solving geometric analogies by applying mental transformations such as rotate, change size, and add a part, the order of performing the transformations is unconstrained and does not in principle affect solution accuracy. Nevertheless, solvers may bring cognitive constraints with them to the analogy task that influence the ordering of the transformations. First, we demonstrate that solvers have a preferred order for performing mental transformations during analogy solution. We then investigate three classes of explanations for the preferred order, one based on general information processing considerations, another based on task-specific considerations, and a third based on individual differences in analogy ability. In the first and third experiments, college students solved geometric analogies requiring two or three transformations and indicated the order in which they performed the transformations. There was close agreement on nearly the same order for both types of analogies. In the second experiment, subjects were directed to perform pairs of transformations in the preferred or unpreferred order. Both speed and accuracy were greater for the preferred orders, thus validating subjects' reported orders. Ability differences were observed for only the more difficult three-transformation problems: High- and middle-ability subjects agreed on an overall performance order, but the highs were more consistent in their use of this order. Low-ability subjects did not consistently order the transformations for these difficult problems. The general information processing factor examined was working-memory load. A number of task factors have been shown to affect working-memory load during the solution of inductive reasoning problems. Of these, we chose to examine process difficulty. Because analogies are solved in working memory, performing more difficult transformations earlier may reduce working-memory load and facilitate problem solution. However, the observed performance order was not correlated with transformation difficulty. The first task-specific factor considered was that some transformations may be identified earlier, possibly because of perceptual salience, and that the performance order follows the identification order.(ABSTRACT TRUNCATED AT 400 WORDS)

Cognition↗