David Klahr

Dual Space Search During Scientific Reasoning

The purpose of the two studies reported here wos to develop an integrated model of the scientific reasoning process. Subjects were placed in a simulated scientific discovery context by first teaching them how to use an electronic device and then asking them to discover how a hitherto unencountered function worked. To do this task. subjects had to formulate hypotheses bas’ed on their prior knowledge, conduct experiments, and evaluate the results of their experiments. In t,he first study, using 20 adult subjects, we identified two main strategies that subjects used to generate new hypotheses. One strategy was to scorch memory and the other was to generalize from the results of previous experiments. We described the former group as searching an hypothesis space, and the latter as searching on experiment space. In a second study, with 10 adults, we investigated how subjects search the hypothesis space by instructing them to state all the hypotheses that they could think of prior to conducting any experiments. Following this phase, subjects were then allowed to conduct experiments. Subjects who could not think of the correct rule in the hypothesis generation phase discovered the correct rule only by generalizing from the results of experiments in the experimentol phase. Both studies provide support for the view that scientific reasoning can be characterized as search in two problem spaces. By extending Simon and Lea’s (1974) Generalized Rule Inducer, we present a general model of Scientific Discovery as Dual Search (SDDS) that shows how search in two problem spaces (an hypothesis space and an experiment space) shapes hypothesis generation, experimental design, and the evaluation of hypotheses. The model also shows how these processes interact with each other. Finally, we interpret earlier findings about the psychology of scientific reasoning In terms of the SDDS model.

The Equivalence of Learning Paths in Early Science Instruction: Effects of Direct Instruction and Discovery Learning

In a study with 112 third- and fourth-grade children, we measured the relative effectiveness of discovery learning and direct instruction at two points in the learning process: (a) during the initial acquisition of the basic cognitive objective (a procedure for designing and interpreting simple, unconfounded experiments) and (b) during the subsequent transfer and application of this basic skill to more diffuse and authentic reasoning associated with the evaluation of science-fair posters. We found not only that many more children learned from direct instruction than from discovery learning, but also that when asked to make broader, richer scientific judgments, the many children who learned about experimental design from direct instruction performed as well as those few children who discovered the method on their own. These results challenge predictions derived from the presumed superiority of discovery approaches in teaching young children basic procedures for early scientific investigations.

All Other Things Being Equal: Acquisition and Transfer of the Control of Variables Strategy

The ability to design unconfounded experiments and make valid inferences from their outcomes is an essential skill in scientific reasoning. The present study addressed an important issue in scientific reasoning and cognitive development: how children acquire a domain-general processing strategy (Control of Variables Strategy or CVS) and generalize it across various contexts. Seven- to 10-year-olds (N = 87) designed and evaluated experiments and made inferences from the experimental outcomes. When provided with explicit training within domains, combined with probe questions, children were able to learn and transfer the basic strategy for designing unconfounded experiments. Providing probes without direct instruction, however, did not improve childrens ability to design unconfounded experiments and make valid inferences. Direct instruction on CVS not only improved the use of CVS, but also facilitated conceptual change in the domain because the application of CVS led to unconfounded, informative tests of domain-specific concepts. With age, children increasingly improved their ability to transfer learned strategies to remote situations. A trial-by-trial assessment of childrens strategy use also allowed the examination of the source, rate, path, and breadth of strategy change.

Heuristics for Scientific Experimentation: A Developmental Study.

Scientific discovery involves search in a space of hypotheses and a space of experiments. We describe an investigation of developmental differences in the search constraint heuristics used in scientific reasoning. Sixty-four subjects (technically trained college students, community college students with little technical training, 6th graders, and 3rd graders) were taught how to use a programmable robot. Then they were presented with a new operation, provided with a hypothesis about how it might work, and asked to conduct experiments to discover how the new operation really did work. The suggested hypothesis was always incorrect, as subjects could discover if they wrote informative experiments, and it was either plausible or implausible. The rule for how the unknown operation actually worked was either very similar or very dissimilar to the given hypothesis. Children focused primarily on plausible hypotheses, conducted a limited set of experiments, designed experiments that were difficult to interpret, and were unable to induce implausible (but correct) hypotheses from data. Adults were much better than children in discovering implausible rules. The performance deficits we found were not simply the result of childrens inadequate encoding or mnemonic skills. Instead, the adults appear to use domain-general skills that go beyond the logic of confirmation and disconfirmation and deal with the coordination of search in two spaces: a space of hypotheses and a space of experiments.

Formal assessment of problem-solving and planning processes in preschool children ☆

Abstract While much is known about adult problem-solving, the materials, analyses, and theoretical issues from the adult literature rarely make contact with the tasks typically used to investigate childrens thinking. This paper examines the behavior of 4-, 5-, and 6-year-old children attempting to solve a novel variant of the Tower of Hanoi task. Problems varied in difficulty (one to seven moves for the minimum path solution) and in goal type: tower (all objects on one peg) or flat (all pegs occupied). For each problem, children gave verbal statements of their complete solution plan. The Plan Analysis examined performance as a function of goal type and age. Better performance was observed for tower ending problems, and among older children. The Error Analysis revealed that specific error propensities were related to both age and goal type. The Strategic Analysis compared the first move profiles of 6-year-olds to those of several plausible move selection models, and a high degree of correspondence was obtained between specific models and individual children. Young children appear to have rudimentary forms of many of the problem-solving processes previously identified in adults, but they may differ in encoding and representational processes.

Span and Rate of Apprehension in Children and Adults.

Abstract Children and adults quantified random patterns of dots, under unlimited exposure duration. For adults and children two distinct processes appear to operate. For adults the quantification of collections of from one to three dots is essentially errorless, and proceeds at the rate of 46 msec per item, while the quantification rate for from 4 to 10 dots is 307 msec per dot. For children the same operating ranges appear to hold, however children are much slower. The lower slope is 195 msec per dot, while the upper is 1049. Although the results for adults and children are similar except for the overall rates, the nature of the isomorphism between children and adults is unclear.

Studies of Scientific Discovery: Complementary Approaches and Convergent Findings

This review integrates 4 major approaches to the study of science—histo rical accounts of scientific discoveries, psychological experiments with nonscientists working on tasks related to scientific discoveries, direct observation of ongoing scientific laboratories, and computational modeling of scientific discovery processes—by viewing them through the lens of the theory of human problem solving. The authors provide a brief justification for the study of scientific discovery, a summary of the major approaches, and criteria for comparing and contrasting them. Then, they apply these criteria to the different approaches and indicate their complementarities. Finally, they provide several examples of convergent principles of the process of scientific discovery. The central thesis of this article is that although research on scientific discovery has taken many different paths, these paths show remarkable convergence on key aspects of the discovery processes, allowing one to aspire to a general theory of scientific discovery. This convergence is often obscured by the disparate cultures, research methodologies, and theoretical foundations of the various disciplines that study scientific discovery, including history and sociology as well as those within the cognitive sciences (e.g., psychology, philosophy, and artificial intelligence). Despite these disciplinary differences, common concepts and terminology can express the central ideas and findings about scientific discovery from the various disciplines, treating discovery as a particular species of human problem solving. Moreover, we may be able to use these concepts and this vocabulary over an even broader domain to converge toward a common account of discovery in many areas of human endeavor: practical, scientific, and artistic, occurring both in everyday life and in specialized technical and professional domains. The doing of science has long attracted the attention of philosophers, historians, anthropologists, and sociologists. More recently, psychologists also have begun to turn their attention to the phenomena of scientific thinking, and there is now a large and rapidly growing literature on the psychology of science. (A good description of the field in its infancy can be found in Tweney, Doherty, & Mynatt, 1981, and a recent summary of topics and findings from investigations of the developmental, personality, cognitive, and social psychology of science can be found in Feist & Gorman, 1998). Our review links four major approaches to the study of science—historical accounts of scientific discoveries, laboratory experiments with nonscientists working on tasks related to scientific discoveries, direct observation of ongoing scientific laboratories, and computational modeling of scientific discovery processes—by

Cognitive objectives in a LOGO debugging curriculum: Instruction, learning, and transfer ☆

Abstract In this paper we report two studies in which elementary-school children learned a complex computer-programming skill—how to debug LOGO graphics and list-processing programs—and then transferred the high-level goal structure of that skill to nonprogramming domains. Instruction, its assessment, and the transfer tasks were all derived from an explicit model of the debugging process, cast as a computer simulation. Debugging skills were acquired over a period of several months as part of a LOGO programming course; the transfer tasks involved correcting written instructions in a variety of domains, including arranging items, allocating resources, and following map routes. Students showed clear improvement in the transfer tasks following instruction in debugging programs, and in the second study, amount of transfer was correlated with the degree of debugging skill acquisition. Our results contrast with many earlier studies that found little transfer of problem-solving skills in general and of high-level programming skills in particular. We suggest that the key to the success of our procedure is the fact that we used an extremely precise computer simulation model of the skills required to debug LOGO graphics and list-processing programs as a concrete manifestation of the notion of “cognitive objectives”.

The role of quantification operators in the development of conservation of quantity

Abstract An analysis of the quantitative processes underlying conservation of quantity is presented. Models of quantitative operators (subitizing, counting, estimation) are derived from adult performance in quantification tasks, and some features of the operators are described. The emergence of conservation is described in terms of the development of the operators and a set of rules which evoke them and coordinate their results. Empirical data related to the developmental argument is discussed.

The Representation of Children's Knowledge

Publisher Summary This chapter discusses two related issues—one concerning the ways that children from 5 to 17 years perform a scientific induction task and the other concerning representation of childrens knowledge. A series of experiments designed to investigate questions about initial knowledge, instructional effectiveness, and individual differences in both initial performance and responsiveness to instruction is summarized. The two issues in question are related simply because the researchers decision about how to represent knowledge plays a central role in guiding both the kind of theory that gets formulated and the kind of experiment that gets run. The historical trend in instructional psychology that has made the representation of knowledge a central issue is described and criteria that might be useful in choosing and evaluating different representations is introduced. In addition to a set of evaluative criteria, the chapter lists five central questions for research in developmental and instructional psychology. A formal model—using a particular representation—is presented for different levels of knowledge that children might have about how to do the task.