Closely related to this is Mr. Bruner's "evolutionary instrumentalism," his conception of instruction as the means of transmitting the tools and skills of a ...

The current research investigates a combination of two instructional approaches, tutored problem solving and worked examples. Tutored problem solving with automated tutors has proven to be an effective instructional method. Worked‐out examples have been shown to be an effective complement to untutored problem solving, but it is largely unknown whether they are an effective complement to tutored problem solving. Further, while computer‐based learning environments offer the possibility of adaptively transitioning from examples to problems while tailoring to an individual learner, the (...) effectiveness of such machine‐adapted example fading is largely unstudied. To address these research questions, one lab and one classroom experiment were conducted. Both studies compared a standard Cognitive Tutor with two example‐enhanced Cognitive Tutors, in which the fading of worked‐out examples occurred either in a fixed way or adaptively. Results indicate that the adaptive fading of worked‐out examples leads to higher transfer performance on delayed posttests than the other two methods. (shrink)

The goal of this study was to investigate interindividual differences in learning from worked-out examples with respect to the quality of self-explanations. Restrictions of former studies (e.g., lacking control of time-on-task) were avoided and additional research questions (e.g., reliability and dimensionality of self-explanation characteristics) were addressed. An investigation with 36 university freshmen of education working in individual sessions was conducted. The domain was probability calculus. As predictors of learning, prior knowledge and the quality of self-explanations (thinking aloud protocols) were assessed. (...) A post-test was employed to measure the learning gains as dependent variable. The following main results were obtained. Most self-explanation characteristics can be regarded as relatively stable person characteristics. The interindividual differences in the quality of self-explanations were, however, found to be multidimensional. Most importantly, even when controlling for time-on-task (quantitative aspect), learning gains could be substantially predicted by qualitative differences of self- explanation characteristics. Successful learners tended to employ more principle-based explanations, more anticipative reasoning and more explication of operator-goal combinations. (shrink)

Classroom discussion practices that can lead to reasoned participation by all students are presented and described by the authors. Their research emphasizes the careful orchestration of talk and tasks in academic learning. Parallels are drawn to the philosophical work on deliberative discourse and the fundamental goal of equipping all students to participate in academically productive talk. These practices, termed Accountable TalkSM, emphasize the forms and norms of discourse that support and promote equity and access to rigorous academic learning. They have (...) been shown to result in academic achievement for diverse populations of students. The authors outline Accountable Talk as encompassing three broad dimensions: one, accountability to the learning community, in which participants listen to and build their contributions in response to those of others; two, accountability to accepted standards of reasoning, talk that emphasizes logical connections and the drawing of reasonable conclusions; and, three, accountability to knowledge, talk that is based explicitly on facts, written texts, or other public information. With more than fifteen years research into Accountable Talk applications across a wide range of classrooms and grade levels, the authors detail the challenges and limitations of contexts in which discourse norms are not shared by all members of the classroom community. (shrink)

Max Wertheimer, in his classic Productive Thinking, linked understanding to transfer: Understanding is important because it provides the ability to generalize the solution of one problem to apply to another. Recent work in human and machine learning has led to the development of a new class of generalization mechanism, called here analysis‐based generalization, which can be used to provide a concrete account of the linkage Wertheimer suggested: these mechanisms all, in different ways, use understanding of examples in the generalization process. (...) In this paper I review this class of mechanism, and describe a method for causal attribution that can produce the analyses of examples that the generalization methods require, in the domain of simple procedures in human‐computer interaction. This causal analysis method is linked with analysis‐based generalization to form EXPL, an implemented model which is a concrete, though limited, instontiation of Wertheimer s scheme. EXPL constructs an understanding of an example procedure and generalizes it on the basis of that understanding. Results of an empirical study suggest that some of EXPL's attribution heuristics are used by people, and that while a subclass of analysis‐based methods, called superstitious methods, seem to provide a more plausible account of people's generalization under the conditions of the study than a contrasting class of rationalistic methods, at least some participants appear to use methods from both classes. The results also show that explanation‐based methods, which rely on comprehensive domain theories, must be used in conjunction with a means for extending the domain theory. If thus enhanced, explanation‐based methods are able to mimic the effects of other analysis‐based methods, and can provide a good account of the data, though combinations of other methods must also be considered. Finally, I return to Wertheimer s ideas to argue that none of the current analysis‐based generalization methods fully captures Wertheimer s notion of understanding. Proper choice among different possible analyses of an example is crucial for Wertheimer, but I argue that this problem may be beyond the reach of learning systems. (shrink)

This article explores the complementary strengths and weaknesses of grounded and abstract representations in the domain of early algebra. Abstract representations, such as algebraic symbols, are concise and easy to manipulate but are distanced from any physical referents. Grounded representations, such as verbal descriptions of situations, are more concrete and familiar, and they are more similar to physical objects and everyday experience. The complementary computational characteristics of grounded and abstract representations lead to trade‐offs in problem‐solving performance. In prior research with (...) high school students solving relatively simple problems, Koedinger and Nathan (2004) demonstrated performance benefits of grounded representations over abstract representations—students were better at solving simple story problems than the analogous equations. This article extends this prior work to examine both simple and more complex problems in two samples of college students. On complex problems with two references to the unknown, a “symbolic advantage” emerged, such that students were better at solving equations than analogous story problems. Furthermore, the previously observed “verbal advantage” on simple problems was replicated. We thus provide empirical support for a trade‐off between grounded, verbal representations, which show advantages on simpler problems, and abstract, symbolic representations, which show advantages on more complex problems. (shrink)

The purpose of the two studies reported here was 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 based on their prior knowledge, conduct experiments, and evaluate the results of their experiments. In the first study, using 20 adult subjects, (...) we identified two main strategies that subjects used to generate new hypotheses. One strategy was to search 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 an 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 experimental 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. (shrink)

The purpose of the two studies reported here was 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 based on their prior knowledge, conduct experiments, and evaluate the results of their experiments. In the first study, using 20 adult subjects, (...) we identified two main strategies that subjects used to generate new hypotheses. One strategy was to search 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 an 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 experimental 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. (shrink)

We present five experiments and simulation studies to establish late analogical abstraction as a new psychological phenomenon: Schema abstraction from analogical examples can revive otherwise inert knowledge. We find that comparing two analogous examples of negotiations at recall time promotes retrieving analogical matches stored in memory—a notoriously elusive effect. Another innovation in this research is that we show parallel effects for real‐life autobiographical memory (Experiments 1–3) and for a controlled memory set (Experiments 4 and 5). Simulation studies show that a (...) unified model based on schema abstraction can capture backward (retrieval) effects as well as forward (transfer) effects. (shrink)

The implicit-explicit distinction is applied to knowledge representations. Knowledge is taken to be an attitude towards a proposition which is true. The proposition itself predicates a property to some entity. A number of ways in which knowledge can be implicit or explicit emerge. If a higher aspect is known explicitly then each lower one must also be known explicitly. This partial hierarchy reduces the number of ways in which knowledge can be explicit. In the most important type of implicit knowledge, (...) representations merely reflect the property of objects or events without predicating them of any particular entity The dearest cases of explicit knowledge of a fact are representations of one's own attitude of knowing that fact. These distinctions are discussed in their relationship to similar distinctions such as procedural-declarative, conscious unconscious, verbalizable-nonverbalizable, direct-indirect tests, and automatic voluntary control. This is followed by an outline of how these distinctions can be used to integrate and relate the often divergent uses of the implicit-explicit distinction in different research areas. We illustrate this for visual perception, memory, cognitive development, and artificial grammar learning. (shrink)

The present paper analyzes the self‐generated explanations (from talk‐aloud protocols) that “Good” and “Poor” students produce while studying worked‐out examples of mechanics problems, and their subsequent reliance on examples during problem solving. We find that “Good” students learn with understanding: They generate many explanations which refine and expand the conditions for the action parts of the example solutions, and relate these actions to principles in the text. These self‐explanations are guided by accurate monitoring of their own understanding and misunderstanding. Such (...) learning results in example‐independent knowledge and in a better understanding of the principles presented in the text. “Poor” students do not generate sufficient self‐explanations, monitor their learning inaccurately, and subsequently rely heavily on examples. We then discuss the role of self‐explanations in facilitating problem solving, as well as the adequacy of current AI models of explanation‐based learning to account for these psychological findings. (shrink)

The present paper analyzes the self‐generated explanations (from talk‐aloud protocols) that “Good” and “Poor” students produce while studying worked‐out examples of mechanics problems, and their subsequent reliance on examples during problem solving. We find that “Good” students learn with understanding: They generate many explanations which refine and expand the conditions for the action parts of the example solutions, and relate these actions to principles in the text. These self‐explanations are guided by accurate monitoring of their own understanding and misunderstanding. Such (...) learning results in example‐independent knowledge and in a better understanding of the principles presented in the text. “Poor” students do not generate sufficient self‐explanations, monitor their learning inaccurately, and subsequently rely heavily on examples. We then discuss the role of self‐explanations in facilitating problem solving, as well as the adequacy of current AI models of explanation‐based learning to account for these psychological findings. (shrink)

The representation of physics problems in relation to the organization of physics knowledge is investigated in experts and novices. Four experiments examine the existence of problem categories as a basis for representation; differences in the categories used by experts and novices; differences in the knowledge associated with the categories; and features in the problems that contribute to problem categorization and representation. Results from sorting tasks and protocols reveal that experts and novices begin their problem representations with specifiably different problem categories, (...) and completion of the representations depends on the knowledge associated with the categories. For, the experts initially abstract physics principles to approach and solve a problem representation, whereas novices base their representation and approaches on the problem's literal features. (shrink)

We propose that people typically reason about realistic situations using neither content-free syntactic inference rules nor representations of specific experiences. Rather, people reason using knowledge structures that we term pragmatic reasoning schemas, which are generalized sets of rules defined in relation to classes of goals. Three experiments examined the impact of a “permission schema” on deductive reasoning. Experiment 1 demonstrated that by evoking the permission schema it is possible to facilitate performance in Wason's selection paradigm for subjects who have had (...) no experience with the specific content of the problems. Experiment 2 showed that a selection problem worded in terms of an abstract permission elicited better performance than one worded in terms of a concrete but arbitrary situation, providing evidence for an abstract permission schema that is free of domain-specific content. Experiment 3 provided evidence that evocation of a permission schema affects not only tasks requiring procedural knowledge, but also a linguistic rephrasing task requiring declarative knowledge. In particular, statements in the form if p then q were rephrased into the form p only if q with greater frequency for permission than for arbitrary statements, and rephrasings of permission statements produced a pattern of introduction of modals totally unlike that observed for arbitrary conditional statements. Other pragmatic schemas, such as “causal” and “evidence” schemas can account for both linguistic and reasoning phenomena that alternative hypotheses fail to explain. (shrink)

In this paper we attempt to identify which peer collaboration characteristics may be accountable for conceptual change through interaction. We focus on different socio‐cognitive aspects of the peer dialog and relate these with learning gains on the dyadic as well as the individual level. The scientific topic that was used for this study concerns natural selection, a topic for which students’ intuitive conceptions have been shown to be particularly robust. Learning tasks were designed according to the socio‐cognitive conflict instructional paradigm. (...) After receiving a short instructional intervention on natural selection, paired students were asked to collaboratively construct explanations for certain evolutionary phenomena while engaging in dialectical argumentation. Two quantitative coding schemes were developed, each with a different granularity. The first assessed discrete dialog moves that pertained to dialectical argumentation and to consensual explanation development. The second scheme characterized the dialog as a whole on a number of socio‐cognitive dimensions. Results from analyses on the dyadic as well as the individual level revealed that the engagement in dialectical argumentation predicted conceptual learning gains, whereas consensual explanation development did not. These findings open up new venues for research on the mechanisms of learning in and from peer collaboration. (shrink)

Much of cognitive psychology focuses on effects measured in tens of milliseconds while significant educational outcomes take tens of hours to achieve. The task of bridging this gap is analyzed in terms of Newell's (1990) bands of cognition—the Biological, Cognitive, Rational, and Social Bands. The 10 millisecond effects reside in his Biological Band while the significant learning outcomes reside in his Social Band. The paper assesses three theses: The Decomposition Thesis claims that learning occurring at the Social Band can be (...) reduced to learning occurring at lower bands. The Relevance Thesis claims that instructional outcomes at the Social Band can be improved by paying attention to cognition at the lower bands. The Modeling Thesis claims that cognitive modeling provides a basis for bridging between events on the small scale and desired outcomes on the large scale. The unit-task level, at the boundary of the Cognitive and Rational Bands, is useful for assessing these theses. There is good evidence for all three theses in efforts that bridge from the unit-task level to educational applications. While there is evidence for the Decomposition Thesis all the way down to the 10 millisecond level, more work needs to be done to establish the Relevance Thesis and particularly the Modeling Thesis at the lower levels. (shrink)

Dienes & Perner (D&P) argue that nondeclarative knowledge can take multiple forms. We provide empirical support for this from two related lines of research about the development of mathematical reasoning. We then describe how different forms of procedural and declarative knowledge can be effectively modeled in Anderson's ACT-R theory, contrasting this computational approach with D&P's logical approach. The computational approach suggests that the commonly observed developmental progression from more implicit to more explicit knowledge can be viewed as a consequence of (...) accumulating and strengthening mental representations. (shrink)

Recent studies have shown that self‐explanation is an effective metacognitive strategy, but how can it be leveraged to improve students' learning in actual classrooms? How do instructional treatments that emphasizes self‐explanation affect students' learning, as compared to other instructional treatments? We investigated whether self‐explanation can be scaffolded effectively in a classroom environment using a Cognitive Tutor, which is intelligent instructional software that supports guided learning by doing. In two classroom experiments, we found that students who explained their steps during problem‐solving (...) practice with a Cognitive Tutor learned with greater understanding compared to students who did not explain steps. The explainers better explained their solutions steps and were more successful on transfer problems. We interpret these results as follows: By engaging in explanation, students acquired better‐integrated visual and verbal declarative knowledge and acquired less shallow procedural knowledge. The research demonstrates that the benefits of self‐explanation can be achieved in a relatively simple computer‐based approach that scales well for classroom use. (shrink)

Self‐explaining is an effective metacognitive strategy that can help learners develop deeper understanding of the material they study. This experiment explored if the format of material (i.e., text or diagrams) influences the self‐explanation effect. Twenty subjects were presented with information about the human circulatory system and prompted to self‐explain; 10 received this information in text and 10 in diagrams. Results showed that students given diagrams performed significantly better on post‐tests than students given text. Diagrams students also generated significantly more self‐explanations (...) that text students. Furthermore, the benefits of self‐explaining were much greater in the diagrams condition. To discover why diagrams can promote the self‐explanation effect, results are interpreted with reference to the multiple differences in the semantic, cognitive and affective properties of the texts and diagrams studied. (shrink)

In this book, Newell makes the case for unified theories by setting forth a candidate.

It was investigated to what extent example variability and the elicitation of sophisticated self-explanations foster the acquisition of applicable and transferable knowledge by learning from worked-out examples. To this end, we had 56 apprentices from a bank learn calculation of compound interest and real interest. The subjects were randomly assigned to the four conditions of a 2´2-factorial design (factor 1: uniform vs. multiple examples; factor 2: spontaneous vs. Elicited self-explanations). The learning results were measured by a post-test comprising application problems (...) and transfer problems. It was found that the acquisition of applicable and transferable knowledge can be supported by eliciting self-explanations. This underlines the "causal" relevance of the quality of self-explanations for knowledge acquisition by learning from worked-out examples. The assumption that multiple examples foster transfer performance, at least when sophisticated self-explanations are elicited, is not unequivocally supported. Without learner support in form of an elicitation procedure, multiple examples even seem to be detrimental. (shrink)