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This study investigated whether instruction that involves comparing the equal sign with other relational symbols is more effective at imparting a relational interpretation of the equal sign than instruction about the equal sign alone. Third- and fourth-grade students in a comparing symbols group learned about the greater than, less than, and equal signs and had the opportunity to compare the inequality symbols with the equal sign. Students in an equal sign group learned about the equal sign only. A third group of students served as a control group. Three aspects of students’ knowledge were assessed before and after the lesson: (a) conceptual understanding of the equal sign, (b) equation encoding, and (c) problem solving. Students in the comparing symbols group showed greater gains in conceptual understanding from pretest to posttest than students in the other two groups, and students in the comparing symbols group also scored higher on a posttest that assessed knowledge about inequality symbols and inequality problem solving. Thus, they learned about three symbols in the same amount of time as other students learned about the equal sign alone or not at all. Therefore, an instructional approach involving comparison can be an effective tool for learning about concepts in mathematics. 相似文献
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This study investigated effects of feedback and exposure to alternative strategies on strategy change in children (N = 106, age range = 7;3–10;0) learning about mathematical equivalence. Children’s strategies were evaluated before and after a brief instructional intervention. During the intervention, children either were exposed to a set of 4 alternative strategies (2 correct, 2 incorrect) without information about the validity of the strategies or completed a control task. In addition, some children received feedback about existing strategies, and others did not. Exposure to alternative strategies led to more strategy change and better performance on a problem-solving task. The effect of feedback on strategy change depended on children’s confidence in their existing strategies and on their pretest knowledge. 相似文献
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How do children’s interpretations of the generality of learning episodes affect what they encode? In the present studies, we investigated the hypothesis that children encode distinct aspects of learning episodes containing generalizable and non-generalizable properties. Two studies with preschool (N = 50) and young school-aged children (N = 49) reveal that their encoding is contingent on the generalizability of the property they are learning. Children remembered generalizable properties (e.g., morphological or normative properties) more than non-generalizable properties (e.g., historical events or preferences). Conversely, they remembered category exemplars associated with non-generalizable properties more than category exemplars associated with generalizable properties. The findings highlight the utility of remembering distinct aspects of social learning episodes for children’s future generalization. 相似文献
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Lisa A. Haverty Kenneth R. Koedinger David Klahr Martha W. Alibali 《Cognitive Science》2000,24(2):249-298
This study investigated the cognitive processes involved in inductive reasoning. Sixteen undergraduates solved quadratic function–finding problems and provided concurrent verbal protocols. Three fundamental areas of inductive activity were identified: Data Gathering, Pattern Finding, and Hypothesis Generation. These activities are evident in three different strategies that they used to successfully find functions. In all three strategies, Pattern Finding played a critical role not previously identified in the literature. In the most common strategy, called the Pursuit strategy, participants created new quantities from x and y, detected patterns in these quantities, and expressed these patterns in terms of x. These expressions were then built into full hypotheses. The processes involved in this strategy are instantiated in an ACT‐based model that simulates both successful and unsuccessful performance. The protocols and the model suggest that numerical knowledge is essential to the detection of patterns and, therefore, to higher‐order problem solving. 相似文献
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A common practice in textbooks is to introduce concepts or strategies in association with specific people. This practice aligns with research suggesting that using “real‐world” contexts in textbooks increases students’ motivation and engagement. However, other research suggests this practice may interfere with transfer by distracting students or leading them to tie new knowledge too closely to the original learning context. The current study investigates the effects on learning and transfer of connecting mathematics strategies to specific people. A total of 180 college students were presented with an example of a problem‐solving strategy that was either linked with a specific person (e.g., “Juan's strategy”) or presented without a person. Students who saw the example without a person were more likely to correctly transfer the novel strategy to new problems than students who saw the example presented with a person. These findings are the first evidence that using people to present new strategies is harmful for learning and transfer. 相似文献
16.
Adrienne Wood Jared D. Martin Martha W. Alibali Paula M. Niedenthal 《Cognition & emotion》2019,33(6):1196-1209
Recognising a facial expression is more difficult when the expresser's body conveys incongruent affect. Existing research has documented such interference for universally recognisable bodily expressions. However, it remains unknown whether learned, conventional gestures can interfere with facial expression processing. Study 1 participants (N?=?62) viewed videos of people simultaneously producing facial expressions and hand gestures and reported the valence of either the face or hand. Responses were slower and less accurate when the face-hand pairing was incongruent compared to congruent. We hypothesised that hand gestures might exert an even stronger influence on facial expression processing when other routes to understanding the meaning of a facial expression, such as with sensorimotor simulation, are disrupted. Participants in Study 2 (N?=?127) completed the same task, but the facial mobility of some participants was restricted, which disrupted face processing in prior work. The hand-face congruency effect from Study 1 was replicated. The facial mobility manipulation affected males only, and it did not moderate the congruency effect. The present work suggests the affective meaning of conventional gestures is processed automatically and can interfere with face perception, but does not suggest that perceivers rely more on gestures when sensorimotor face processing is disrupted. 相似文献
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This paper reviews research on learners’ knowledge of three arithmetic principles: Commutativity, Relation to Operands, and Inversion. Studies of arithmetic principle knowledge vary along several dimensions, including the age of the participants, the context in which the arithmetic is presented, and most importantly, the type of knowledge assessment (e.g., application of procedures, evaluation of examples). The vast majority of studies utilize single-faceted knowledge assessments, which can lead to incomplete or misleading views of learners’ knowledge. Both context and type of knowledge assessment can influence conclusions about learners’ arithmetic principle knowledge. However, relatively few studies directly address the possible effects of context or type of knowledge assessment on their results. To move the field forward, research that utilizes multifaceted knowledge assessments is needed. 相似文献
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Who Benefits from Diagrams and Illustrations in Math Problems? Ability and Attitudes Matter
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How do diagrams and illustrations affect mathematical problem solving? Past research suggests that diagrams should promote correct performance. However, illustrations may provide a supportive context for problem solving, or they may distract students with seductive details. Moreover, effects may not be uniform across student subgroups. This study assessed the effects of diagrams and illustrations on undergraduates' trigonometry problem solving. We used a 2 (Diagram Presence) × 2 (Illustration Presence) within‐subjects design, and our analysis considered students' mathematics ability and attitudes towards mathematics. Participants solved problems more accurately when they included diagrams. This effect was stronger for students who had more positive mathematics attitudes, especially when there was an illustration present. Illustrations were beneficial for students with high mathematics ability but detrimental for students with lower ability. Considering individual differences in ability and attitude is essential for understanding the effects of different types of visual representations on problem solving. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
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Visible embodiment: Gestures as simulated action 总被引:1,自引:0,他引:1
Spontaneous gestures that accompany speech are related to both verbal and spatial processes. We argue that gestures emerge from perceptual and motor simulations that underlie embodied language and mental imagery. We first review current thinking about embodied cognition, embodied language, and embodied mental imagery. We then provide evidence that gestures stem from spatial representations and mental images. We then propose the gestures-as-simulated-action framework to explain how gestures might arise from an embodied cognitive system. Finally, we compare this framework with other current models of gesture production, and we briefly outline predictions that derive from the framework. 相似文献