Showing papers by "Martha W. Alibali published in 2018"

Who Benefits from Diagrams and Illustrations in Math Problems? Ability and Attitudes Matter

Abstract: Summary: 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.

Perceptual support promotes strategy generation: Evidence from equation solving.

Abstract: Over time, children shift from using less optimal strategies for solving mathematics problems to using better ones. But why do children generate new strategies? We argue that they do so when they begin to encode problems more accurately; therefore, we hypothesized that perceptual support for correct encoding would foster strategy generation. Fourth-grade students solved mathematical equivalence problems (e.g., 3 + 4 + 5 = 3 + __) in a pre-test. They were then randomly assigned to one of three perceptual support conditions or to a Control condition. Participants in all conditions completed three mathematical equivalence problems with feedback about correctness. Participants in the experimental conditions received perceptual support (i.e., highlighting in red ink) for accurately encoding the equal sign, the right side of the equation, or the numbers that could be added to obtain the correct solution. Following this intervention, participants completed a problem-solving post-test. Among participants who solved the problems incorrectly at pre-test, those who received perceptual support for correctly encoding the equal sign were more likely to generate new, correct strategies for solving the problems than were those who received feedback only. Thus, perceptual support for accurate encoding of a key problem feature promoted generation of new, correct strategies. Statement of Contribution What is already known on this subject? With age and experience, children shift to using more effective strategies for solving math problems. Problem encoding also improves with age and experience. What the present study adds? Support for encoding the equal sign led children to generate correct strategies for solving equations. Improvements in problem encoding are one source of new strategies.

Embodied Cognition in Learning and Teaching : Action, Observation, and Imagination

Abstract: A central claim of theories of embodied cognition is that cognitive processes are rooted in the perceptions and actions of the body. In this chapter, we focus on three implications of this view for learning and instruction. First, action matters for cognitive performance and learning. Actions that are well aligned with target ideas can promote performance and learning, whereas actions that are not well aligned can interfere. Second, observing others’ actions can activate action-based knowledge; therefore, learners need not produce actions themselves in order for action to influence performance and learning. Third, imagining or mentally simulating actions can activate action-based knowledge, and simulated actions are sometimes manifested in gestures, which are a form of representational action. These principles highlight the importance of actions—both real and imagined—in cognitive performance, learning and instruction. We consider implications of this perspective for instructional design, assessment, and educational technology.

Promoting Strategy Change: Mere Exposure to Alternative Strategies Helps, but Feedback Can Hurt.

Abstract: 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...

Relational Equity and Mathematics Learning: Mutual Construction During Collaborative Problem Solving

Abstract: We present an emerging interdisciplinary approach to the study of mathematics learning, which brings together strands from psychology and mathematics education. Our aim was to examine how students navigate the cognitive and social aspects of peer collaboration as they generate and adopt new strategies. We analyzed video data from a laboratory study involving pairs of elementary students working collaboratively to solve mathematical equivalence problems (e.g., 8 + 5 + 4 = 4 + ___). We adopted a qualitative micro-analytic approach that focused on multimodal action (i.e., verbal utterance, gesture, inscription production, body positioning, and eye gaze) to examine three cases. These cases illustrate the complex ways that students interacted in this particular context and, in some instances, attempted to teach one another. Our findings show how “relational equity” (Boaler, 2008) and mathematics knowledge were co-constructed differently in each case. We argue that a micro-analytic approach, complemented by a blending of theory from these two fields, reveals hidden aspects of the interaction that may help explain, for example, why some students generate or adopt correct strategies and others do not. As such, this interdisciplinary approach offers a rich account of the learning processes that occur in peer collaboration.

Does visual salience of action affect gesture production

Abstract: Past research suggests that speakers gesture more when motor simulations are more strongly activated. We investigate whether simulations of a perceptual nature also influence gesture production. Participants viewed animations of a spider moving with a manner of motion that was either highly salient (n = 29) or less salient (n = 31) and then described each motion event. Speakers in the high-salience condition produced significantly more gestures that depicted manner information. However, they did not produce significantly more gestures overall, more gestures that depicted the spider's path and direction of motion, or more manner descriptions in speech. Moreover, the effect of visual salience on manner gestures persisted after controlling for expression of manner in speech. These findings suggest that speakers selectively produce gestures expressing features of perceptual representations that are highly salient. (PsycINFO Database Record

Bridging Psychology and Mathematics Education: Reflections on Boundary Crossing

Abstract: Collaborations between psychology and mathematics education have the potential to yield progress on critical questions about the teaching and learning of mathematics. In this paper, we describe our experience of collaborating at this boundary. We have found that collaboration has many benefits: it strengthens the research, it is professionally enriching, and it brings novel perspectives to disciplinary communities. However, collaboration is also challenging, because different views about the nature of knowledge and the aims of inquiry can be difficult to bridge. Collaboration can also raise difficult questions about professional identity. We consider several factors that are critical to success in interdisciplinary collaboration, including methodological openness, a broad view of what constitutes “basic” and “applied” research, and an appreciation for diverse perspectives and varying levels of analysis. We close by offering some advice for others who wish to collaborate at the boundary of psychology and mathematics education.