Showing papers by "Martha W. Alibali published in 2017"

How Do Gestures Influence Thinking and Speaking? The Gesture-for-Conceptualization Hypothesis

Abstract: People spontaneously produce gestures during speaking and thinking. We focus here on gestures that depict or indicate information related to the contents of concurrent speech or thought (i.e., representational gestures). Previous research indicates that such gestures have not only communicative functions, but also self-oriented cognitive functions. In this paper, we propose a new theoretical framework, the Gesture-for-Conceptualization Hypothesis, which explains the self-oriented functions of representational gestures. According to this framework, representational gestures affect cognitive processes in four main ways: gestures activate, manipulate, package and explore spatio-motoric representations for speaking and thinking. These four functions are shaped by gesture’s ability to schematize information, that is, to focus on a small subset of available information that is potentially relevant to the task at hand. The framework is based on the assumption that gestures are generated from the same system that generates practical actions, such as object manipulation; however, gestures are distinct from practical actions in that they represent information. The framework provides a novel, parsimonious and comprehensive account of the self-oriented functions of gestures. We discuss how the framework accounts for gestures that depict abstract or metaphoric content, and we consider implications for the relations between self-oriented and communicative functions of gestures.

Creating a context for learning: Activating children’s whole number knowledge prepares them to understand fraction division

Abstract: When children learn about fractions, their prior knowledge of whole numbers often interferes, resulting in a whole number bias. However, many fraction concepts are generalizations of analogous whole number concepts; for example, fraction division and whole number division share a similar conceptual structure. Drawing on past studies of analogical transfer, we hypothesize that children’s whole number division knowledge will support their understanding of fraction division when their relevant prior knowledge is activated immediately before engaging with fraction division. Children in 5th and 6th grade modeled fraction division with physical objects after modeling a series of addition, subtraction, multiplication, and division problems with whole number operands and fraction operands. In one condition, problems were blocked by operation, such that children modeled fraction problems immediately after analogous whole number problems (e.g., fraction division problems followed whole number division problems). In another condition, problems were blocked by number type, such that children modeled all four arithmetic operations with whole numbers in the first block, and then operations with fractions in the second block. Children who solved whole number division problems immediately before fraction division problems were significantly better at modeling the conceptual structure of fraction division than those who solved all of the fraction problems together. Thus, implicit analogies across shared concepts can affect children’s mathematical thinking. Moreover, specific analogies between whole number and fraction concepts can yield a positive, rather than a negative, whole number bias.

Teachers' gestures and students' learning: sometimes "hands off" is better.

Abstract: During mathematics instruction, teachers often make links between different representations of mathematical information, and they sometimes use gestures to refer to the representations that they link. In this research, we investigated the role of such gestures in students’ learning from lessons about links between linear equations and corresponding graphs. Eighty-two middle-school students completed a pretest, viewed a video lesson, and then completed a posttest comparable to the pretest. In all of the video lessons, the teacher explained the links between equations and graphs in speech. The lessons varied in whether the teacher referred to the equations in gesture and in whether she referred to the graphs in gesture, yielding four conditions: neither equations nor graphs, equations only, graphs only, and both equations and graphs. In all conditions, the gestures were redundant with speech, in the sense that the referents of the gestures were also mentioned in speech (e.g., pointing to “2” while saying “2”). Students showed substantial learning in all conditions. However, students learned less when the teacher referred to the equations in gesture than when she did not. This was not the case for gesture to graphs. These findings are discussed in terms of the processing implications of redundancy between gesture and speech, and the possibility of “trade-offs” in attention to the visual representations. The findings underscore the need for a more nuanced view of the role of teachers’ gestures in students’ comprehension and learning.

What We Say and How We Do: Action, Gesture, and Language in Proving

Abstract: Author(s): Caroline (Caro) Williams-Pierce, Elizabeth L. Pier, Candace Walkington, Rebecca Boncoddo, Virginia Clinton, Martha W. Alibali and Mitchell J. Nathan Source: Journal for Research in Mathematics Education, Vol. 48, No. 3 (May 2017), pp. 248260 Published by: National Council of Teachers of Mathematics Stable URL: http://www.jstor.org/stable/10.5951/jresematheduc.48.3.0248 Accessed: 19-02-2018 06:28 UTC

How Revisions to Mathematical Visuals Affect Cognition: Evidence from Eye Tracking.

Abstract: Mathematics curricula are frequently rich with visuals, but these visuals are often not designed for optimal use of students’ limited cognitive resources. The authors of this study revised the visuals in a mathematics lesson based on instructional design principles. The purpose of this study is to examine the effects of these revised visuals on students’ cognitive load, cognitive processing, learning, and interest. Middle-school students (N = 62) read a lesson on early algebra with original or revised visuals while their eye movements were recorded. Students in the low prior knowledge group had less cognitive load and cognitive processing with the revised lesson than the original lesson. However, the reverse was true for students in the middle prior knowledge group. There were no effects of the revisions on learning. The findings are discussed in the context of the expertise reversal effect as well as the cognitive theory of multimedia learning and cognitive load theory.

The Promise and Pitfalls of Making Connections in Mathematics.

Abstract: Making connections during math instruction is a recommended practice, but may increase the difficulty of the lesson. We used an avatar video instructor to qualitatively examine the role of linking multiple representations for 24 middle school students learning algebra. Students were taught how to solve polynomial multiplication problems, such as (2x + 5)(x + 2), using two representations. Students who viewed an explicit linking episode were more likely to make important connections, but less likely to exhibit problem-solving success than students who did not view the linking episode. Further, the quality of the connections made by the students was negatively related to subsequent problem solving and transfer. Thus, although focusing on connections may support rich understanding, it may decrease learning of solution methods. The results showcase the promise and pitfalls of making connections in mathematics.