Gesture and Mental Representations 1 The Role of Gesture in Supporting Mental Representations

People frequently gesture when problem-solving, particularly on tasks that require spatial transformation. Gesture often facilitates task performance by interacting with internal mental representations, but how this works is poorly understood. We investigated this question by exploring the case of Mental Abacus (MA), a technique in which users imagine moving beads on an abacus to compute sums, while moving their hands as though using an abacus. Because the content of MA is transparent and readily manipulated, it offers a unique window into how gestures interface with mental representations. We find that the size and number of MA gestures reflect the length and difficulty of math problems. Also, by selectively interfering with aspects of gesture, we find that motor planning is critical for MA, but perceptual feedback is not. We conclude that planning gestures – rather than seeing or feeling them – is critical to mental representation in MA. Gesture and Mental Representations 3 INTRODUCTION When people solve difficult problems, they often move their hands (Goldin-Meadow, Alibali & Church, 1993; Goldin-Meadow, 2003). Gesturing can affect performance on a variety of tasks (Goldin-Meadow & Beilock, 2010; Goldin-Meadow, Cook, & Mitchell, 2009; Novack, Congdon, Hemani-Lopez, & Goldin-Meadow, 2014). For example, encouraging children to gesture when explaining how they solved math problems can improve their ability to learn from instruction (Broaders, Cook, Mitchell, & Goldin-meadow, 2007); And gesturing about mental rotation appears to facilitate spatial transformation (Chu & Kita, 2011). The fact that gesture impacts task performance demonstrates that the physical and motor representations formed while gesturing interact with mental representations of objects, space, mathematics, and language (Goldin-Meadow & Beilock, 2010). However, it is often challenging to relate the content of gestures directly to their cognitive effects. The gestures that are most frequently studied are produced along with speech, making it difficult to disentangle their cognitive and communicative functions. Gestures produced without speech may offer a more transparent window into cognitive functioning. However, these gestures lack the framing that speech provides, making it difficult to infer the underlying mental representations with which gestures co-occur. The goal of the current study is to explore how gesture relates to mental representation in a case where gesture is produced without speech, but where the underlying representations are highly constrained and well understood: the case of Mental Abacus (MA). MA is a mental computation technique in which users imagine manipulating beads on an abacus (Menninger, 1969, see Figure 1). In a typical MA curriculum, students first learn to use a physical abacus, and progress to using the abacus method in the absence of the physical device. MA experts mentally invoke these same procedures to manipulate a visual image of an abacus Gesture and Mental Representations 4 (Stigler, 1984). Because MA calculations require a precise set of bead movements performed in a specific order, it is possible to infer the specific sequence of mental states that users represent while solving a problem. Figure 1. An abacus displaying the number 123,456,789. Values are represented on the abacus by moving beads toward the black center bar. Each column in the abacus represents a place value (e.g. ones, tens, etc.). Beads above the center bar have a value of 5, and lower beads have a value of 1. The MA phenomenon has caught the interest of cognitive scientists, in part, because MA users do not seem to rely on verbal resources when solving arithmetic problems. MA experts can solve arithmetic problems while answering simple verbal questions with no reduction in reaction time (Hatano, Miyake, & Binks, 1977) and are relatively unaffected by verbal shadowing (Frank & Barner, 2012). Further, limits on MA computations are consistent with limits on visual working memory (Frank & Barner, 2012), suggesting that they are supported by visual resources. This idea is supported by neuroimaging data, which indicate that MA is processed in regions associated with vision and spatial working memory (Chen et al., 2006; Hu et al., 2011; Tanaka, Michimata, Kaminaga, Honda, & Sadato, 2002). Together, these findings suggest that when MA users solve arithmetic problems, they perform a specific sequence of manipulations on a visual Gesture and Mental Representations 5