The hands that guide the thinking: Interactivity in mental arithmetic

The Hands That Guide the Thinking: Interactivity in Mental Arithmetic Lisa G. Guthrie (l.guthrie@kingston.ac.uk) Department of Psychology, Kingston University, Kingston upon Thames, KT1 2EE, UNITED KINGDOM Julia K. Mayer ( j.mayer@kingston.ac.uk) Faculty of Psychology and Neuroscience, Maastricht University 6200 MD Maastricht, THE NETHERLANDS Frederic Vallee-Tourangeau ( f.vallee-tourangeau@kingston.ac.uk) Department of Psychology, Kingston University, Kingston upon Thames, KT1 2EE, UNITED KINGDOM Abstract Whether it is in mining distal cultural influences or using more proximal artefacts, problem solving in the wild routinely scaffolds on the basis of interacting with resources outside the head. Individuals often gesture, point or use objects as an aid to solving quotidian arithmetic problems. Interactivity has been linked to better performance in problem solving, possibly due to a more efficient allocation of attentional resources and better distribution of cognitive load. Previous research suggests an interplay between the cognitive and motor system whereby the later can lighten the strain on working memory capacity (Goldin- Meadow, Nusbaum, Kelly & Wagner, 2001; Carlson, Avraamedes, Cary & Strasberg, 2007; Vallee-Tourangeau, 2013). In attempting to simulate these moves made in the world, different levels of interactivity were examined with a series of mental arithmetic problems. Participants were also profiled in terms of attitude to varying problem presentations as an assessment of their engagement in the task. The integration of artifacts, such as tokens or a pen, provided individuals with the possibility to explore the opportunities afforded by a dynamic modification of the problem. Mental arithmetic performance was more accurate and more efficient under these conditions. Participants also felt more positive about and better engaged with the task when they could reconfigure the problem presentation through interactivity. These findings underscore the importance of engineering task environments that support distributed problem representation and adequate levels of interactivity that creates a dynamically shifting topography of action affordances. Keywords: Interactivity; Mental arithmetic; Problem solving; Distributed Representation; Task engagement. Introduction Mathematical problems are embedded in everyday life in a variety of different shapes and forms. When confronted with an arithmetic task, people often rearrange the physical display by interacting with the environment. They might move coins while counting their money, note subtotals with a pen or use their hands to gesture, point or count (Kirsh, 1995; Neth & Payne, 2001). Mental arithmetic tasks often entail strategic thinking and deliberate information processing, which require time and effort (Vallee-Tourangeau, 2013). Besides basic, well-rehearsed sums, computations are generally said to pose a relatively high cognitive load on an individual’s internal resources, such as working memory (Ashcraft, 1995; DeStefano & Lefevre, 2004). Numbers are held, added and manipulated in order to solve the problem employing different working memory subsystems, including storage, retrieval and allocation of attentional resources. Dependent on the complexity and length of a mental arithmetic task, the demands of finding a solution may impose a relatively low or high cognitive load, potentially imposing substantial demands on working memory capacity. This capacity may, however, be stretched or reduced by certain internal or external factors, which can subsequently paint a misleading profile of an individual’s true arithmetic capabilities (Ashcraft & Moore, 2009). Interactivity The internal cognitive and physical resources deployed to tackle a problem may be taxed by various features of the task—such as time pressure, level of difficulty, and fatigue. Reasoners naturally recruit artefacts and use the physical space to make thinking easier and more efficient. Increased levels of interactivity have been linked to better performance, possibly due to a stronger focus of attention and better distribution of cognitive load (Goldin-Meadow et al., 2001; Carlson, Avraamides, Cary & Strasberg, 2007; Vallee-Tourangeau, Sirota & Villejoubert, 2013). Previous research implicates an interplay between the cognitive and motor system whereby the later can lighten the strain on working memory capacity reducing the expenditure of internal resources (Goldin-Meadow, Alibali & Church, 1993). Improved effectiveness, indicated by increased accuracy and speed, has also been related to movement execution, such as nodding and pointing (Goldin-Meadow et al., 2001), as well as manipulations of the problem’s spatial arrangement (Vallee-Tourangeau, 2013). So it seems that the shaping and re-shaping of the problem presentation can help surpass the original limitations of working memory capacity by lowering the expense of internal resources necessary to solve the task and guide attention. This could subsequently increase efficiency.