Touchscreen Tablets: Coordinating Action and Perception for Mathematical Cognition

Abstract

Proportional reasoning is important and yet difficult for many students, who often use additive strategies, where multiplicative strategies are better suited. In our research we explore the potential of an interactive touchscreen tablet application to promote proportional reasoning by creating conditions that steer students toward multiplicative strategies. The design of this application (Mathematical Imagery Trainer) was inspired by arguments from embodied-cognition theory that mathematical understanding is grounded in sensorimotor schemes. This study draws on a corpus of previously treated data of 9–11 year-old students, who participated individually in semi-structured clinical interviews, in which they solved a manipulation task that required moving two vertical bars at a constant ratio of heights (1:2). Qualitative analyses revealed the frequent emergence of visual attention to the screen location halfway along the bar that was twice as high as the short bar. The hypothesis arose that students used so-called “attentional anchors” (AAs)—psychological constructions of new perceptual structures in the environment that people invent spontaneously as their heuristic means of guiding effective manual actions for managing an otherwise overwhelming task, in this case keeping vertical bars at the same proportion while moving them. We assumed that students’ AAs on the mathematically relevant points were crucial in progressing from additive to multiplicative strategies. Here we seek farther to promote this line of research by reanalyzing data from 38 students (aged 9–11). We ask: (1) What quantitative evidence is there for the emergence of AAs?; and (2) How does the transition from additive to multiplicative reasoning take place when solving embodied proportions tasks in interaction with the touchscreen tablet app? We found that: (a) AAs appeared for all students; (b) the AA-types were few across the students; (c) the AAs were mathematically relevant (top of the bars and halfway along the tall bar); (d) interacting with the tablet was crucial for the AAs’ emergence; and (e) the vast majority of students progressed from additive to multiplicative strategies (as corroborated with oral utterances). We conclude that touchscreen applications have the potential to create interaction conditions for coordinating action and perception into mathematical cognition.

Using a cluster-based regime-switching dynamic model to understand embodied mathematical learning

“…We conducted a secondary data analysis from a previous study [10]. In the study, forty-five fifth-and sixth-graders of ages 9-11 (M = 135.37 months, SD = 8.37 months, and Female = 17) participated in task-based semi-structured interviews at schools in the Netherlands.…”

“…Our study develops upon the works of Dor Abrahamson and colleagues who have studied the development of the mathematical concept of proportionality. To ground the learning of proportionality on its physical enactment, Abrahamson and colleagues developed an embodied learning platform called the Mathematics Imagery Training of Proportion (MIT-P) [3,10]. A recent version of the MIT-P developed by the embodied cognition group at the University of Utrecht uses a touchscreen tablet to help students explore the concept of proportion physically (see Figure 1).…”

“…Using the MIT-P, researchers have advanced arguments as to how action-based learning environments foment spontaneous coordination of sensorimotor activity, which, in turn, supports the learning of mathematical concepts [17]. For instance, various studies with the MIT-P have investigated relevant changes in students' sensorimotor coordination and have advanced hypotheses as to how the development of dynamic coordination represents the learning of the concept of proportion [1,10]. In particular, using qualitative approaches, researchers have found empirical evidence of various patterns of coordination dynamics.…”

Numerical Affordance Influences Action Execution: A Kinematic Study of Finger Movement

“…Last but not least, our protocol – based on a self-motivating and engaging task – would allow to investigate numerical cognition and its relation with space without the anxiety which usually disadvantages children with problems in mathematical comprehension (for the use of an innovative approach on mathematical learning with Touchscreen Tablets, see Duijzer et al, 2017 ). Highly math-anxious persons have a common and strong tendency to avoid math, which reduces their possibility to increase their math competences ( Ashcraft, 2002 ).…”

Secondary Benefits to Attentional Processing Through Intervention With an Interactive Maths App

“…However, in the current study, children actively engaged and interacted with the maths app rather than passively being exposed to screen time. Specifically, the interactive, multi-sensory learning environment provided by the maths app may have provided attentional anchors that may have guided children's action and perception, which together with the multi-touch nature of the tablet device may have allowed children to dynamically engage with the new mathematical concepts (Duijzer et al, 2017). As such, this high level of attentional processing of the mathematical content required to progress within the maths app may have contributed to the observed, secondary benefit of an increase in core attentional skills.…”