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Kinemathics: Kinetically Induced Mathematical Learning—Overview of Rationale 1
Abstract
plays more than a supportive or epiphenomenal role in the communication of essentially abstract concepts. 2
... Since the general theory of embodiment did not constrain concrete design decisions of what students were to do (Bakker, Shvarts, & Abrahamson, 2014), design-based research was used (Bakker, 2018), in which iterative testing of embodied theoretical conjectures, through the design of embodied technologies, and empirical study on students' and teachers' embodied processes were intricately linked. The initial conjecture was that mathematical knowing could be elicited by inducing an ''image'' of proportionality (Abrahamson & Howison, 2008). As shown in Fig. 1a, a mechanical pulley design hand-held students' hands to move in a 1:2 proportion (Abrahamson & Howison, 2010a), but, despite students undergoing an embodied experience of proportionality, this passive design did not yield sufficient ground for mathematical knowing (Howison, Trninic, Reinholz, & Abrahamson, 2011). ...
... Research into action-based embodied design was initiated in the domain of proportions. Design considerations for proportions were first described in 2008 (Abrahamson & Howison, 2008), in which small scale design-testing work was done towards the final design. The first empirical study of the type of design that is now known as action-based with students was conducted in 2010 (Abrahamson & Howison, 2010a). ...
... Prototyping:Abrahamson and Howison (2008, 2010a, 2010b,Howison et al. (2011) andTrninic et al. (2010); Qualitative empirical: Abrahamson et al. (2014), Abrahamson, Negrete et al. (2012), Abrahamson, Trninic and Gutiérrez (2012), Reinholz et al. (2010), Trninic and Abrahamson (2011) and Trninic et al. (2011); Quantitative: Pardos, Hu, Meng, Neff, and Abrahamson (2018); collaborative reflection: Abrahamson et al. (2012b), Flood (2018), Flood and Abrahamson (2015) and Flood et al. (2016); Virtual tutor: Flood, Neff, and Abrahamson (2015), Flood, Schneider, and Abrahamson (2014); Artifacts: Abrahamson et al. (2012a), Abrahamson, Gutierrez et al. (2011), Abrahamson, Trninic et al. (2011), Charoenying and Trninic (2011) and Gutiérrez et al. (2011); Ecologic/REC: Abrahamson (2016), Abrahamson and Sánchez-García (2015, 2016), Abrahamson, Sánchez-García and Trninic (2016), Abrahamson and Shulman (2019), Abrahamson and Trninic (2015, 2016), Hutto and Abrahamson (0000) and Hutto et al. (2015); Dance/martial: Abrahamson and Shulman (2017), Duijzer et al. (2019), ...
Embodied cognition theory emphasizes that bodily interaction with the environment is important for all forms of learning, including mathematics. This theoretical trend coincides well with developments in motion responsive technology, and has resulted in numerous embodied technologies for mathematics learning. This review aims to contribute to clarifying theoretically and empirically grounded design principles, of action-based embodied designs for mathematics learning. We analyzed 79 publications between 2010 and 2019, containing 15 studies assessing 15 sensorimotor problems for five mathematical domains (proportion, angle, area, parabola, and sine function), and explicated the characteristics of the technologies, their learning sequences and elicited learning processes, and the influence of within-task variations on students’ learning. We found that action-based designs pose motor control problems using continuous motion feedback to facilitate learners to discover and practice a challenging new ways of moving their hand(s) in which to ground mathematical cognition. The state of discovery of the sensorimotor solution is important, and passive and readymade designs are cautioned. The learning sequence in which these technologies are embedded elicit mathematical knowing through necessary and sequential phases in which personal idiosyncratic experiences increasingly converge into a culturally shared symbolic mathematical discourse. In the pre-symbolic stage, an acting step elicits students to actively establish new motor coordination-patterns through the emergence of new perceptual structures known as attentional anchors. In the subsequent reflecting step, students’ personal sensorimotor experiences and attentional anchors become the ground for referencing in (a shared) mathematical discourse through multimodal (words, gestures) collaboration with a tutor. In the symbolic stage cultural artifacts (grids, protractors, numbers) are included in students’ field of promoted action, which discretizes and formalize students’ actions and subsequent reflection into culturally recognizable quantitative and symbolic forms. Critically, task factors such as the type of objects students manipulate (cursors icons, bars, rectangles), and the direction these objects are moved (parallel, orthogonal) affect students’ attentional anchors and subsequent reflections in the pre-symbolic stage, but converge to similar mathematical insights in the symbolic stage. These insights help to better use (new) motion responsive technology in eliciting child–computer interaction that can lead to mathematical cognition and beyond.
... Since the general theory of embodiment did not constrain concrete design decisions of what students were to do (Bakker, Shvarts, & Abrahamson, 2014), design-based research was used (Bakker, 2018), in which iterative testing of embodied theoretical conjectures, through the design of embodied technologies, and empirical study on students' and teachers' embodied processes were intricately linked. The initial conjecture was that mathematical knowing could be elicited by inducing an ''image'' of proportionality (Abrahamson & Howison, 2008). As shown in Fig. 1a, a mechanical pulley design hand-held students' hands to move in a 1:2 proportion (Abrahamson & Howison, 2010a), but, despite students undergoing an embodied experience of proportionality, this passive design did not yield sufficient ground for mathematical knowing (Howison, Trninic, Reinholz, & Abrahamson, 2011). ...
... Research into action-based embodied design was initiated in the domain of proportions. Design considerations for proportions were first described in 2008 (Abrahamson & Howison, 2008), in which small scale design-testing work was done towards the final design. The first empirical study of the type of design that is now known as action-based with students was conducted in 2010 (Abrahamson & Howison, 2010a). ...
... Prototyping:Abrahamson and Howison (2008, 2010a, 2010b,Howison et al. (2011) andTrninic et al. (2010); Qualitative empirical: Abrahamson et al. (2014), Abrahamson, Negrete et al. (2012), Abrahamson, Trninic and Gutiérrez (2012), Reinholz et al. (2010), Trninic and Abrahamson (2011) and Trninic et al. (2011); Quantitative: Pardos, Hu, Meng, Neff, and Abrahamson (2018); collaborative reflection: Abrahamson et al. (2012b), Flood (2018), Flood and Abrahamson (2015) and Flood et al. (2016); Virtual tutor: Flood, Neff, and Abrahamson (2015), Flood, Schneider, and Abrahamson (2014); Artifacts: Abrahamson et al. (2012a), Abrahamson, Gutierrez et al. (2011), Abrahamson, Trninic et al. (2011), Charoenying and Trninic (2011) and Gutiérrez et al. (2011); Ecologic/REC: Abrahamson (2016), Abrahamson and Sánchez-García (2015, 2016), Abrahamson, Sánchez-García and Trninic (2016), Abrahamson and Shulman (2019), Abrahamson and Trninic (2015, 2016), Hutto and Abrahamson (0000) and Hutto et al. (2015); Dance/martial: Abrahamson and Shulman (2017), Duijzer et al. (2019), ...
We study the augmented reality sandbox (ARSB) as an embodied learning environment to foster meaning making in the context of bivariable calculus. We present the case of Tiago, a first-year bachelor chemistry student, performing a series of tasks based on embodied design, including perception-based, action-based and incorporation-based tasks. Tiago’s work demonstrates the affordances of the ARSB, e.g. to trace a height line and to manipulate plastic planes either with or without feedback from projected height lines. Tiago’s reasoning about mathematical concepts, e.g. the parameters in a plane equation and the gradient vector, is supported by perceptual structures that he discovers during these embodied tasks. We distinguished two ways in which ARSB affordances were used in the learning sequence. In perception-based and action-based tasks, the affordances of the ARSB were immediately available and intensively involved in the interaction. In incorporation tasks, on the contrary, a critical affordance was deliberately removed and the student was able to reproduce its functionality without technology.
... In a very rough sense, the older group is academically on par with the younger group, being both verbally weaker and less articulate than their academic track peers. The tasks were variations on the Mathematical Imagery Trainer for Proportion (MITP) [Abrahamson, Gutiérrez, Charoenying, Negrete, & Bumbacher, 2012;Abrahamson & Howison, 2008;Abrahamson, Trninic, Gutiérrez, Huth, & Lee, 2011;Howison, Trninic, Reinholz, & Abrahamson, 2011]. The MITP is an interactive technological device designed for students first to develop new sensorimotor operatory schemes underlying mathematical concepts and only then mathematize these schemes using standard frames of references (e.g., a grid, numerals). ...
The combination of two methodological resources-natural user interface and multimodal learning analytics-is creating opportunities for educational researchers to empirically evaluate theoretical models accounting for the emergence of concepts from situated sensorimotor activity. Seventy-six participants (9-14 years old) solved tablet-based presymbolic manipulation tasks designed to foster grounded meanings for the mathematical concept of proportional equivalence. Data gathered in task-based semi-structured clinical interviews included action logging, eye-gaze tracking, and videography. Analysis of these data indicates that successful task performance coincided with spontaneous emergence of stable dynamical gaze path patterns soon followed by multimodal articulation of strategy. Significantly, gaze patterns included unmanipulated, non-salient screen locations. We present cumulative evidence that these gaze patterns served as "attentional anchors" mediating participants' problem solving. By way of further contextualizing our claim, we also present case studies from the various experimental conditions. We interpret the findings as enabling us to revisit, support, refine, and perhaps elaborate on seminal claims from Piaget's theory of genetic epistemology and in particular his insistence on the role of situated motor-action coordination in the process of reflective abstraction.
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