skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Almost in Our Grasp: The (Slow) Digital Return of Multimodal Educational Resources
Whereas I empathize with Penny’s grave concern over current modalist instructional technology – “modalist” in the sense of privileging one modality, predominantly vision, at the expense of all others – I do not quite share his bleak assessment of future offerings. Following some hopefully inspiring words from historical philosophers of education, I showcase the Quad, a haptic-tactile mechatronic device built by three US-based laboratories collaborating to create modally expansive learning tools for classrooms that are inclusive of sensorially diverse students. While the Quad is “digital” in the familiar computational sense, it is at once “digital” in the corporeal sense of evoking the fingers – it reintroduces mutimodal engagement into mathematics learning.  more » « less
Award ID(s):
1814220
PAR ID:
10500439
Author(s) / Creator(s):
Publisher / Repository:
Alexander Riegler
Date Published:
Journal Name:
Constructivist Foundations
Volume:
18
Issue:
2
ISSN:
1782-348X
Page Range / eLocation ID:
202-206
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. One of the current limitations in digital educational experiences is the lack of touch. Touch is a critical component in the learning process and in creating inclusive educational experiences for sensorially diverse learners. From haptic devices to tangible user interfaces (TUI), a growing body of research is investigating ways to bring touch back into the digital world, yet many focus on a specific dimension (e.g. haptic feedback or kinesthetic manipulation) of touch. Learning, however, is a multi-dimensional touch experience - it is about moving and being moved. This work presents the Action Quad - a novel haptic-TUI design for teaching geometry (specifically quadrilaterals). The Action Quad is a multi-point-of-contact, reconfigurable tool that synergizes the affordances of both kinesthetic interaction and haptic feedback into a single form factor. We present findings from an initial user study (N=11) investigating how sighted- hearing individuals approach, interact, and experience the Action Quad, and we present a case study with an individual with blindness. We share key takeaways from the design process and participant feedback on interactions with this novel haptic-TUI device, sharing design insights on an emerging area of research that could support a new class of educational learning tools rooted in touch. 
    more » « less
  2. A joint project of design-based educational researchers, mechatronic engineers, and digital accessibility experts has created a new genre of pedagogical technologies — hybrid material–digital multimodal artifacts for collaborative learning of sensorily diverse students in inclusive classrooms. Here we present the Quad, a manipulable quadrilateral hand-held object that is linked in real time to its digital screen-based simulation, whose own transformation, in turn, activates content-oriented voice description and output sonification. Pilot studies with blind and visually-impaired student-participants suggest the Quad’s potential in grounding geometric reasoning, insight, and generalization in exploratory haptic–proprioceptive investigation. In its conception and development, the Quad exemplifies the ethical, philosophical, and theoretical perspectives of its collaborating designers respecting all children’s universal right to access and participate in cultural practices, including techno–scientific activities. As researchers, we harness technological innovations to realize moral obligations and, through that, to promote the study of human perception, action, and cognition. We look forward to mutual growth of our research program along with parallel efforts advancing an Italian project to promote teachers’ pre-service training and professional development surrounding implications of the embodiment turn in the cognitive sciences for school-based instructional practice. 
    more » « less
  3. Aims. We analyze the behavior of the argument of pericenter ω 2 of an outer particle in the elliptical restricted three-body problem, focusing on the ω 2 resonance or inverse Lidov-Kozai resonance. Methods. First, we calculated the contribution of the terms of quadrupole, octupole, and hexadecapolar order of the secular approximation of the potential to the outer particle’s ω 2 precession rate (d ω 2 ∕d τ ). Then, we derived analytical criteria that determine the vanishing of the ω 2 quadrupole precession rate (d ω 2 /d τ ) quad for different values of the inner perturber’s eccentricity e 1 . Finally, we used such analytical considerations and described the behavior of ω 2 of outer particles extracted from N-body simulations developed in a previous work. Results. Our analytical study indicates that the values of the inclination i 2 and the ascending node longitude Ω 2 associated with the outer particle that vanish (d ω 2 /d τ ) quad strongly depend on the eccentricity e 1 of the inner perturber. In fact, if e 1 < 0.25 (>0.40825), (d ω 2 /d τ ) quad is only vanished for particles whose Ω 2 circulates (librates). For e 1 between 0.25 and 0.40825, (d ω 2 /d τ ) quad can be vanished for any particle for a suitable selection of pairs (Ω 2 , i 2 ). Our analysis of the N-body simulations shows that the inverse Lidov-Kozai resonance is possible for small, moderate, and high values of e 1 . Moreover, such a resonance produces distinctive features in the evolution of a particle in the (Ω 2 , i 2 ) plane. In fact, if ω 2 librates and Ω 2 circulates, the extremes of i 2 at Ω 2 = 90° and 270° do not reach the same value, while if ω 2 and Ω 2 librate, the evolutionary trajectory of the particle in the (Ω 2 , i 2 ) plane shows evidence of an asymmetry with respect to i 2 = 90°. The evolution of ω 2 associated with the outer particles of the N-body simulations can be very well explained by the analytical criteria derived in our investigation. 
    more » « less
  4. This paper describes the application of the code generated by the CAMPARY software to accelerate the solving of linear systems in the least squares sense on Graphics Processing Units (GPUs), in double double, quad double, and octo double precision. The goal is to use accelerators to offset the cost overhead caused by multiple double precision arithmetic. For the blocked Householder QR and the back substitution, of interest are those dimensions at which teraflop performance is attained. The other interesting question is the cost overhead factor that appears each time the precision is doubled. Experimental results are reported on five different NVIDIA GPUs, with a particular focus on the P100 and the V100, both capable of teraflop performance. Thanks to the high Compute to Global Memory Access (CGMA) ratios of multiple double arithmetic, teraflop performance is already attained running the double double QR on 1,024-by-1,024 matrices, both on the P100 and the V100. For the back substitution, the dimension of the upper triangular system must be as high as 17,920 to reach one teraflops on the V100, in quad double precision, and then taking only the times spent by the kernels into account. The lower performance of the back substitution in small dimensions does not prevent teraflop performance of the solver at dimension 1,024, as the time for the QR decomposition dominates. In doubling the precision from double double to quad double and from quad double to octo double, the observed cost overhead factors are lower than the factors predicted by the arithmetical operation counts. This observation correlates with the increased performance for increased precision, which can again be explained by the high CGMA ratios. 
    more » « less
  5. Abstract How do learners make sense of what they are learning? In this article, I present a new framework of sense-making based on research investigating the benefits and boundaries of generative learning activities (GLAs). The generative sense-making framework distinguishes among three primary sense-making modes—explaining, visualizing, and enacting—that each serve unique and complementary cognitive functions. Specifically, the framework assumes learners mentally organize and simulate the learning material (via the visualizing and enacting modes) to facilitate their ability to generalize the learning material (via the explaining mode). I present evidence from research on GLAs illustrating how visualizations and enactments (instructor-provided and/or learner-generated) can facilitate higher quality learner explanations and subsequent learning outcomes. I also discuss several barriers to sense-making that help explain when GLAs are not effective and describe possible ways to overcome these barriers by appropriately guiding and timing GLAs. Finally, I discuss implications of the generative sense-making framework for theory and practice and provide recommendations for future research. 
    more » « less