scholarly journals Mathematics in the Digital Age: The Case of Simulation-Based Proofs

2021 ◽  
Author(s):  
Moritz Lucius Sümmermann ◽  
Daniel Sommerhoff ◽  
Benjamin Rott
Keyword(s):  
Dynamic Geometry ◽  
User Interaction ◽  
Alternative Form ◽  
Sociomathematical Norms ◽  
Mathematical Proofs ◽  
Mathematical Simulations ◽  
Simulation Based ◽  
Actual Use ◽  
Theory Yield ◽  
Functions Of Proof

AbstractDigital transformation has made possible the implementation of environments in which mathematics can be experienced in interplay with the computer. Examples are dynamic geometry environments or interactive computational environments, for example GeoGebra or Jupyter Notebook, respectively. We argue that a new possibility to construct and experience proofs arises alongside this development, as it enables the construction of environments capable of not only showing predefined animations, but actually allowing user interaction with mathematical objects and in this way supporting the construction of proofs. We precisely define such environments and call them “mathematical simulations.” Following a theoretical dissection of possible user interaction with these mathematical simulations, we categorize them in relation to other environments supporting the construction of mathematical proofs along the dimensions of “interactivity” and “formality.” Furthermore, we give an analysis of the functions of proofs that can be satisfied by simulation-based proofs. Finally, we provide examples of simulation-based proofs in Ariadne, a mathematical simulation for topology. The results of the analysis show that simulation-based proofs can in theory yield most functions of traditional symbolic proofs, showing promise for the consideration of simulation-based proofs as an alternative form of proof, as well as their use in this regard in education as well as in research. While a theoretical analysis can provide arguments for the possible functions of proof, they can fulfil their actual use and, in particular, their acceptance is of course subject to the sociomathematical norms of the respective communities and will be decided in the future.

scholarly journals The Implementation Gap in Laparoscopic Simulation Training

2018 ◽  
Vol 108 (2) ◽  
pp. 109-116 ◽  
Author(s):  
K. Fjørtoft ◽  
L. Konge ◽  
I. Gögenur ◽  
E. Thinggaard
Keyword(s):  
Online Survey ◽  
Simulation Training ◽  
Improve Patient Safety ◽  
Medical Doctors ◽  
Implementation Gap ◽  
Simulation Based ◽  
Actual Use ◽  
Training Courses ◽  
Baseline Characteristics ◽  
Improve Patient

Background and Aims: Simulation-based training in laparoscopy can improve patient safety and efficiency of care, but it depends on how it is used. Research in medical education has moved from demonstrating transferability of simulation training to the operating room to how to best implement it. This study aims to investigate how simulation-based training in laparoscopy has been implemented Scandinavia. Material and Methods: An online survey was sent out to medical doctors at surgical, gynecological, and urological departments at 138 hospitals in Denmark, Norway, and Sweden. The questionnaire included questions on respondents’ baseline characteristics, opinions, access, and actual use of simulation-based training in laparoscopy. Results: In total, 738 respondents completed the survey. Of these, 636 (86.2%) of respondents agreed or strongly agreed that simulation-based training in laparoscopy should be mandatory. A total of 602 (81.6%) had access to simulation-based training in laparoscopy. Of the total 738 respondents, 141 (19.1%) were offered structured training courses, 129 (17.5%) were required to reach a predefined level of competency, and 66 (8.9%) had mandatory courses in laparoscopy. In all, 72 (9.8%) had never used simulation-based training in laparoscopy. Conclusion: An implementation gap in laparoscopic simulation-based training still exists in Scandinavia. Simulation equipment is generally available, but there is a lack of structured simulation-based training.

scholarly journals An Inverse Kinematics Demonstration of a Custom Robot using C# and CoppeliaSim

2021 ◽  
pp. 78-87
Author(s):  
Sudip Chakraborty ◽  
P. S. Aithal
Keyword(s):  
Inverse Kinematics ◽  
Design Methodology ◽  
Excellent Result ◽  
User Interaction ◽  
Arm Movement ◽  
Robotic Arm ◽  
The Real ◽  
Simulation Based ◽  
Real Robot ◽  
Definite Result

Purpose: Inverse Kinematics (I.K.) is not as easy as Forward kinematics (F.K.), where we get a definite result. I.K. algorithm provides several possible solutions. From those finding the best solution is such a critical task. For standard robots which are commercially available in the market, the user is not concerned about I.K.'s complexity. They provide the control board and programming IDE to make it easy. However, when we develop a robotic arm from our D.H. parameter and driver board, complexity arises due to lots of difficulties for executing and successful completion. To make life easy, keeping CoppeliaSim background can eliminate the calculation overhead and get good results. The custom robot is running with less computation power. It may be a good approach. We are using C# for User Interaction. Following step by step, anyone can create a robust I.K. engine with little effort. The complete code is available in GitHub to test and experiment further. Design/Methodology/Approach: The data are propagated through Interprocess communication. For the user interaction, we use visual studio IDE using the most accessible language, C#. The user interaction data are sent to another application, CoppeliaSim, which calculates inverse kinematics, and effective results are displayed through robotic arm movement. Findings/Result: Implementing this procedure can get the excellent result of the robotics arm. Furthermore, by imposing the Value on the real robot, we can get effective results. It minimizes the research overhead on I.K. calculation. Originality/Value: Without knowing I.K. calculation complexity, receiving the Value, we can apply it to the real robot. Two issues we can solve here. One is the calculation, and another one is experiment overhead. Paper Type: Simulation-based Research.

scholarly journals GeoGebra as facilitator of a hypotrochoid generalization in an initiation scientific research project at undergraduate level

2018 ◽  
Vol 6 (10) ◽  
pp. 242-252
Author(s):  
Ana Maria Amarillo Bertone ◽  
Lucia Resende Pereira ◽  
Ingrid da Silva Pacheco ◽  
Layla Giovanna Girotto
Keyword(s):  
Undergraduate Students ◽  
Dynamic Geometry ◽  
Scientific Research ◽  
Mathematical Induction ◽  
Computational Tool ◽  
Research Project ◽  
Undergraduate Level ◽  
Mathematical Proofs ◽  
Scientific Research Project ◽  
Theoretical Results

An initiation to scientific research project was proposed for two undergraduate students in Environmental Engineering, with the porpuse of studing a generalization of the hypotrochoid and epitrochoid curves.  The GeoGebra software is the facilitator of the team of two professors and the students. The difficulties of the mathematical proofs become, in the environment of the dynamic geometry, exercises of construction of curves that, arranged in sequence, determined the generalization of the well-known hypotrochoid curve, result that is the detailed in this work. From this first discovery, the transition to epitrochoid curves or more general curve,s becomes an iterative application and an applicattion of mathematical induction. This study   has demonstrated the importance of the computational tool, specially for its contribution in the visualization of theoretical results as well as for its simplicity in coding.

scholarly journals Accommodating Practices During Episodes of Disillusionment with Mobile IT

2019 ◽  
Author(s):  
Efpraxia D. Zamani ◽  
Nancy Pouloudi ◽  
George Giaglis ◽  
Jonathan Wareham
Keyword(s):  
User Interaction ◽  
Decision Making Process ◽  
Data Frame ◽  
Individual Level ◽  
Actual Use ◽  
Adoption Research ◽  
The Individual ◽  
It Artifact ◽  
Different Levels ◽  
Practical Level

AbstractThis study investigates how tablet users react when technology falls short of their expectations. We deploy a data/frame model to study this process and investigate resistance-related reactions and the deployment of accommodating practices at the individual level. Analyzing user blogs that provide narratives on user interaction with tablets, we identify triggers of episodes of disillusionment and illustrate five sensemaking paths that users follow, eventually leading to one of three practices: 1) users choose to defer tasks until the situation changes, or they abandon the platform altogether; 2) they develop workarounds at different levels of proficiency; or 3) they proceed by reframing their expectations of the platform. By revealing user decision-making process during episodes of disillusionment, the findings contribute to information systems post-adoption research. At a practical level, the findings inform IT artifact and application design by offering insights on how users process discrepancies between their expectations and actual use experience.

A Review of 21 iPad Applications for Augmentative and Alternative Communication Purposes

2012 ◽  
Vol 21 (2) ◽  
pp. 60-71 ◽  
Author(s):  
Ashley Alliano ◽  
Kimberly Herriger ◽  
Anthony D. Koutsoftas ◽  
Theresa E. Bartolotta
Keyword(s):  
Augmentative And Alternative Communication ◽  
Cost Effective ◽  
Alternative Form ◽  
Alternative Communication ◽  
Text To Speech ◽  
Reference Guide ◽  
Expressive Communication ◽  
Communication Needs ◽  
User Friendly ◽  
Ipad Applications

Abstract Using the iPad tablet for Augmentative and Alternative Communication (AAC) purposes can facilitate many communicative needs, is cost-effective, and is socially acceptable. Many individuals with communication difficulties can use iPad applications (apps) to augment communication, provide an alternative form of communication, or target receptive and expressive language goals. In this paper, we will review a collection of iPad apps that can be used to address a variety of receptive and expressive communication needs. Based on recommendations from Gosnell, Costello, and Shane (2011), we describe the features of 21 apps that can serve as a reference guide for speech-language pathologists. We systematically identified 21 apps that use symbols only, symbols and text-to-speech, and text-to-speech only. We provide descriptions of the purpose of each app, along with the following feature descriptions: speech settings, representation, display, feedback features, rate enhancement, access, motor competencies, and cost. In this review, we describe these apps and how individuals with complex communication needs can use them for a variety of communication purposes and to target a variety of treatment goals. We present information in a user-friendly table format that clinicians can use as a reference guide.

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