An exploratory study to improve reading and comprehending mathematical expressions in braille

2021 ◽  
pp. 026461962110449
Author(s):  
Annemiek van Leendert ◽  
LG Boonstra ◽  
Michiel Doorman ◽  
Paul Drijvers ◽  
Johannes van der Steen ◽  
...  
Keyword(s):  
Retention Test ◽  
Exploratory Study ◽  
Reading Strategies ◽  
Mathematical Structure ◽  
Test Results ◽  
Finger Movements ◽  
Mathematical Structures ◽  
Braille Reader ◽  
Mathematical Expressions ◽  
Braille Display

Braille readers read and comprehend mathematical expressions while moving their fingertips over braille characters. The aim of this exploratory study was to investigate the effect of an intervention that teaches braille readers who use a braille display to use finger movements with a focus on the expression’s mathematical structure. The finger movements involved movements where the two index fingers are about one or two braille cells apart and movements where the index fingers explore different parts of the expression. We investigated to what extent the intervention supports an interplay between finger movements and the expression’s mathematical structure to make the process of calculating the value of an expression easier and to make braille readers more aware of the expression’s structure. Three braille readers, respectively in Grades 7, 8, and 11, received the intervention consisting of five individual lessons. During the pre-, post-, and retention test, the braille readers’ finger movements were video recorded, as well as the time needed to read and process the mathematical tasks. Four expressions were selected for further analysis. The results show that during the posttest, each braille reader required at least 29% less time to read and process the expressions. The retention test results were even better. Scanpaths indicated that braille readers picked up features of mathematical structures more easily after the intervention. Based on our findings, we recommend that braille readers receive lessons in tactile reading strategies that support the reading and processing of mathematical expressions and equations.

scholarly journals An Exploratory Study of Reading Mathematical Expressions by Braille Readers

2019 ◽  
Vol 113 (1) ◽  
pp. 68-80
Author(s):  
Annemiek van Leendert ◽  
Michiel Doorman ◽  
Paul Drijvers ◽  
Johan Pel ◽  
Johannes van der Steen
Keyword(s):  
Exploratory Study ◽  
Reading Strategies ◽  
Mathematical Structure ◽  
Mathematical Expressions ◽  
Mathematical Problems ◽  
Visual Reading ◽  
Motion Capturing

Introduction: Braille readers encounter difficulties when reading mathematical expressions. In this exploratory study, we created a setting to investigate these difficulties. Method: Using a motion-capturing system, we analyzed the tactile strategies of three braille readers while they read mathematical expressions. To compare tactile with visual reading strategies, we also analyzed the oculomotor performance in five print readers. Results: The analysis showed that the two experienced braille readers needed about 3.5 times as much time as print readers to read and solve four items involving mathematical expressions. The braille readers used personal reading strategies for all items with little use of the structure of the expression. In contrast, the reading strategies of print readers showed item-dependent and structure-related characteristics. Discussion: The braille readers had difficulties, within the constraints of tactile reading, to align their reading strategies with the solution procedures required by the mathematical structure of the items. Implications for practitioners: Teachers need to become aware of the kind of problems that braille readers confront when they try to comprehend and solve mathematical problems.

scholarly journals Patient and provider perceptions of a novel cognitive functioning report for patients with systemic lupus erythematosus: a qualitative study

2021 ◽  
Vol 8 (1) ◽  
pp. e000476
Author(s):  
Laura Plantinga ◽  
Ann Vandenberg ◽  
Felicia Goldstein ◽  
Brian Jones ◽  
Jeremy Johnson ◽  
...  
Keyword(s):  
Lupus Erythematosus ◽  
Cognitive Assessment ◽  
Exploratory Study ◽  
Cognitive Test ◽  
Test Results ◽  
Assessment Data ◽  
Provider Perceptions ◽  
Potential Barriers ◽  
Cognitive Information ◽  
Multiple Domains

ObjectiveTo determine whether and how cognitive assessment data should be included in a report for patients with SLE and their providers.MethodsLeveraging experiences from prior studies, we created a cognitive report that included a hypothetical patient’s results on tests of multiple domains based on the NIH Toolbox Fluid Cognition Battery. In focus groups that comprised patients with SLE (two groups) and their providers (two groups), feedback was sought on the presentation of results as well as the potential value of the report in the clinical setting.ResultsFeedback regarding the presentation of the report was generally positive. Both patients with SLE and their providers liked its simple graphics and use of a colour-gradated scale to indicate performance. However, both groups stressed the importance of using non-stigmatising language in describing results. Several potential purposes of the report, including distinguishing cognitive versus other issues, explaining cognitive challenges, improving patient–provider interactions, guiding decision-making, improving functioning or preventing impairment and tracking cognitive function over time, were noted by the participants. Potential barriers, such as inadequate clinical staffing or time and lack of potential treatments for identified issues, were also discussed.ConclusionIn this exploratory study, we found that both patients with SLE and their providers were receptive to the idea of a patient-friendly report of cognitive test results. This study provides important information to guide future pragmatic research to optimise the delivery of cognitive information to patients with SLE.

scholarly journals Do Children Benefit External Focus of Attention as Much as Adults? A Motor Learning Study

2017 ◽  
Vol 11 (7) ◽  
pp. 85 ◽  
Author(s):  
Somaye Roshandel ◽  
Hamidreza Taheri ◽  
Amir Moghadam
Keyword(s):  
Motor Skills ◽  
Retention Test ◽  
Attentional Focus ◽  
Focus Of Attention ◽  
Learning Study ◽  
Test Results ◽  
Future Studies ◽  
External Focus ◽  
Internal Focus ◽  
And Task

Recent evidence supports advantages of an external focus of attention on learning motor skills, however, there is a need to retest these finding for children and comparing them with adults. Thus, the purpose of current study was to determine the effect of different attentional focus on learning a motor skill in children and adults. Thirty children (8-12 year) and thirty adults (25-42 years) were randomly assigned to one of four groups: (1) Children external focus of attention (EFA), (2) Children- internal focus of attention (IFA), (3) Adults- External focus of attention (EFA), (4) Adults- internal focus of attention (IFA). Following initial instructions and task demonstration, participants performed 60 darts throwing in six blocks and 24 hours later performed 10 additional throws for retention test. Results revealed that children benefited from EFA and IFA instruction in the same manner, however, adults benefited from EFA more than IFA instruction. Future studies should continue to examine effects of different attentional focus on other skills.

Automatic Assessment of Benton Visual Retention Test Results: A Pilot Study

2021 ◽  
pp. 1-8
Author(s):  
Dominika Gabor ◽  
Rafał Doniec ◽  
Szymon Sieciński ◽  
Natalia Piaseczna ◽  
Konrad Duraj ◽  
...  
Keyword(s):  
Pilot Study ◽  
Retention Test ◽  
Test Results ◽  
Automatic Assessment ◽  
Benton Visual Retention Test

Abstraction and Representational Capacity in Computational Structures

2019 ◽  
pp. 210-229
Author(s):  
Michael Weisberg
Keyword(s):  
Mathematical Models ◽  
Computational Models ◽  
Mathematical Structure ◽  
Narrative Form ◽  
Mathematical Structures ◽  
Computational Structure ◽  
Representational Capacity ◽  
Computational Structures

Michael Weisberg’s book Simulation and Similarity argued that although mathematical models are sometimes described in narrative form, they are best understood as interpreted mathematical structures. But how can a mathematical structure be causal, as many models described in narrative seem to be? This chapter argues that models with apparently narrative form are actually computational structures. It explores this suggestion in detail, examining what computational structure consists of, the resources it offers modelers, and why attempting to re-describe computational models as imaginary concrete systems fails even more dramatically than it does for mathematical models.

scholarly journals Unification of Gravity and Electromagnetism

2021 ◽  
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Mathematical Structure ◽  
Momentum Tensor ◽  
Dirac Field ◽  
Field Equations ◽  
Mathematical Structures ◽  
Gravitational Field Equations ◽  
Definition Of ◽  
Two Sides

Gravity and electromagnetism are two sides of the same coin, which is the clue of this unification. Gravity and electromagnetism are representing by two mathematical structures, symmetric and antisymmetric respectively. Einstein gravitational field equation is the symmetric mathematical structure. Electrodynamics Lagrangian is three parts, for electromagnetic field, Dirac field and interaction term. The definition of canonical energy momentum tensor was used for each term in Electrodynamics Lagrangian to construct the antisymmetric mathematical structure. Symmetric and antisymmetric gravitational field equations are two sides of the same Lagrangian

scholarly journals A New Kind of Aesthetics – The Mathematical Structure of the Aesthetic

2017 ◽  
Author(s):  
Akihiro Kubota ◽  
Hirokazu Hori ◽  
Makoto Naruse ◽  
Fuminori Akiba
Keyword(s):  
Human Activity ◽  
Category Theory ◽  
Mathematical Structure ◽  
Derived Category ◽  
New Method ◽  
Work Of Art ◽  
New Approach ◽  
Mathematical Structures ◽  
Dynamic Relations ◽  
The Aesthetic

This paper proposes a new approach to investigation into the aesthetics. Specifically, it argues that it is possible to explain the aesthetic and its underlying dynamic relations with axiomatic structure (the octahedral axiom derived category) based on contemporary mathematics – namely, category theory – and through this argument suggests the possibility for discussion about the mathematical structure of the aesthetic. If there was a way to describe the structure of aesthetics with the language of mathematical structures and mathematical axioms – a language completely devoid of arbitrariness – then we would make possible a synthetical argument about the essential human activity of “the aesthetics”, and we would also gain a new method and viewpoint on the philosophy and meaning of the act of creating a work of art and artistic activities. This paper presents one hypothesis as a first step in constructing the science of dynamic generative aesthetics based on axiomatic functionalism, which is in turn based on a new interdisciplinary investigation into the functional structure of aesthetics.

scholarly journals Reality and Super-Reality: Properties of a Mathematical Multiverse

Axiomathes ◽  
2019 ◽  
Vol 30 (4) ◽  
pp. 453-478
Author(s):  
Alan McKenzie
Keyword(s):  
Quantum Theory ◽  
Mathematical Structure ◽  
Self Awareness ◽  
Complete Structure ◽  
Mathematical Structures ◽  
Structural Environment ◽  
Parallel Universes ◽  
Definition Of ◽  
Rudimentary Form ◽  
The Universe

Abstract Ever since its foundations were laid nearly a century ago, quantum theory has provoked questions about the very nature of reality. We address these questions by considering the universe—and the multiverse—fundamentally as complex patterns, or mathematical structures. Basic mathematical structures can be expressed more simply in terms of emergent parameters. Even simple mathematical structures can interact within their own structural environment, in a rudimentary form of self-awareness, which suggests a definition of reality in a mathematical structure as simply the complete structure. The absolute randomness of quantum outcomes is most satisfactorily explained by a multiverse of discrete, parallel universes. Some of these have to be identical to each other, but that introduces a dilemma, because each mathematical structure must be unique. The resolution is that the parallel universes must be embedded within a mathematical structure—the multiverse—which allows universes to be identical within themselves, but nevertheless distinct, as determined by their position in the structure. The multiverse needs more emergent parameters than our universe and so it can be considered to be a superstructure. Correspondingly, its reality can be called a super-reality. While every universe in the multiverse is part of the super-reality, the complete super-reality is forever beyond the horizon of any of its component universes.

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