Making sense of eigenvalue–eigenvector relationships: Math majors’ linear algebra – Geometry connections in a dynamic environment

Çağlayan, Günhan

doi:10.1016/j.jmathb.2015.08.003

Cited by 25 publications

(6 citation statements)

References 17 publications

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“…One of the most frequently applied methods to determine how much information is available in the examined data is to use the eigenvalue with its attributes as the indicator [ 30 ]. For this purpose, we have quantified the eigenvalues of the dimensions according to the correspondence analysis, as shown in Table 5 .…”

Section: Resultsmentioning

confidence: 99%

Regional disparities in medical equipment distribution in the Slovak Republic – a platform for a health policy regulatory mechanism

2017

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BackgroundThis study aims to examine the localisation of selected parameters in the deployment and use of medical equipment in the Slovak Republic and to verify potential regional disparities. The study evaluates the benefits of an analytical platform for regulatory mechanisms in the healthcare system.MethodsThe correspondence analysis is applied to the entire data set containing information regarding medical equipment distribution and mortality.ResultsThe results highlight regional differences in the use of medical equipment throughout the analysed period from 2008 to 2014. The total amount of medical equipment increased slightly to 9192 devices during the time span. In 2014, there was a significant decrease of 16.44%. Disparities are found in the frequencies and structure of medical equipment. In some regions, medical equipment is not present or is present in low numbers.ConclusionsThe results regarding regional disparities demonstrate the regional development of the amount of medical equipment. The deployment of medical equipment is not proportional, and not all of the analysed devices are available in each region. The tests also indicate the appropriateness of the amount of medical equipment and create a platform for further investigation. The results of the analysis suggest the unsuitable distribution of medical equipment throughout the Slovak regions, where there are significant regional disparities. These findings can serve as a monitoring platform to evaluate the accessibility and efficiency of medical equipment usage.Trial registrationNo human participants were involved in the research.

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Section: Resultsmentioning

confidence: 99%

Regional disparities in medical equipment distribution in the Slovak Republic – a platform for a health policy regulatory mechanism

2017

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“…Although they did not use MRC in framing their work, both of these papers present findings consistent with the importance of representational fluency in students' mathematical development in linear algebra. We only found one study in linear algebra that explicitly attended to MRC; Çağlayan [27] had students explore eigenvalues and eigenvectors in a dynamic software program and argued that this provided opportunities for students to invent and develop, critique, and compare the adequacy of various representations, which are key aspects of MRC.…”

Section: B Literature On Student Understanding Of Symbols and Represmentioning

confidence: 99%

Students’ metarepresentational competence with matrix notation and Dirac notation in quantum mechanics

Wawro

Watson

Christensen

2020

Phys. Rev. Phys. Educ. Res.

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This article shares analysis regarding quantum mechanics students' metarepresentational competence (MRC) that is expressed as they engaged in solving an expectation value problem, which involves linear algebra concepts. The particular characteristic of MRC that is the focus of this analysis is students' critiquing and comparing the adequacy of representations, specifically matrix notation and Dirac notation, and judging their suitability for various tasks. With data of students' work during semistructured individual interviews, components of students' MRC were analyzed and categorized according to value-based preferences, problem-based preferences, and purpose and utility awareness. Detail is provided on two students who serve as paradigmatic examples of students' power and flexibility within different notation systems, and detail of a third student is given as a point of contrast. In addition to adapting MRC as a helpful construct for characterizing student understanding at the intersection of undergraduate mathematics and physics, we aim to demonstrate how students' rich understanding of linear algebra and quantum mechanics includes and is aided by their understanding and flexible use of different notational systems. For example, the problem-based preference aspects of MRC highlight that any particular problem-solving approach is itself intrinsically tied to a notational system. We suggest that any instruction with the goal of helping students develop a deep understanding of quantum mechanics and linear algebra should provide opportunities for students to use and improve their MRC.

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“…Several studies emphasized the use of DGE for the visualization, especially in Geometer's Sketchpad (Gol Tabaghi, 2014;Caglayan, 2015) and GeoGebra (Beltrán-Meneu, Murillo-Arcila, & Albarracin, 2016;Turgut, 2019). Cooley et al (2014) availed themselves of the affordances of GeoGebra to aid students' visualization of the ways in which points on polygons are transformed.…”

Section: Literature Reviewmentioning

confidence: 99%

Interactive Tools for Linear Algebra: Geouniud

Lepellere

Zucconi

Asbahi

et al. 2020

SIE

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GeoUniud is a user-friendly platform built-in interactive tutors which allow students to investigate specific tasks by selecting their own input values and working through a problem in a step-by-step fashion together with immediate feedback at each step. Lessons and exercises are stored and organized with a careful use of randomized controlled contents as exercises, geometrical pictures and abstract reasoning. The lessons are augmented by a virtually infinite collection of examples, and by interactive representations of concepts. As example we show the design of two interactive tools about linear transformation and change of basis in order to develop students’ sense-making in a dynamic geometry environment (DGE) within the perspective of semiotic mediation.

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Making sense of eigenvalue–eigenvector relationships: Math majors’ linear algebra – Geometry connections in a dynamic environment

Cited by 25 publications

References 17 publications

Regional disparities in medical equipment distribution in the Slovak Republic – a platform for a health policy regulatory mechanism

Regional disparities in medical equipment distribution in the Slovak Republic – a platform for a health policy regulatory mechanism

Students’ metarepresentational competence with matrix notation and Dirac notation in quantum mechanics

Interactive Tools for Linear Algebra: Geouniud

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