Disconnect between undergraduates’ understanding of the algebraic and geometric aspects of vectors

Liu, Dan; Kottegoda, Yasanthi

doi:10.1088/1361-6404/ab0509

Cited by 11 publications

(11 citation statements)

References 17 publications

(30 reference statements)

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“…They found that the average students' performance in problems involving the algebraic notationîĵk was better than the performance in the graphical (arrow) format, both in the context of mathematics and in the context of physics. Consistently, Liu and Kottegoda [86] highlighted a disconnect between undergraduates' understanding of the algebraic and geometric aspects of vectors.…”

Section: Theoretical Backgroundmentioning

confidence: 92%

Testing students ability to use derivatives, integrals, and vectors in a purely mathematical context and in a physical context

Carli

Lippiello

Perona³

et al. 2020

Phys. Rev. Phys. Educ. Res.

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In this article, we discuss the development and the administration of a multiple-choice test, which we named Test of Calculus and Vectors in Mathematics and Physics (TCV-MP), aimed at comparing students' ability to answer questions on derivatives, integrals, and vectors in a purely mathematical context and in the context of physics. The comparison between the two contexts was achieved by using parallel (isomorphic) questions in mathematics and physics. The final version of the test contains 34 items (17 in a purely mathematical context and 17 in the context of physics) involving different representations (graphs, words, numbers, and formal expressions) of the concepts covered by the test. The test was administered in Spring 2018 to 1252 first-year students enrolled in 23 different degree programs of the School of Science and the School of Engineering of the University of Padua. We assessed the validity, reliability, and discriminatory power of the test both as a whole and at the single-item level, obtaining values within the desired ranges. The analysis of students' answers to individual items and the comparison between parallel mathematics and physics items provides insights into the factors that affect students' ability to use derivatives, integrals, and vectors in the context of introductory physics. We believe that the instrument we have developed can be useful not only for research purposes, but also for instructors and for students.

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Section: Theoretical Backgroundmentioning

confidence: 92%

Testing students ability to use derivatives, integrals, and vectors in a purely mathematical context and in a physical context

Carli

Lippiello

Perona³

et al. 2020

Phys. Rev. Phys. Educ. Res.

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“…The topic of vectors, as a modelling system, allows students to imagine complex dynamics embedded in physical phenomena, like Newtonian mechanics (Doerr, 1997; White, 1983) and electro‐magnetism (Pepper, Chasteen, Pollock, & Perkins, 2012). Learning how to use vector representations in problem solving requires integrating MERs used in and in equations, and therefore students face many difficulties in understanding and operating with vectors, especially in their geometric form (Aguirre, 1988a; Appova & Berezovski, 2013; Barniol & Zavala, 2014; Flores, Kanim, & Kautz, 2004; Liu & Kottegoda, 2019).…”

Section: Model‐based Reasoning (Mbr) Using Vectors: Limitations Of Stmentioning

confidence: 99%

“…Physics educators have reported similar findings at the school level (Barniol & Zavala, 2014; Nguyen & Meltzer, 2003; Wutchana & Emarat, 2011), even at the postgraduate level (Aguirre, 1988b; Knight, 1995; Usharani & Meera, 2018). When trying to use vectors, most students struggle with the geometry‐algebra integration (Liu & Kottegoda, 2019), which is important for conceptual understanding in general (Hohenwarter & Jones, 2007). A lack of this integration is reflected in students' struggles with vectors while modelling physical phenomena (Aguirre & Erickson, 1984; Aguirre & Rankin, 1989).…”

Section: Model‐based Reasoning (Mbr) Using Vectors: Limitations Of Stmentioning

confidence: 99%

“…A lack of this integration is reflected in students' struggles with vectors while modelling physical phenomena (Aguirre & Erickson, 1984; Aguirre & Rankin, 1989). These learning problems are acknowledged to be non‐trivial, requiring systematic investigation (e.g., Flores et al, 2004; Liu & Kottegoda, 2019).…”

Section: Model‐based Reasoning (Mbr) Using Vectors: Limitations Of Stmentioning

confidence: 99%

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Touchy feely vectors: A compensatory design approach to support model‐based reasoning in developing country classrooms

Karnam

Agrawal

Parte

et al. 2020

Computer Assisted Learning

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Educational technology designs in developing countries mostly focus on making knowledge resources widely available, through MOOCs, repositories and computer‐based tutoring. The use of digital media for cognitive augmentation, particularly interactive designs that help learners understand modelling topics in STEM, is underexplored. We report a 3‐year design study examining this potential in the Indian context, testing two iterations of an interactive system, Touchy‐Feely Vectors (TFV). The design supports learning vectors, a modelling topic pre‐university students struggle with. Virtual lesson‐plans were co‐designed with teachers to augment — but not replace — their existing practices, and to address classroom and resource constraints. Pre‐post testing of TFV‐1 (a computer‐based prototype) showed that it helped students develop a more integrated vector concept, and improved their reasoning. Field‐implementation of TFV‐2 (a textbook‐linked touch‐screen based design) in 6‐classrooms (3‐Control, N=135; 3‐Experimental, N=131) showed that it fostered cognitive engagement in average‐students and geometry‐algebra integration (model‐based reasoning) in good‐students. These results, along with a requirements analysis based on textbooks, indicate that the interaction possibilities supported by different representational media critically shape student reasoning. The study also illustrates a systematic approach to design and test digital media systems that support cognitive augmentation in developing countries.

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“…Based on the responses, they developed a taxonomy of the most frequent errors [2]. Our recent investigation revealed that several learning di culties are due to a lack of understanding of the connections between the algebraic and geometric aspects of vectors [3].…”

Section: Introductionmentioning

confidence: 99%

A study of undergraduates' understanding of vector - decomposition of forces on inclined planes

Liu¹,

Mohattala²

2021

2021 Physics Education Research Conference Proceedings

Self Cite

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Students often struggle to decompose a vector, especially when calculating the force components of an object on an inclined plane. In this study, we designed an online vector survey in the context of physics and implemented it in a primarily undergraduate university. The study focuses on the students' learning difficulties and teaching strategies associated with vector decomposition on inclined planes. The analysis of the students' responses indicates that translating a vector to the position with geometric convenience can help them identify angles and calculate vector components on inclined planes more accurately; when students are provided with the definition of the angle in the vector component formula, their performance improves.

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Disconnect between undergraduates’ understanding of the algebraic and geometric aspects of vectors

Cited by 11 publications

References 17 publications

Testing students ability to use derivatives, integrals, and vectors in a purely mathematical context and in a physical context

Testing students ability to use derivatives, integrals, and vectors in a purely mathematical context and in a physical context

Touchy feely vectors: A compensatory design approach to support model‐based reasoning in developing country classrooms

A study of undergraduates' understanding of vector - decomposition of forces on inclined planes

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