An analysis of different representations for vectors and planes in ℝ 3 $\mathbb {R}^{3}$

Sandoval, Ivonne; Possani, Edgar

doi:10.1007/s10649-015-9675-2

Cited by 25 publications

(8 citation statements)

References 7 publications

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“…When Stian explained the situation, he used three different representations to describe the same phenomenon; his hands, his words and his drawing. This indicates that the rope-pulling situation has a certain quality as teaching material; it is line with Sandoval and Possani (2016), who suggest that designing teaching material where students become aware of different representations, together with appropriate treatments and conversions, will promote students' flexibility and contribute to a richer understanding.…”

Section: Closing Wordssupporting

confidence: 67%

What happens when a climber falls? Young climbers mathematise a climbing situation

Fyhn

2017

EUROPEAN J SCI MATH ED

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Students in Norway and other countries experience vectors as a difficult topic. Four young skilled climbers, who all did well in mathematics at school, participated in the Vector Study (VS). They participated for free and each lesson lasted until the students decided it was over. The idea was to investigate how climbing may function as a basis for students' development of a vector concept. The teaching goal was the parallelogram law of vector addition. The students investigated what happens when a climber falls. They discussed the situation, and they tested it out in practice. They also performed a supporting activity, a rope-pulling situation, which provides insight into what happens in the climbing situation. The students' development is analysed by identifying a) Bishop's six basic activities, b) the role of angles, and c) manipulation of mental objects. The analysis reveals that relations between a vector's magnitude and direction was central in the students' investigations. It is important that students develop two aspects of vectors before the parallelogram law of addition is introduced. These are a) relations between angles and vectors, and b) the zero vector.

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Section: Closing Wordssupporting

confidence: 67%

What happens when a climber falls? Young climbers mathematise a climbing situation

Fyhn

2017

EUROPEAN J SCI MATH ED

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“…In line with the findings of Beckmann & Izsák (2015) it is argued that the appearance of geometric representations is considered difficult for some subjects, this is because they must involve knowledge of transformation and spatial. Sandoval and Possani (2016) specifically summarizes the difficulties experienced by students when representing problems geometrically, namely geometric language, description modes, problem representations, and translating and translating algebraic problems into geometric. However, this situation can be minimized by involving geometric representations in the learning process.…”

Section: Discussionmentioning

confidence: 99%

“…Likewise with the opinion of Dogan-dunlap (2010) that geometrical representation helps the subject to consider various representational aspects of a flexible concept. In particular, geometrical representations enrich and provide the basis for algebraic manipulation (Sandoval & Possani, 2016).…”

Section: Discussionmentioning

confidence: 99%

Multi-representation raised by prospective teachers in expressing algebra

Sirajuddin

Sa’dijah

Parta

et al. 2020

Journal for the Education of Gifted Young Scientists

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This research investigated types of multi-representations raised by prospective teachers in expressing algebra. This study used a qualitative approach with case study methods. As many as 112 prospective mathematics education teachers from Universitas Negeri Malang of Indonesia participated. Researchers used Algebra Task Sheet and Interview Guide Sheet as data collection tools. Then an analysis is carried out so that the following categories are obtained: subjects that symbolically express algebra, pictorial, and geometric. The results obtained showed that 74% of subjects expressed symbolically algebra, while 15% of subjects expressed pictorially, and 11% of subjects expressed geometrically. The research findings showed that there are three forms of representation raised by the subject in expressing algebra, namely the representation of algebraic symbols, image representations, and geometric representations. Most of the participants produced algebraic symbolic representations and some of them experienced obstacles in producing pictorial representations and geometric representations, also researcher found similar patterns in producing geometric representation namely, perception, appearance, strategy, and re-examination. Researchers recommend geometric representations for further research because they tend to be done by subjects with high mathematical abilities and rarely found research that produces geometrical representations when solving algebraic problems.

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“…Research regarding SLE is limited but growing. In this small pool of research, some regard solutions to SLE, whether through task development (e.g., Possani et al, 2010;Sandoval & Possani, 2016) or examining students' understanding of solutions algebraically and geometrically (e.g., Harel, 2017;Huntley et al, 2007;Oktaç, 2018;Zandieh & Andrews-Larson, 2019). Possani et al (2010) developed a task about a set of streets, asking students which streets could be closed for road work without disrupting the flow of traffic.…”

Section: Literature Reviewmentioning

confidence: 99%

Una progresión de la simbolización de estudiantes: Soluciones de un sistema de ecuaciones lineales

Smith

Lee

Zandieh

et al. 2022

AIEM

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Los sistemas de ecuaciones lineales (SEL) corresponden a un concepto fundamental del álgebra lineal, pero hay relativamente poca investigación, pero hay relativamente poca investigación acerca de la enseñanza y el aprendizaje de los SEL, particularmente de las concepciones de los estudiantes acerca de sus soluciones. Se ha encontrado que la resolución de sistemas con un número infinito de soluciones o sin solución tiende a ser menos intuitivo para los estudiantes, lo cual indica la necesidad de más investigación en la enseñanza y aprendizaje de este tema. Entrevistamos a dos estudiantes de matemáticas que eran también maestros en formación a través de un experimento de enseñanza por parejas para mirar cómo razonaban acerca de las soluciones de SEL en ℝ3. Presentamos los resultados enfocando en la progresión del razonamiento de los estudiantes sobre las soluciones de los SEL a través del lento de simbolización. Documentamos la progresión de su razonamiento como una acumulación de significados numéricos, algebraicos y gráficos coordinados y las simbolizaciones de sus conjuntos solución.

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An analysis of different representations for vectors and planes in ℝ 3 $\mathbb {R}^{3}$

Cited by 25 publications

References 7 publications

What happens when a climber falls? Young climbers mathematise a climbing situation

What happens when a climber falls? Young climbers mathematise a climbing situation

Multi-representation raised by prospective teachers in expressing algebra

Una progresión de la simbolización de estudiantes: Soluciones de un sistema de ecuaciones lineales

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