Secondary teachers’ conception of various forms of complex numbers

Karakok, Gulden; Soto-Johnson, Hortensia; Dyben, Stephenie Anderson

doi:10.1007/s10857-014-9288-1

Cited by 22 publications

(12 citation statements)

References 7 publications

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“…On the Final, few students (9.5%, N=21) made trigonometry related errors, how- ever, the geometry associated with i − 1 may be simpler for students than √ 3 − i. This may be similar to other studies which showed in-service secondary mathematics teachers also exhibited a lack of flexibility between forms of complex numbers despite extensive instruction [8].…”

Section: Changing and Selecting Formssupporting

confidence: 76%

“…Previous empirical studies explore secondary students' [1], undergraduate students' [2][3][4][5], prospective and inservice secondary teachers' [6][7][8], and experts' [9] algebraic and geometric understanding of complex numbers in mathematics and engineering contexts. Some of these studies cover calculational aspects of complex number fluency we discuss including complex algebra [2] and changing between [8], and appropriately selecting [4], forms of complex numbers.…”

Section: Introductionmentioning

confidence: 99%

“…Some of these studies cover calculational aspects of complex number fluency we discuss including complex algebra [2] and changing between [8], and appropriately selecting [4], forms of complex numbers. While one study included a physics expert [9], we were unable to identify studies which focus on undergraduate physics students' understanding of complex numbers.…”

Section: Introductionmentioning

confidence: 99%

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Student difficulties with complex numbers

Smith¹,

Zwolak²,

Manogue³

2015

2015 Physics Education Research Conference Proceedings

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Complex numbers and functions are used in multiple subfields in undergraduate physics. We use pretests, quizzes, and exams administered throughout the junior year to identify middle-division students' difficulties with complex number fluency. These difficulties are classified into three categories: performing calculations, switching between forms, and appropriately selecting forms to simplify calculations. Our exploration suggests that students in middle-division physics courses have varying levels of fluency with complex number manipulations. Some of these difficulties persist over time.

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Section: Changing and Selecting Formssupporting

confidence: 76%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Student difficulties with complex numbers

Smith¹,

Zwolak²,

Manogue³

2015

2015 Physics Education Research Conference Proceedings

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“…This is in line with the findings of Fujita et al (2017) that expressing geometric representations is seen as a process of productive reasoning that impacts on the subject's thinking. In addition, this representation can be used as a reference for long-term research, as recommended by (Karakok et al 2014). Likewise with the opinion of Dogan-dunlap (2010) that geometrical representation helps the subject to consider various representational aspects of a flexible concept.…”

Section: Discussionmentioning

confidence: 96%

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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“…Las evidencias apuntan, entre otras, a un fuerte trabajo desde lo aritmético-algebraico y uno casi nulo desde lo geométrico-vectorial (Danenhower, 2000;Panoura et al, 2006;Aznar et al, 2010;Distéfano et al, 2012). En lo específico, las investigaciones han reportado que los aprendices no tienen construido un significado geométrico de número complejo (Distéfano et al, 2012), reflejando una falta de flexibilidad en el uso de sus diferentes representaciones (Panoura et al, 2006;Aznar et al, 2012;Karakok et al, 2015;Smith et al, 2015) y, por tanto, una comprensión fragmentada de este. Y es que lograr la comprensión del sistema de los números complejos (SNC) no es una tarea fácil, pues dados los elementos que lo definen, requiere para su comprensión que los aprendices alcancen niveles superiores de abstracción y contrapongan ideas arraigadas sobre conceptos que han construido previamente en el sistema de los números reales.…”

Section: Introductionunclassified

Comprensión del Sistema de los Números Complejos: Un Estudio de Caso a Nivel Escolar y Universitario

Randolph

Parraguez

2019

Form. Univ.

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ResumenSe reporta una investigación sobre cómo estudiantes de educación escolar y universitaria comprenden el Sistema de los Números Complejos y sobre cómo es posible alcanzar la comprensión profunda de éste. Desde un enfoque cognitivo, se utiliza la teoría de los Modos de Pensamiento que permite, mediante sus elementos, situar tres modos de pensar el objeto matemático: el modo Sintético-Geométrico, el modo Analítico-Aritmético y el modo Analítico-Estructural. A partir de un estudio histórico-epistemológico y matemático, se caracterizan los tres modos de pensar el sistema numérico y se aplican dos cuestionarios de actividades matemáticas a cinco casos de estudio. El análisis de las producciones de los estudiantes da cuenta de una falta de articulación de los modos de pensamiento, privilegiando el modo Analítico-Aritmético y careciendo de tránsitos hacia los otros dos modos. Esto permite concluir que existe una comprensión fragmentada del objeto y que es necesario potenciar el trabajo desde el punto de vista geométrico y estructural. Palabras clave: números complejos; sistema numérico; modos de pensamiento; comprensión de los números; articuladores del pensamiento AbstractThe results of an investigation on how students from school education and university education understand the Complex Number System and how it is possible to achieve a deep understanding of it is reported. From a cognitive approach, the theory of Thinking Modes is used, which allows, by mean of its elements, to situate three ways of thinking the mathematical object: The Synthetic-Geometric mode, the Analytic-Arithmetic mode and the Analytic-Structural mode. From a historical-epistemological and mathematical study, the three thinking modes of the numeric system are characterized and two questionnaires about mathematical activities to five case studies are applied. The analysis of the questionnaires reveals a lack of articulation of the thinking modes, privileging the Analytic-Arithmetic mode and an absence of the transit towards the other two modes. This allows to conclude that there exists a fragmented understanding of the mathematical object and that it is necessary to increase the work from the geometric and structural point of view.

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Secondary teachers’ conception of various forms of complex numbers

Cited by 22 publications

References 7 publications

Student difficulties with complex numbers

Student difficulties with complex numbers

Multi-representation raised by prospective teachers in expressing algebra

Comprensión del Sistema de los Números Complejos: Un Estudio de Caso a Nivel Escolar y Universitario

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