Developing Students’ Geometric Reasoning about the Derivative of Complex Valued Functions

Troup, Jonathan; Soto-Johnson, Hortensia; Karakok, Gulden; Diaz, Ricardo

doi:10.1007/s40751-017-0032-1

Cited by 9 publications

(3 citation statements)

References 35 publications

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“…With the aid of this geometric representation, Dittman et al (2016) sought to develop the geometric knowledge of pre-service secondary mathematics teachers by exploring the geometric behavior of complex functions. In Soto-Johnson and Hancock (2019) and Troup et al (2017), this epistemological basis provided a geometric meaning to the concept of derivative of a complex function through the notion of Amplitwist (Needham, 1997), a notion that describes how a small circle dilates and rotates around a point. Finally, this epistemological basis allowed Oehrtman et al (2019) and Soto-Johnson and Oehrtman (2022) to address the concept of complex integral.…”

Section: Discussion: the Use Of Geometric Formulations In Mathematics...mentioning

confidence: 99%

What enabled the production of mathematical knowledge in complex analysis?

Piña-Aguirre

Farfán

2023

INT ELECT J MATH ED

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With the objective of identifying intrinsic forms of mathematical production in complex analysis (CA), this study presents an analysis of the mathematical activity of five original works that contributed to the development of Cauchy’s integral theorem. The analysis of the mathematical activity was carried out through the identification of the types of expressions used and the way they were used by the historical subjects when communicating their results, to subsequently identify transversal elements of knowledge production. The analysis was refined by the notion of confrontation, which depicts the development of mathematical knowledge through the idea of building knowledge against previous knowledge. As a result of the study we established epistemological hypothesis, which are conceived as conjectures that reveal ways in which mathematical knowledge was generated in CA.

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Section: Discussion: the Use Of Geometric Formulations In Mathematics...mentioning

confidence: 99%

What enabled the production of mathematical knowledge in complex analysis?

Piña-Aguirre

Farfán

2023

INT ELECT J MATH ED

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“…Linear function material is mathematical content chosen to develop various mathematical abilities, including reasoning abilities as researched by Ellis (2007) and Troup et al (2017). The focus of Ellis's (2007) research is junior high school students' generalized and justified while exploring linear functions, while in Troup et al (2017) undergraduate students' geometric reasoning on the subtopic of line slope using the help of the Geometer's Sketchpad (GSP). Apart from that, research on linear function content to develop mathematical representation skills was carried out by Adu-Gyamfi & Bosse (2014).…”

Section: A Introductionmentioning

confidence: 99%

Exploring Students Learning Difficulties in Linear Function: A Diagnosis of Grade 9

Inayah,

Jupri,

Darhim

et al. 2024

JTAM

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The aim of this research is to determine students' learning difficulties in completing diagnostic tests on linear function material. In managing data, quantitative procedures are used with the aim of reducing data. After that the data is analyzed using inductive data analysis and the processed data will be presented in narrative form. So this type of research is qualitative research. The subjects in this research were class IX students at a junior high school in Cianjur. The instruments used in this research were documentation, tests and interviews. The conclusions of the research results obtained include the types of student difficulties in straight line equation material are (1) difficulties in algorithmic abilities including a lack of planning abilities (strategy knowledge) and in solving abilities (algorithmic knowledge) which are shown from incomplete answers or lack of steps , the lack of accuracy of students in working; (2) difficulties in using the principle of linear functions, lack of mastery of the basics of algebra and lack of understanding (schematic knowledge) as indicated by difficulties in recognizing linear functions in contextual problems, errors in algebraic computations, difficulty in determining the point through which the line passes, and difficulty in apply the principle of parallel or perpendicular gradients; and (3) difficulties in using the concept including the inability to remember the concept, the inability to deduce useful information from a concept and the lack of understanding skills (schematic knowledge) which is shown by incompleteness in writing formulas. This research will be useful as a preliminary study in making learning designs to overcome student learning difficulties in linear function material based on empirical findings.

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“…In regard to the visualisation of mathematical objects, e.g. functions of a complex variable (Troup et al, 2017), Taylor polynomials (Wojas, Krupa, 2017) play an important role in new education technologies and enable students to comprehend complicated mathematical notions.…”

Section: Introductionmentioning

confidence: 99%

Advantages of Using the CAS Mathematica in a Study of Supplementary Chapters of Probability Theory

Mezhennaya¹,

Pugachev²

2019

European Journal of Contemporary Education

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Typical difficulties in learning probabilistic subjects are concerned with big data, complicated formulas and inconvenient figures in statistical analyses. The present research considers the usage of innovative teaching methods (e.g. electronic summary of lectures, presentations of lecture courses, task solution templates, electronic training materials for seminar studies) supported by the CAS (computer algebra system) Mathematica, as suggested by the authors for several topics of the course 'Supplementary Chapters of Probability Theory'. These methods help to solve tasks requiring routine calculation and simplify the ability to find analytical and graphical dependencies in the tasks under consideration. Visualisation possibilities built in the CAS contribute to students' comprehension of new theoretical material and complicated probabilistic notions. The article contains examples of CAS-performed tasks including the calculation and visualisation of the notions of the conditional probability density function, conditional expectation, order statistics and running maximum. The purpose of the suggested CAS-based materials is to solve a whole class of tasks of similar types; it is possible to obtain new results by varying the input data without spending much time elaborating the solution method. The methods using innovative teaching materials yield advantages to both students and teachers. These methods simplify and individualise the process of education, shorten the time necessary for students' independent work and motivate students to achieve the results. Moreover,

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Developing Students’ Geometric Reasoning about the Derivative of Complex Valued Functions

Cited by 9 publications

References 35 publications

What enabled the production of mathematical knowledge in complex analysis?

What enabled the production of mathematical knowledge in complex analysis?

Exploring Students Learning Difficulties in Linear Function: A Diagnosis of Grade 9

Advantages of Using the CAS Mathematica in a Study of Supplementary Chapters of Probability Theory

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