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Vozzo, Enzo – Australian Senior Mathematics Journal, 2017
Ever since their serendipitous discovery by Italian mathematicians trying to solve cubic equations in the 16th century, imaginary and complex numbers have been difficult topics to understand. Here the word complex is used to describe something consisting of a number of interconnecting parts. The different parts of a complex number are the…
Descriptors: Mathematics Instruction, Mathematics, Professional Personnel, Numbers
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Soto-Johnson, Hortensia – International Journal for Technology in Mathematics Education, 2014
The Common Core State Standards Initiative stresses the importance of developing a geometric and algebraic understanding of complex numbers in their different forms (i.e., Cartesian, polar and exponential). Unfortunately, most high school textbooks do not offer such explanations much less exercises that encourage students to bridge geometric and…
Descriptors: Arithmetic, Mathematics Instruction, High School Students, Secondary School Mathematics
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Karakok, Gulden; Soto-Johnson, Hortensia; Dyben, Stephenie Anderson – Journal of Mathematics Teacher Education, 2015
This study explores in-service high school mathematics teachers' conception of various forms of complex numbers and ways in which they transition between different representations of these forms. One 90-min interview was conducted with three high school mathematics teachers after they completed three professional development sessions, each 4 h, on…
Descriptors: Secondary School Teachers, Numbers, Mathematics Teachers, Concept Formation
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Garcia, Stephan Ramon – PRIMUS, 2017
A second course in linear algebra that goes beyond the traditional lower-level curriculum is increasingly important for students of the mathematical sciences. Although many applications involve only real numbers, a solid understanding of complex arithmetic often sheds significant light. Many instructors are unaware of the opportunities afforded by…
Descriptors: Algebra, Mathematics Instruction, Numbers, College Mathematics
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Caglayan, Gunhan – Computers in the Schools, 2016
This qualitative research, drawing on the theoretical frameworks by Even (1990, 1993) and Sfard (2007), investigated five high school mathematics teachers' geometric interpretations of complex number multiplication along with the roots of unity. The main finding was that mathematics teachers constructed the modulus, the argument, and the conjugate…
Descriptors: Geometry, Mathematics Teachers, Visualization, Numbers
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Nordlander, Maria Cortas; Nordlander, Edvard – International Journal of Mathematical Education in Science and Technology, 2012
A study of how Swedish students understand the concept of complex numbers was performed. A questionnaire was issued reflecting the student view of own perception. Obtained answers show a variety of concept images describing how students adopt the concept of complex numbers. These concept images are classified into four categories in order to…
Descriptors: Numbers, Classification, Misconceptions, Mathematics Instruction
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Wan, Tong; Emigh, Paul J.; Shaffer, Peter S. – Physical Review Physics Education Research, 2019
In quantum mechanics, probability amplitudes are complex numbers and the relative phases between the terms in superposition states have measurable effects. This article describes an investigation into sophomore- and junior-level students' reasoning patterns in relating relative phases and real-world quantum phenomena. The investigation involved…
Descriptors: Physics, Science Instruction, Difficulty Level, Quantum Mechanics
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Vincent, Jill; Pierce, Robyn; Bardini, Caroline – Australian Senior Mathematics Journal, 2017
In this article the authors analyze the written solutions of some first year undergraduate mathematics students from Victorian universities as they answered tutorial exercise questions relating to complex numbers and differentiation. These students had studied at least Mathematics Methods or its equivalent at secondary school. Complex numbers was…
Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Foreign Countries
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Hwang, Suk-Geun – College Mathematics Journal, 2012
In this capsule we give an elementary proof of the principal axis theorem within the real field, i.e., without using complex numbers.
Descriptors: Mathematics Instruction, College Mathematics, Validity, Mathematical Logic
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Dittman, Marki; Soto-Johnson, Hortensia; Dickinson, Scott; Harr, Tim – PRIMUS, 2017
In this paper, we describe how we integrated complex analysis into the second semester of a geometry course designed for preservice secondary mathematics teachers. As part of this inquiry-based course, the preservice teachers incorporated their geometric understanding of the arithmetic of complex numbers and complex-valued functions to create a…
Descriptors: Secondary School Teachers, Secondary School Mathematics, Geometry, Preservice Teachers
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Sabag, Nissim – Research in Science & Technological Education, 2017
Background: The importance of knowledge and skills in mathematics for electrical engineering students is well known. Engineers and engineering educators agree that any engineering curriculum must include plenty of mathematics studies to enrich the engineer's toolbox. Nevertheless, little attention has been given to the possible contribution of…
Descriptors: Laboratory Experiments, Mathematics Education, Case Studies, Engineering Education
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Smith, Emily M.; Zwolak, Justyna P.; Manogue, Corinne A. – Physical Review Physics Education Research, 2019
Mathematical reasoning with algebraic and geometric representations is essential for success in upperdivision and graduate-level physics courses. Complex algebra requires student to fluently move between algebraic and geometric representations. By designing a task for middle-division physics students to translate a geometric representation to…
Descriptors: College Students, Physics, Science Instruction, Algebra
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D'Angelo, John P. – PRIMUS, 2017
We offer many specific detailed examples, several of which are new, that instructors can use (in lecture or as student projects) to revitalize the role of complex variables throughout the curriculum. We conclude with three primary recommendations: revise the syllabus of Calculus II to allow early introductions of complex numbers and linear…
Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Calculus
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Bauldry, William C. – PRIMUS, 2018
The standard technique taught in calculus courses for partial fraction expansions uses undetermined coefficients to generate a system of linear equations; we present a derivative-based technique that calculus and differential equations instructors can use to reinforce connections to calculus. Simple algebra shows that we can use the derivative to…
Descriptors: Fractions, Calculus, Mathematics Instruction, Undergraduate Students
Trudgian, Timothy – Australian Senior Mathematics Journal, 2009
One of the difficulties in any teaching of mathematics is to bridge the divide between the abstract and the intuitive. Throughout school one encounters increasingly abstract notions, which are more and more difficult to relate to everyday experiences. This article examines a familiar approach to thinking about negative numbers, that is an…
Descriptors: Numbers, Number Concepts, Number Systems, Mathematical Applications
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