Making connections among representations of eigenvector: what sort of a beast is it?

Three cases that demonstrate how students connect the domains of mathematics and computing

“…Additionally, we recognize Karakok's (2019) flexible shifts between multiple modes of thinking in these connections: Code, Output and Math are the labels we have ascribed to these modes. In Case A we see Gina and Benjamin treat the whiteboard work differently when interpreting it as a representation of the code as opposed to when they treat it at something inherently mathematical.…”

“…An example of a study grounded in AOT that explores connections in a mathematical setting is that of Karakok (Karakok, 2019), who looked at physics students' connections among representations of eigenvectors. In this context, Karakok reports on "the necessity of developing flexible shifts between different modes of thinking" and links this to the development of "instructional materials and interventions that emphasize opportunities for students to inquire and connect multiple modes of thinking" [emphasis added].…”

“…The modes of thinking Karakok describe correspond to different representations of eigenvectors that each corresponds to a certain point of view about them. These points of view have different affordances for the students, for instance, some ways of thinking about eigenvectors are particularly useful when using them in the context of quantum mechanics (Karakok, 2019). The term affordances has often been used in the mathematics education research literature, most notably in the context of technology.…”

Multi-representation raised by prospective teachers in expressing algebra

“…In this case, the subject involves an internal cognitive scheme to bring up geometric representations that are used as mental objects. In addition, the appearance of geometric representation is caused by the magnitude of the subject's visual geometric ability when dealing with problems (Karakok, 2019). In terms of the conceptual framework of geometric c constructions, outlines three main components that cause the subject to bring up geometric representations and serve as literacy materials that are easily accessed by the teacher (Amir et al 2019;Yang & Li, 2018).…”

Classroom Methodologies for Teaching and Learning Ordinary Differential Equations: A Systemic Literature Review and Bibliometric Analysis

“…[50] Active learning Scalar: first order, linear, Bernoulli [51] Active learning Scalar: first order, applications to exponential decay problems [52] Projects-based learning [53] Projects-based learning Scalar and systems: populations model, linear system [54] Mathematical modeling Scalar: first order, applications to mixing problems [55] Active learning [56] Geometric Active learning [82] Traditional methodology Scalar: first order, higher order [83] Others [84] Geometric and qualitative solutions, Active learning Scalar: first order, autonomous differential equations, slope fields [85] Active learning Scalar: first order, Newton's law of cooling [86] Active learning Systems: first order, linear, slope fields, Lotka-Volterra models [87] Active learning Scalar: first order, autonomous differential equations, slope fields [88] Mathematical modeling Systems: Lotka-Volterra model, phase plane, equilibrium solutions, phase trajectories Active learning [107] Active learning Scalar and systems: Verhulst equation, bifurcation [108] Active learning [109] Active learning Scalar and systems: first order, slope fields, second order with spring-mass applications, linear systems, straight-line solutions, Lotka-Volterra models [110] Geometric and qualitative solutions, Active learning [111] Active learning Scalar: existence and uniqueness theorem of first order [112] Active learning Scalar: concept of solution of first order equation [113] Active learning Scalar: first order [114] Active learning Scalar and systems: several topics [115] Mathematical modeling, Information and communication technology Systems: applications to electronic circuits [116] Mathematical modeling Scalar: second order, applications of Newton's second law [117] Others Scalar and systems: second order, applications of Newton's second law [119] Mathematical modeling Scalar: first order [118] Mathematical modeling Scalar: first order [120] Information and communication technology Scalar: first order, Laplace transform [121] Activ...…”