Representations of a mathematical model as a means of analysing growth phenomena

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

“…[1] Traditional methodology Scalar: first order, second order, orthogonal curves, existence and uniqueness theorem [2] Traditional methodology Scalar: first order, second order, orthogonal curves, existence, and uniqueness theorem [3] Geometric and qualitative solutions, Active learning, Information and communication technology Scalar: first order, applications to exponential decay problems [4] Geometric and qualitative solutions, Mathematical modeling, Information and communication technology Scalar: Malthus model, logistic generalized [5] Mathematical modeling Scalar: second order and applications to electronic circuits [6] Active learning Scalar and systems: Laplace Transform [7] Active learning [8] Mathematical modeling Scalar: first order, applications to mixing problems, freefall problems [9] Mathematical modeling Scalar: first order, applications to mixing problems, second order [10] Information and communication technology Systems: Lotka-Volterra model [11] Information and communication technology Systems: plane phase, linear system, qualitative behavior [12] Information and communication technology Scalar: first order, slope fields, asymptotic behavior [13] Mathematical modeling, Information and communication technology Scalar: first order, logistic generalized [14] Geometric and qualitative solutions, Active learning Scalar: rate of change [15] Active learning Scalar and systems: several topics [16] Active learning Scalar and systems: several topics [17] Mathematical modeling Scalar: first order, applications to electronic circuits [18] Information and communication technology Scalar: first order, applications to electronic circuits [19] Information and communication technology Scalar: first order, second order, graphical solution, Laplace transform [20] Mathematical modeling Scalar: Malthus model, Verhulst model, equilibrium analysis.…”

“…If the answer is ambiguous or has clear limitations, the modeler can repeat the cycle by considering new and more insightful observations and then improving the mathematical model. Specifically, in the retained list, the articles [4,5,8,9,12,13,17,18,20,22,48,49,54,56,58,63,65,68,74,78,88,91,94,98,100,101,115,116,118,119,127,128,130,134] are related to some approaches to the mathematical modeling for the teaching of ordinary differential equations. These works were developed between the years 2004 and 2019, with the exception of [78,130].…”

“…(c) Language games, representations, and relations of mathematics with other sciences. There are some papers paying attention to some aspects like the different language games developed by the students involved in modeling activities [48], the usage of registers of representation for making relationships between the context and elements in ordinary differential equations [13], and the role of mathematical modeling to establish a relation between mathematics and other sciences [4,5,98]. (d) Modeling activities using ordinary differential equations to teach other concepts.…”

“…The teaching and learning of ordinary differential equations has experienced a dramatic change in the last two decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. The motivation for innovation in the traditional teaching obey different reasons, at least three of those are given below.…”

Differential Equations: Between the Theoretical Sublimation and the Practical Universalization

“…Additional details can be found in(Guerrero Ortiz, Mejía Velasco, & Camacho-Machín, 2015). 7 See for example,(Hall, Keene, & Fortune, 2016) and(Tournès, 2018).Acta Scientiae, Canoas, v.21, n.1, p.55-63, jan./fev.…”