Building Context with Tumor Growth Modeling Projects in Differential Equations

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

“…[21] Others [22] Geometric and qualitative solutions Mathematical modeling Systems: applications for asthma [23] Active learning Scalar: first order [27] Information and communication technology Systems: applications for Chemical reactions [28] Information and communication technology Scalar: first order, second order, graphical solution, Laplace transform [29] Information and communication technology Scalar: first order, freefall problems [30] Project-based learning [31] Projects-based learning Scalar: first order, applications to tumor growth, Gompertz model, graphical solutions, bifurcation [32] Information and communication technology Scalar and systems: several topics [33] Information and communication technology Scalar and systems: first order, Laplace transform, application to chemical reaction and control [34] Information and communication technology Scalar and systems: several topics [39] Traditional methodology, Geometric and qualitative solutions Scalar: first order, applications to exponential decay problems [48] Mathematical modeling Scalar: Newton's law of cooling and laws for velocity, acceleration and volume Table 6. Cont.…”

“…Hereinafter, unless stated otherwise, the retained list or the retrieved list refer to the 120 papers which will be analyzed and are explicitly given by the following references: [1- 23,[27][28][29][30][31][32][33][34]39,. The other 285 articles (notes and curriculum) will be presented and analyzed in a forthcoming work by the authors.…”

“…Concerning the application of project-based learning in differential equations, we refer to the following articles from our retained list: [30,31,52,53,90,101,135]. The authors of [31] use mathematical projects arising in biology in the context of modeling tumor growth by differential equations.…”

“…In particular, the information technologies have increased the innovation and application of numerical methods which are essential to solve a wide class of differential equations and are also useful to understand some qualitative properties [10,11,19,[27][28][29][30]. Third, as a consequence of the above, in the last years, more attention has been given to the transformation of teaching and learning mathematical concepts by incorporating didactic methodologies to encourage students to be actively engaged in their learning process [21,[31][32][33][34]. Thus, in a brief sense, the changes in the teaching of differential equations has been mainly influenced by the incorporation of active learning didactic methodologies and technology enriched learning environments.…”

A Three-Fold Approach to the Heat Equation: Data, Modeling, Numerics

“…Incorporating data and/or numerical experiments in classroom examples of mathematical models is a popular way to motivate student interest and learning. See [1,3,4,6,7] as a small sample. Moreover, students can gain insight into the application, intuition for the mathematical analysis and confirmation of the theoretical results by using real data and numerical simulations to complement the theory [2].…”