Students today, by virtue of the computer games they play, experience computer simulations in 3D. Perhaps it is time to teach them in ways more comparable with their technological experiences.
Consider how undergraduate students learn the theories of continuum mechanics, the study of how objects deform. They learn two things at the same time: first, the general theory of material deformation; and second, how the general 3D theory reduces to two dimensions.
Materials deform in three-dimensional space: pull an object in one direction and it contracts in the other two. The general 3D theory of elasticity is straightforward. However, it produces coupled equations that are not amenable to finding a solution. In response, the discipline of mechanics introduced the reduction of 3D theory to 2D, or way to reduce 3D object to 2D spaces.
Visualize the wing and fuselage of a plane. While still being 3D objects, they can also be described in a geometric 2D space: thin planes and shells. In such cases, thickness deformations are ignored and the resulting equations are more easily solved. But, the price paid is that students have a harder time learning a general deformation theory and how, or why, a problem is reduced to 2D in order to solve it.
The same happens in dynamics, the study of motion. When students learn theories of dynamics, they must learn both the general theory of dynamics and how the general three-dimensional theory is reduced to two dimensions using vectors (and the restrictions that come with them). They have to learn double the material in order to understand the basic principle.
In a world of powerful computer processing, I wonder why we do this. Students today approach undergraduate education with an appreciation for three-dimensional simulations, often fed by 3D video games. Why must we encumber students with the burden of learning general theory and, at the same time, the theoretical reduction to 2D? (And why must we also disappoint them, since 2D theory is hardly exciting engineering?) I wonder how many students we lose in the process. Perhaps it is time to invert our courses and teach the full 3D theories first, and the necessary 2D implementations later.
Software packages can readily simulate the 3D world. Math packages can solve the system of three linear and non-linear equations. Students would be able to understand the general theory as it applies to the 3D world they experience, rather than the iconic 2D world they learn about in classrooms.
Teach them how to program, and then introduce fourth generation math packages. The 3D theory should come first.