This applet from MIT allows you to select from 8 examples of differential equations. It allows you to select the step size. As you toggle through, the step size you selected traces out the "solution" in the vector field. You can then change the step size. It demonstrates the value of a small step size and also provides the actual solution.
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An example of an outdated vision is a Facebook post that has gone viral. In it, Jack Severt, the father of a second grader in Cary, North Carolina, expressed his exasperation at a mathematics problem his son brought home.
I have a Bachelor of Science degree in Electronics [sic] Engineering which included extensive study in differential equations and other higher math applications. Even I cannot explain the Common Core mathematics