I would look at actual math education research and research-based materials and lessons and tools, such as at sites like NCTM and MAA. Most educational research is not consistent with Lockhart's views.
> Most educational research is not consistent with Lockhart's views.
This sounds suspicious, and I imagine there are differing goals and motivations here. For example, much of math education research also centers around standards and testing.
As an example, here's a summary of research-based best practices for teaching Calculus: https://edtechdev.wordpress.com/2014/06/03/calculus/