I am a renegade math parent. I find it difficult to grasp that the author of this article did not challenge the use of calculators in grade 4. There is a time and place for conceptual understanding and elementary school is not it. Math is nice and simple and mechanistic. There is a method for solving problems using pencil and paper. If Math is to be truly intuitive then you need a database of problems (memorizing multiplication tables). This sets the stage for learning through Algebra. The first real conceptual problems arise in geometry.
The idea that the same problem can be solved in multiple ways works only for speed. Choose the fastest method for solving. this works in the grocery store, but hardly anywhere else. Concepts are usually for applied math, like chemistry or physics, or biology.
I would argue that stopping the focus on politically correct and confusing word problems is the first step. Concentrate on real world problems if you must. But keep the focus on building the database. The key to quality education is to provide math and its applications; keep them at the same pace; make the classes build together. the more you see it, the better you learn it.
Tis is fundamentally why calculators are so bad. they just punch numbers. why have the mental database when you have a calculator. Soon enough it becomes commonplace that mechanics are learned rather than the material.