Siegfried Engelmann [0] (the author of
Teach Your Child to Read in 100 Easy Lessons, referenced in the story), developed a pedagogical model he named Direct Instruction [1] in the '60s as a direct result of being focused on at-risk, low-performing children. Here is a video [2] from the 60s of him working with one of his initial kindergarten classes (doing complex math, etc), and using many of the hallmarks of Direct Instruction. DI has become popular in many primary charter schools across the country (ex, Thales Academy [3]), although many schools transition to an inquiry-based model [4] after primary grades.
DI is similar to rote learning, which is used throughout much of the rest of the world. Lessons are heavily scripted, down to the minute, although there is an emphasis for only focusing on practicing skills that have not yet been mastered. One of the most controversial aspects of DI, and probably one of the main reasons it has not been used in US public schools despite having a strong history of effectiveness (here is a meta-analysis of over 300 studies over 50 years [5]), is that children are grouped according to skill, not age.
My kids are not quite yet old enough to learn to read, but I plan on using Teach Your Child to Read in 100 Easy Lessons. DI might not work for every child, but it has clearly been shown to be one of the most effective methods that helps the most children.
[0] - http://www.zigsite.com
[1] - https://www.nifdi.org/what-is-di/basic-philosophy.html
[2] - http://www.zigsite.com/video/zig_math_video.html
[3] - https://www.thalesacademy.org/academics/what-is-direct-instr...
[4] - https://en.wikipedia.org/wiki/Inquiry-based_learning
[5] - https://journals.sagepub.com/doi/abs/10.3102/003465431775191...