Some 20 years ago, when I first embarked on my classical Lutheran education trek, I followed many leads. One of them led to "Direct Instruction" (capital D, capital I) for a number of reasons which appealed to me.
1) They emphasized the mastery of material.
2) They promoted a direct, highly orchestrated method of instruction utilizing hand signals and scripted lessons rather than "discovery learning" wherein students were permitted to self-discover material or to work in groups. (To be sure, not the best approach for every subject, but it was wonderful in making certain each and every student was engaged in the lesson.)
3) They had done quite a bit of research on Project Follow-Through, a little-known, highly-documented government program which followed on the heels of the Head Start program.
4) It was through this program that I was introduced to the Orton-Gillingham approach to teaching phonics which was language-based, multisensory, structured, sequential, cumulative, cognitive, and flexible -- the most widely used and familiar version is Romalda Spalding's method, The Writing Road to Reading produced by Spalding Education International.
5) It really showed its strength with children in inner-city schools (one of which I was serving at the time), but also worked well with children in other socio-economic environments.
6) It led me to learn about the Baltimore Curriculum Project, a curriculum which, in form if not in fact, has elements worth emulating in classical Lutheran schools.
While I don't know that I would endorse any of their materials without qualification for classical Lutheran education, I think it would be worth one's while to become familiar with the organization and history of The National Institute for Direct Instruction which still seems to be going strong in some parts of the country.