Why did we depart from these methodologies ? Because that prepares you to be a civil servant in the 1950s.
First thing that needs to change is schools should have to employ teachers to teach.
Government should step back and let teachers get on with it.
Dump league tables, dump SATs.
Junior school children are drilled and drilled for SATs then they have a few 'fun' weeks before leaving for secondary, then 6 weeks holiday, is it a wonder they have slipped by the time they get to secondary.
Exam boards and teachers should be able to agree common parts of the curriculum. Eg maths can overlap with various subjects, most obviously physics and some computer science but also geography and cooking but the curriculum doesn't do that.
This would mean children can apply things learned in one subject to another. Eg if you have done Venn diagrams in maths then Karnaugh maps make more sense. If you have learned ratios then that means you can work out the distance on a map or increase a recipe.
I know some of these things are taught in maths but I also know there are different curricula.
Forget PISA, yes Singapore and Korea have fantastic maths results but children in Korea study 9am to 12 midnight. We have a different culture. Look at the things we are good at as a country / culture.
Some better practical subjects, possibly with links to local businesses.