Much less to do with socialism than with immigration and local politics. This is a comparison of public programs that are equally socialistic.
There is a lot of dancing around the issue of the fact that the proportion of Mexican immigrants and their children among public K-12 pupils is approaching a majority. Of course the state average is depressed. And the "Inland Empire" - the Central Valley - has plenty of Mexican kids. The proper comparison is by ethnic groups, such as reported by the NAEP.
Even here CA does not do well - Texas for instance does a much better job with Mexicans than California. That is a genuine ding against how CA handles K-12. The short answer here is that CA overpays teachers so the state can afford many fewer, even while spending a lot more per kid than Texas, wastes a lot of resources on special education, and the curriculum/testing/incentive system is not as tight and does not work as well. Most of this is because the CA teachers union is much more powerful than Texas'.
The other "study" of "intelligence" is almost too silly for words. It confuses inputs like class size with outcome measures. Their approach would prove that Singapore is full of idiots.