I'd be intrigued to see that, at least if we're talking about the same New Math that was basically "Hey, let's teach kindergartners number theory and 'cardinality' and the soon-to-be-vital skill of doing math in octal so they can use computers". The name got tagged on to a lot of things over the years, and some of them have some merit, but I'd have a hard time believing the original New Math ever tested well in a fair analysis. It's a violation of basic developmental theory, expecting young children to handle levels of abstraction they won't be ready for for another 5-15 years to do basic concrete math.
I may be misremembering, but I think we had simple topology, linear programming (mainly just 2D, but I remember a 5D problem at the end of the section), matrices with eigenvalues and eigenvectors, set theory, and a bit of group theory. No programming, though there was some in the text book. It was pretty good fun. I don't remember anyone finding it conceptually difficult.
It would also be worth mentioning Nuffield Physics. I thought that was a really great course for learning how to do physics. Very oriented towards finding solutions, devising experiments.
School Mathematics Project covered secondary school, and was very much part of the New Maths project. And yes, we did cover set theory in primary school.
