A big problem for high school students is to know what is cutting-edge research. I agree that knowing the math is rarely the problem. But I agree with timr's statement that "no high school student can do graduate-level scientific research." (We're excluding the very rare exceptions, like timr's example of high school students who have been working in a lab for years.)

There are two "cans" here; a high school student can do graduate-level scientific research from a techniques standpoint, like implementing a program for X or solving equation Y. But very few can do the interesting hypothesis generation aspect of graduate school.

I actually started in MD, though from a physics/math/CS background. I didn't understand the biology at all, and while I implemented a parallelized version of CHARMM back in 1992 (using PVM 2.x, no less), so was certainly capable of understanding the math and doing cutting-edge scientific research, I couldn't have come up with that research topic on my own.

Being unable to come up with an interesting research topic :) I left MD, did bioinformatics for a bit, and for the last 16 years I've been doing cheminformatics. The first 10 years was as a practitioner, and the last few years as an actual researcher, albeit self-funded. Implementation and research are different things. The younger me could have done all of the programming I do now, and the math is no more advanced than what's taught at the junior level of college, but didn't know the history of the field to identify what was actually cutting-edge vs. a technique described 20 years previous in the literature.

The current me, now with decades of experience in writing molecule-oriented software, and having read many articles across the 75 year history of the field, has found where there are interesting areas for new research.

The article says "students [with two exceptions] struggle with their projects because they lack inquiry skills, motivation, and an ability to reflect on what they’ve learned." I'm not sure I could convince the high school version of me to understand that subgraph isomorphism coupled with subgraph enumeration could be use to implement a groupwise maximum common subgraph, which can be used to identify a common scaffold for 2D depiction of a cluster of structures. There are a lot of intermediate steps to put it all together.

(In fact, I implemented this problem in the late 1990s, using a straight-forward backtracking algorithm from the 1980s. My newer version from 4 years ago is not only more clever and sophisticated, it's also a new algorithm.)

Nor should we expect a high school student to dig through the papers from the 1970s, which is the last time something like this approach was taken, figure out why it was put aside for several decades, and identify its connection to frequent subgraph mining. But it is something that we would expect from a graduate student.

FWIW, my most advanced high school science project was to build a radio telescope from an old clock radio and makeshift Yagi antenna. I managed to detect the sun. I also wanted to build a mass spectrometer, but couldn't get better than 1mm of vacuum out of an A/C vacuum. For government class, on the topic of the Strategic Defense Initiative, I built a railgun that could shoot about 2 inches using a few spools of wire, some old relays, and a borrowed power supply. Had I access to a school labs, mentors, and more than about $20 to spend, I could probably have had a much better science project.

Instead, I was part of the "vast majority of kids who get few resources beyond their parents." (Which came in handy when I wanted to get the glass cut for bottle I used for my mass spec. The owner of the glass store knew my grandfather from when both lived in Cuba, and cut the holes for free.)

I don't think any of those projects helped my greater understanding of science or doing research, which was the supposed goal of the science fair in the first place.