5 ms·

> Almost none can understand the math See this is the point I disagree with. I think plenty of high school students can understand the math necessary to do cu

> Almost none can understand the math See this is the point I disagree with. I think plenty of high school students can understand the math necessary to do cutting-edge scientific research. No need for child prodigies at all. Maybe for work that's Nobel prize winning or something, but your average run-of-the-mill PhD student? I imagine tons of 14-18 year olds are capable of it. I was writing my own Metropolis light transport programs when I was 17 by looking up articles on WoS and Google Scholar. Now I'm doing the same kind of thing -- just with MD instead. I don't think I've become any more intelligent since high school (or even that much more knowledgeable), and in fact, I was probably better at focusing back then than I am now since I didn't have so many distractions in my life. There's nothing atypical about me; I'm nowhere near the level of "genius", and I was not a child prodigy. So yes, I'm quite sure of my statement.

deleted 12y ago
[deleted]
mixedmath 12y ago
At this point, it might sound like graduate student bias; but I am also a graduate student, and I also think plenty of high school students can understand the math necessary to do cutting-edge scientific research. I'm actually a math graduate student, and I've been thinking about how capable a high school student would be of doing math research. This started because two years ago, I was asked to facilitate a summer program for gifted high school students that opens up the possibility of math research for high school students. Interestingly, this too suffered from some of the problems highlighted in the article. Many of the students who got into this program were clearly parentally guided, and they floundered. But many were not, and did really well. This last summer, I had a pair of students particularly interested in cryptography [I'm a number theorist, and some of my bias comes through]. There is plenty of intersection between content a high schooler can understand and cryptography research, especially if it's interest-driven instead of industry-driven [I don't want to get into trials and travails of cryptographers here]. Would their ideas make money in the "real world of cryptography?" No. But they would make fantastic science fair projects, and they would especially benefit from several months of work instead of the 6 weeks that we had. tldr; I agree with you. A good number a of high schoolers are capable of performing research.
dalke 12y ago
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.
washadjeffmad 12y ago
Can understand versus could understand. One implies current background while the other implies potential ability. Given that many high school seniors graduate with only a basic grasp of Alg I, you're probably placing too high a value on the normalcy of your own experiences. I understand this because I once ranked in the top 10 in my state for mathematics when I was a kid. So I potentially could have understood specialized maths if they were explained to me, sure, but where would I have gotten that exposure? When I was in school, there was no Google Scholar or Wolfram or edX. We had EBSCOhost, but the librarian only knew how to pull up old issues of Forbes and Sports Illustrated. My generation's great boon was that we would grow up to live in a world where we would have free access to educational materials and other wonderful information over the internet. I'm not making this an argument about privilege, but we should deeply consider whether our resources and backgrounds were so typical as we believe them to have been that any child put in our place would have had our abilities.
- Xcelerate 12y ago
  That's a fair point. I do think it's changing though. My sister is a fifth grade elementary school teacher (she teaches sixth grade math to the advanced class though). She was telling me the other day about how the students are all writing apps for their phones nowadays. I laughed and said, "Haha, no way. 5th graders??" She replied, "Yeah, one girl has been working on an app for organizing health information. She wants to go into the medical field and cure cancer when she's older. Her app lets you input names, body weight, height, and other health information". My jaw dropped. She went on, "It's strange; when we were younger, you were the only one I knew doing this weird stuff. Now they all are." Granted, she's teaching a gifted class at a top ranked (public) elementary school, but still -- that many fifth graders know how to program for iOS or Android? I was surprised. So I think your point is spot on. The next generation is going to "grow up to live in a world where we would have free access to educational materials and other wonderful information over the internet." The "could" will turn into a "can".

deleted 12y ago

[deleted]

mixedmath 12y ago

At this point, it might sound like graduate student bias; but I am also a graduate student, and I also think plenty of high school students can understand the math necessary to do cutting-edge scientific research. I'm actually a math graduate student, and I've been thinking about how capable a high school student would be of doing math research. This started because two years ago, I was asked to facilitate a summer program for gifted high school students that opens up the possibility of math research for high school students. Interestingly, this too suffered from some of the problems highlighted in the article. Many of the students who got into this program were clearly parentally guided, and they floundered. But many were not, and did really well. This last summer, I had a pair of students particularly interested in cryptography [I'm a number theorist, and some of my bias comes through]. There is plenty of intersection between content a high schooler can understand and cryptography research, especially if it's interest-driven instead of industry-driven [I don't want to get into trials and travails of cryptographers here]. Would their ideas make money in the "real world of cryptography?" No. But they would make fantastic science fair projects, and they would especially benefit from several months of work instead of the 6 weeks that we had. tldr; I agree with you. A good number a of high schoolers are capable of performing research.

dalke 12y ago

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.

washadjeffmad 12y ago

Can understand versus could understand. One implies current background while the other implies potential ability. Given that many high school seniors graduate with only a basic grasp of Alg I, you're probably placing too high a value on the normalcy of your own experiences. I understand this because I once ranked in the top 10 in my state for mathematics when I was a kid. So I potentially could have understood specialized maths if they were explained to me, sure, but where would I have gotten that exposure? When I was in school, there was no Google Scholar or Wolfram or edX. We had EBSCOhost, but the librarian only knew how to pull up old issues of Forbes and Sports Illustrated. My generation's great boon was that we would grow up to live in a world where we would have free access to educational materials and other wonderful information over the internet. I'm not making this an argument about privilege, but we should deeply consider whether our resources and backgrounds were so typical as we believe them to have been that any child put in our place would have had our abilities.

Xcelerate 12y ago
That's a fair point. I do think it's changing though. My sister is a fifth grade elementary school teacher (she teaches sixth grade math to the advanced class though). She was telling me the other day about how the students are all writing apps for their phones nowadays. I laughed and said, "Haha, no way. 5th graders??" She replied, "Yeah, one girl has been working on an app for organizing health information. She wants to go into the medical field and cure cancer when she's older. Her app lets you input names, body weight, height, and other health information". My jaw dropped. She went on, "It's strange; when we were younger, you were the only one I knew doing this weird stuff. Now they all are." Granted, she's teaching a gifted class at a top ranked (public) elementary school, but still -- that many fifth graders know how to program for iOS or Android? I was surprised. So I think your point is spot on. The next generation is going to "grow up to live in a world where we would have free access to educational materials and other wonderful information over the internet." The "could" will turn into a "can".