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For me, science in elementary school was a lot of fun. I may have simply been lucky in terms of my teachers and curriculum, but what I mostly remember was learning about those "big ideas"-- although in a simplified form-- for the very first time. It was in middle school that the details really began to matter, and in spite of the efforts of the teachers, the sheer volume of rote learning discouraged many of the students (including me.
I think that one of the biggest difficulties, though (and one not addressed directly in Greene's article) is the way that the scientific method is taught and labs are run. Like pretty much every students in this country, I learned the scientific method as one linear sequence of steps. You define one small problem or question, come up with one hypothesis, test it in one well-defined and very confined experiment under unrealistic conditions, and come up with an answer: true or false. Yes, teachers would mention that follow-up experiments could be made, but it was hard to see each experiment as part of a larger process, part of an ongoing search.
Labs, in middle school and high school, didn't help contribute to understanding at all. Some of them were fun to do, it's true-- but they were ultimately very frustrating, because the point of conducting experiments, in the real world, is to discover something new or at least provide support for an existing theory. The point of conducting experiments in high school was to get the results that the manual said to. The most exciting thing you could discover was a failure in the lab equipment, in which case you had to copy the "right" results from someone else to get a good grade. Yes, if your results were right you'd verified whatever theory was involved-- but knowing exactly what you're out to prove before the results come in was the exact opposite of the attitude we were taught. I'm not sure how schools with limited resources could resolve this problem-- but finding out the expected results after rather than before the lab would be a good start, and would cut down on the data-juggling that everyone engaged in at some point or another.