There is cheating in science. It’s not inconsequential cheating either. It’s the sort of cheating that deprives others of grants, drives them out of the field, and keeps those who know of it from ever wanting to go into it. I worked in science for many years and I saw, firsthand, the results of that cheating. People lost grants. People couldn’t get their work published. Other work, some of which wasn’t done by the author who originally, couldn’t be reproduced precisely because it hadn’t really been done. Some scientists steal from other labs and try to pass it off as their work. Some, such as one at MSK, made claims that were completely false. There was a ton of publicity until it came out that this investigator had used magic marker to fake transplantation experiments in white mice by blackening patches of their skin with a pen (See this for more: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1457763 Yes, he was caught but there are more examples of very subtle cheating that aren’t and they are rewarded while the honest ones lose.
If they learned Peano Axioms and proofs of addition law, they would understand mathematical thinking. They would then not need to cheat in math and in their science classes.
Understanding the proof of the associative law of addition would also give them confidence they can learn.
once, i taught in a school where everyone was really, really poor so i had to keep an eye on my purse at all times. then i went to a school where all the students were very, very rich and i had to keep an eye on my test booklets, exam answers,, etc. [but, somehow, they still found a way to cheat.]