Education critics' contention that the use of calculators in mathematics classes will undermine students' knowledge of the rationale underlying calculational procedures is clearly false.
Conclusion (clearly = opinion)
The contention that is clearly false. rephrase: Using calculators in math isn't going to undermine students' knowledge of the rationale underlying calculational procedures.
Evidence
Every new information-handling technology has produced virtually the same accusation.
Evaluate
This doesn't seem like any of the ten famous flaws, so let's switch into "Find an Objection" mode:
Given that ... every time there's been a new information-handing technology, there's been accusations that it will somehow corrupt the way we think,
How can we argue that ... using calculators in math will undermine students' knowledge of the rationale underlying calculation processes?
We could say a couple different things: 1. These accusations have been correct! Each new information-handling technology has corrupted our thinking.
2. Sure, those previous accusations turned out to be false. But this one's different! In the case of calculators, it really will mess up how people think.
Goal
The author is assuming that the previous times when people freaked out about a new technology, it just a bunch of overblown fear. It didn't turn out to be any sort of problem.
And the author is also failing to consider that even if a pattern were true in the past (concerns about a new technology have always turned out to be overblown), it might not be true in the present.