My sister is still in school and the anti-cheating software gives her a lot of anxiety - not that she's a cheater or anything, but because it is well known that this software flags non-cheaters as cheaters. For example, she is not allowed to look around or talk to herself while working on a problem, both of which help her to demonstrate her knowledge effectively. If the goal is for testing to demonstrate a student's knowledge, then employing techniques that hinder a student's ability to do so in the hopes of catching cheaters is counter productive to the original goal. After all, you want to know if she can apply fundamental techniques and skills - not whether she can apply these fundamental techniques and skills while behaving under a very strict set of rules.
Even in early level mathematics, there are plenty of opportunities to introduce word problems that can only be solved by applying the relevant techniques. As long as the teachers are defining these word problems themselves (rather than pulling them from an online resource), they stand as a pretty good guard against cheating since they require students to first recognize the technique that needs to be applied, and then to extract the relevant variables from the word problem to apply that technique.
Furthermore, in early level mathematics, you can still have students present solutions to problems and explain why the solution works. For instance, say you were interested in whether or not a student has grasped the basics of derivatives - simply get on a call with that student, give them a random function to solve the derivative for, and then have them do so in front of you.
These are all things I've quickly thought of that would have at least be partially effective in measuring knowledge. I imagine any person with a career dedicated to instructing students could come up with many more options that could be even more effective.
> Instead, they seem happy we're making their study possible, and accepting of what they're asked to do. They know it's important that they can demonstrate unequivocally that they have particular skills.
Students are happy to be able to study and know that it's important to demonstrate their skills - but that doesn't mean that they wouldn't be happier if they could demonstrate their skills without the invasive testing software. I argue this is setting up a false choice: "you can either learn nothing at all, or do so under this cheating software". But the reality of the situation is that they can still learn and demonstrate their skills without the cheating software.