Can I disable the iPad's "helpful" password/number shadowing?

I use my iPad for lectures. During this, it is connected to a Big Screen that the students can see. Every now and then, I forget to turn off the "auto lock" feature meaning that I have to wake it up and re-enter my passcode. Or I might want to show the students some resource on the local intranet which requires me to enter my university password.

Since the iPad keyboard works by touch and this is a somewhat imprecise method of entering data, it seems that the iPad and its apps echo the last key struck when entering a password (on the keypad for unlocking then each number "glows" as entered). This, then, reveals my password or whatever to any students who happen to be watching (usually, they're asleep by the time I have to wake up the iPad and I've learnt to wake up the iPad before waking up the students).

Before you ask, yes this did happen today. I'm pretty sure that I got my passcode in before the screen or the students woke up, but to play safe I've now changed my iPad password, all my other passwords, my date of birth, my social security number, and my mother's maiden name.

I can turn off the screen, or disconnect the iPad, but that's also a hassle and it involves me remembering that in the middle of the lecture (thinking of two things at once is never a good plan for me).

Is there any way to disable this "helpful" security "feature"?

There is no way to stop the 'last key ghosting' that you mention, it's baked into the OS and not controlled by a setting anywhere. A jailbroken phone may have possibilities if you are happy with hacks etc, but I don't think you are interested in that route (correct me if wrong).

What you can do is tweak the passcode requirements in ways that may reduce the number of times you need to enter your passcode. By default, when you lock your screen (or when it times out and does it itself) you need to re-enter your pin when unlocking. There is an option in Settings > General > Passcode Lock called Require Passcode with options of Immediately, After 1/5/15 minutes.

This is very useful if you want to quickly unlock after it timed out on you without needing to retype your passcode, and does not require you to turn auto-lock off.

Realise this is only a workaround for half of your problem, but may prove useful regardless.

As for other passwords, you could keep them in a password manager program which allows you to copy the passwords whilst keeping them obscured and paste them into password fields. I don't have any specific recommendations, but leave it to other answers who may be able to take inspiration from experience with these apps.