[susan53]

Here it's clear that students haven't understood the meaning of the verbs as it is true that there's a first form/ second form relationship between will/would and shall/should - but the meaning of volition or prediction still need to be there.

Second form verbs can express past time, or hypothetical meaning. So, as an example :

Oh no - the car won't start! - First form verb, present volition.
I'm sorry I'm late - the car wouldn't start. - Second form verb, past volition.

or, for predictions :

I think it will rain
I thought it would rain

It looks as if your students hadn't understood the meaning of the verbs at all and just saw them as a marker for the past tense. Maybe they have one in their own language and assumed English would too?