This system wouldn't work with any of my three because of how unfair it is. All of mine are justice obsessed and this would result in major problem behavior.
I hate to directly challenge teachers, but I would tell her you're troubled by the system, as it seems unfair and unduly punitive. And if she insists, I would ask to see the literature to back up her punishment system, as you have never heard of it, and you believe it is harmful. If she can't provide any support, (she can't) I would go to the principal.
