It doesn’t need to be a full year. For example, under the old system, if your service period i.e. your seniority (年資) is 5 months plus 1 day, it gets rounded up to 6 months, which means your severance pay should equal 0.5 months. It keeps rounding up to the next month i.e. the next 1/12 of a month in terms of payment, so 6 months plus 1 day would give you 7/12 of a month’s salary.
(If you’re part-time, you may be subject to the 60% rule. I don’t quite remember how that goes, but the idea is to give you slightly more than you would otherwise get because the amount is going to be very low anyway.)
The new system is not new per se (2005?), but it’s relatively new for permanent residents (other than foreign spouses, who have been subject to it for years). If you were a PR when the new system began to apply to PR’s, you should have received a notice from your employer regarding the change and your option to remain in the old system. See the discussion here:
And as Tando noted, whether you’re a buxiban or non-buxiban teacher may also make a difference.
If you’re not sure which system you’re in (or should be in), I suggest contacting the Bureau of Labor Insurance, though they don’t always get things right.