Bitcoin is not stable, when it comes for actual price of Bitcoin, while making payments, it can change either higher or low
Bitcoin is not stable, in fact it is volatile but it does not have big crash too often. Usually, it does not fall or increase 3%, 5% or bigger percent every 15 minutes or even a few hours.
but that should not be a barrier of not using Bitcoin as tuition payment, because you can used converter process or even used stable coin to proceed your payment as well
If you accept bitcoin as a tuition fee, you must either consider it as your store of asset and as your investment in bitcoin, indirectly from tuition fees of your students. If you don't want to avoid price change, you can convert bitcoin to stable coin or fiat currency. Stable coin is even risky and bad stable coins can be worse than bitcoin.
the major things is that the country the country you're into have government approved Bitcoin transaction in the country, if yes it added advantage, just a matter of time Bitcoin Will be accepted and approved by government.
Governments don't approve Bitcoin transactions. Miners confirm transactions and Bitcoin nodes verify transactions for you. Governments only legalize or illegalize Bitcoin purchases as either a currency, security or commodity. They can not do anything with Bitcoin transactions, they can not confirm, approve or censor any Bitcoin transaction.