Regardless of your nationality, all people residing in Korea are required to pay taxes.
Income Tax
All teachers are required to pay tax and must are unaware of the amount of tax they pay. Also, tax returns are available to the foreign individual. Yes, tax returns are available, depending on your salary. 

Since your nationality and salary are looked upon a general summary of taxation given through OkayKorea.com

General income tax is done on the earnings from January 1st to December 31st. Special income tax levied on retirement income, transfer income and forestry income. The individual taxpayers are required to pay general income taxes. After the individual reports there one-year of total income and tax amount. The taxpayer's final income tax returns are made between May 1 and May 31 of the following year at the tax office of the region of domicile.

However, in many cases small-sum stock dividends, daily wages of laborers, incomes of foreign corporations without an establishment, and incomes of non-resident foreigners, the tax payment duties are finalized by collection of taxes through withholding, where the employer deducts the income tax at the time of income payment. Tax returns are available in Korea. Depending on your salary, teachers may be able to file for tax returns.

Remember to ask employers for taxation receipts and keep in file. Receipts are needed in order to file for tax returns.

For more information:
Telephone 82-2-536-2742
Fax number 82-2-536-2778