NIA says
An application to change reason for residency under Article 23 Paragraph 2 of the Act shall be limited just to the reasons specified in the subparagraphs thereof (such as for joining family, employment, and investment) and the situations specified in Article 8 of the Foreign Professionals Act. An applicant wishing to change to some other reason not included therein (such as for attending school or missionary work) must still first apply for a resident visa with the Bureau of Consular Affairs, and apply anew for an ARC only after obtaining the relevant resident visa.
BOCA says
Foreigners who come to Taiwan to study Chinese must submit the documents and pay the visa fee at the nearest ROC embassy, consulate or representative agency to apply for a visitor visa.
Those who have already studied Chinese for 4 months and carry on with their enrollment for at least 3 months, if with other conditions also qualified for a residence visa, may submit their application（at least 1 week earlier before the end of the legal stay of their visitor visa）to the Bureau of Consular Affairs or one of the branch offices of the Ministry of Foreign Affairs in Taichung , Kaohsiung, Chiayi or Hualien for converting to a residence visa (Please refer to RESIDENT VISAS FOR STUDYING MANDARIN CHINESE).