The spelling of the word "provencher" can be understood through the use of IPA phonetic transcription. The first syllable is pronounced as "proh-v", with the "o" being pronounced as a short vowel. The second syllable is pronounced as "ehn-sh". The final syllable is pronounced as "ehr", with the "e" being pronounced as a short vowel. Therefore, the correct spelling of the word "provencher" should be "provencher", according to its pronunciation.