Investigating ontogenic and didactical obstacles faced by vocational high school students in solving counting rules problems

Research on the ontogenic and didactical obstacles vocational high school students face in solving counting rule problems has been limited. Ontogenic obstacles involve students' readiness, while didactical obstacles concern the sequence and presentation of instructional materials. Therefore, teachers must consider both when developing effective materials. This research aims to describe the ontogenic and didactical obstacles experienced by vocational high school students in solving counting rule problems. The participants of this study were 24 grade XII students from a public vocational high school in Cirebon. Using a Didactical Design Research (DDR) approach, this qualitative study focuses on the prospective analysis stage, examining these obstacles. The research instrument included five diagnostic essay questions and interview guidelines. The results revealed that students encountered instrumental-type ontogenic obstacles, particularly in understanding factorial operations. Additionally, didactical obstacles arose from incomplete teaching materials and improper notation, which led to learning barriers. This research offers valuable insights for teachers and researchers in designing instructional materials, especially for counting rules in vocational schools.