Dongsan Junior High School, Seoul Special City, South Korea

Abstract: South Korea’s revised 2022 National Mathematics Curriculum Standards focus on five core competencies: problem‑solving, mathematical reasoning, mathematical communication, knowledge connection, and information processing. The standards require middle‑school mathematics classrooms to move beyond traditional lecture‑based teaching and adopt adaptive instructional tools to realise differentiated education and inquiry‑based learning. Geometry teaching in South Korean middle schools has long suffered from homogenised instruction, delayed learning‑situation diagnosis, superficial speculative inquiry, and difficulties in implementing differentiated teaching. Conventional classrooms cannot accurately identify students’ weaknesses in geometric reasoning or provide personalised inquiry‑oriented guidance.

Based on real‑world front‑line teaching practice in middle schools in Seoul, South Korea, this paper takes the key Grade‑8 geometry unit Properties of Parallelograms as a classroom case. It innovatively integrates lightweight AI‑assisted learning tools. Unlike virtual‑simulation or VR‑immersive equipment, the AI tool is only used for pre‑class learning‑situation diagnosis, real‑time in‑class error collection, and post‑class differentiated task assignment. It never replaces students’ hands‑on operations or speculative reasoning. This paper reconstructs classroom educational logic and establishes a new teaching model: AI‑driven pre‑class diagnostic assessment → local‑context‑embedded concrete inquiry → differentiated hands‑on reasoning and verification → dynamic in‑class error‑analysis and speculative discussion → AI‑targeted review and improvement. The paper fully presents the complete classroom implementation procedure, teacher‑student interaction details, practical AI‑assisted operations, and classroom‑generated outcomes. Rooted in the characteristics of South‑Korean middle‑school‑mathematics learning and curriculum‑reform orientations, this original and highly practical case provides front‑line practical references for intelligent, differentiated, and inquiry‑oriented mathematics‑classroom reform in South‑Korean primary and secondary schools.

Keywords: South‑Korean middle‑school mathematics; classroom‑teaching case; AI‑assisted teaching; differentiated inquiry; properties of parallelograms; geometric reasoning