In the context of the “Two New” initiatives, high school mathematics instruction still grapples with three interlocking problems: knowledge fragmentation, limited cultivation of higher-order thinking, and weak alignment among teaching, learning, and assessment. To counter these challenges, we propose an Inquiry–Construction Double-Helix model that uses a domain-specific knowledge graph as its cognitive spine. The model interweaves two mutually reinforcing strands—student-driven inquiry and systematic knowledge construction—into a double-helix trajectory analogous to DNA replication. The Inquiry Strand is launched by authentic, situation-based tasks that shepherd students through the complete cycle: question → hypothesis → verification → reflection. The Construction Strand simultaneously externalizes, restructures, and internalizes core disciplinary concepts via visual, hierarchical knowledge graphs. Within the flow of a lesson, the two strands alternately dominate and scaffold each other, securing the co-development of conceptual understanding, procedural fluency, and mathematical literacy. Empirical evidence demonstrates that this model significantly enhances students’ systematic knowledge integration, problem-solving transfer ability, and core mathematical competencies, offering a replicable and operable teaching paradigm and practical pathway for deepening high school mathematics classroom reform.