<![CDATA[This study aims to describe the alignment of hypothetical learning trajectories (HLT) in SPLTV designed with the actual learning processes that occur in the classroom and the reasoning processes students go through in understanding SPLTV. This present study is the result of the first cycle of the design research method with three stages, namely preliminary design, teaching experiment, and retrospective analysis. Data collection was carried out through interviews with teachers and students, observation in the classroom, study of students' answer sheets during the teaching experiment, and analysis of photos or videos taken during the research. Data analysis was conducted by using data triangulation, which involves comparing the HLT designed as a reference with the actual learning that occurred and reviewing the results of observations, documentation, digital footprints, and interviews. The research findings indicate that students’ learning trajectories develop through levels of thinking, from understanding basic algebraic concepts to discovering formal procedures for solving SPLTV. The study concludes that HLT, designed as a local learning instruction theory, can provide students’ reasoning paths and prove that appropriate instructional design supports the process of independent rediscovery without neglecting the necessary levels of understanding.]]>
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