The study aims at designing the learning for mathematical proof based on APOS theory. This study is just a description of a validation study by Gravemeijer. The research was conducted at SMA 1 Palembang with 6 students for exploring the small group. The Hypothetical Trajectory Learning (HLT) design will be tested in a small group. APOS (Action, Process, Object, and Scheme) is a theory that studies students’ mental structure for learning mathematics. The mathematical proof learning design with APOS theory approach on exponential and radical Form. The results provided insight into the learning trajectory that needs to be improved. Through comparisons made of HTL and ALT, the variations in student ability and prior knowledge can affect their behavior in learning. The findings suggest the frequency of learning mathematical proof needs to be improved and the assessment must also include questions about proof.
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