<![CDATA[The mathematics learning outcomes of vocational school students are still low, including students in Madiun. There are several reasons for this, and the inadequate teaching strategy is one of them. One of Madiun's vocational high schools continues to employ the teacher-centered, direct learning approach to instruction. It is anticipated that using Understanding by Design (UbD) in conjunction with discovery learning will enhance students' learning results in mathematics who attend vocational high schools. Improving students' learning outcomes in mathematics was the aim of this study. Classroom action research (PTK), which is conducted in two cycles. This PTK model has four stages: planning, acting, observing, and reflecting. The test sheets with multiple choice questions and descriptions of exponential material were the data instruments employed, along with observation sheets for the execution of learning activities utilizing discovery learning combined with UbD. The study's findings indicate that the use of discovery learning combined with UbD can: 1) boost students' engagement and confidence in their ability to solve problems; 2) increase discussion, Q&A, and student presentation activities; and 3) improve the learning outcomes of vocational high school students in mathematics, with cycle I completion rates of 41.17% and cycle II completion rates of 76.47%.]]>
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