iarjelIARJELIARJEL2708-5120https://doi.org/10.47310/iajel.2022.v03i02.002The Analysis of the Implementation of Research-based Learning with STEM Approach in Improving the Students Conjecturing Thinking Skill in Solving r-dynamic Vertex Coloring Problem on Building ConstructionDafikR.Z.Riba'ahA.I.KristianaZ.R.RidloConjecturing thinking skill is a predicting skill obtained from the pattern recognition of the phenomenon of mathematical or real life problems. In this study, we will analyze conjecturing students' thinking skills. Conjecture skills assessments (pre-test and post-test), documentation, interviews and observations were employed in this mixed-method study, which integrates the qualitative and quantitative methods. We assess students' conjecturing thinking skills under the implementation of the research-based learning with a STEM approach to develop the students combinatorial thinking skills. The research subjects are mathematics education students at the University of Jember, divided into control and experimental classes. The results show that the significance value of the homogeneity test on the pre-test items was 0.362>0.05, it indicates that the two classes are homogeneous. The independent sample t-test was 0.000<0.05. It implies that the implementation of research-based learning with a STEM approach can improve the students' conjecturing thinking skill in solving r-dynamic vertex coloring problems.