<![CDATA[Mathematical Strategic Competence (MSC) is one of the components of Mathematics Proficiency needed in learning mathematics. After learning of mathematics sometimes students haven't been able to have MSC. So it takes an intruction to learning strategic competence of mathematical students. One of the intructions that can be used, namely the Rigorous Mathematical Thinking (RMT) intruction. RMT can also mediate the intruction makes it easy to process the received knowledge with the cognitive burden of providing the opportunity for constructive happens automatically to students. This study aims to know the effect RMT to MSC and Mathematical Germane Cognitive Load. This study is the research of design experimental with Treatment by Level 2x3 model Group Within Treatment (GWT). The subject is the class XI boarding schools Daar el-Qolam 1 (DQ1), DQ2 and DQ3 DQ4, who were randomized into 8 groups, namely: each one experimental class DQ1, DQ2, DQ3, DQ4 and control class one DQ1, DQ2, DQ3 and DQ4. The analysis of the data using analysis of variance (Anova) two way model GWT. The study results obtained (1) the Learning intruction alone does not effect the MCS of students, (2) Early Mathematics Ability (EMA) alone does not effect the MCS students, (3) there is the influence of the interactions between the learning intruction and EMA effect the MCS students. It appears also that the Group has no effect the MCS students, (4) students who were given RMT intruction is lower than direct intruction to students with high EMA, (5) students who were given RMT intruction is higher than direct intruction to students with medium EMA, (6) students who were given RMT intruction is lower than direct intruction to students with low EMA, (7) Germane Cognitive Load does effect students RMT intruction. Keywords: Rigorous Mathematical Thinking, Mathematical Competence Strategic, Mathematical Germane Cognitive Load and Boarding Schools]]>
