The knowledge of fourth-grade elementary school students about plane geometry, especially flat figures, the use of formulas, and difficulty in understanding problems and solving questions, is not optimal. Most students have difficulty solving questions about the perimeter and area of flat figures. Students usually fail to develop knowledge of plane figure material. The aim of the research is to analyze and evaluate the influence of open and structured Problem-Based Learning (PBL) teaching methods on improving students’ mathematical thinking abilities, considering the interaction between learning, students’ mathematical ability levels, and school qualifications, as well as assessing the difference in mathematical disposition between students who follow open PBL and structured PBL. The research uses an experimental approach comparing between experimental and control groups. Both the experimental and control group designs were given pre-tests and post-tests. The fourth-grade elementary school tested consists of several schools that have parallel classes in the Peusangan sub-district. The school qualifications tested meet three criteria: good, sufficient, and lacking. The research results show that the relationship between the learning model and school qualifications does not impact students’ mathematical thinking abilities. Students in structured and open PBL have different mathematical thinking abilities. Students in open PBL learning have better mathematical thinking abilities compared to students in structured PBL learning. In addition, the interaction between the learning model and students’ abilities affects their mathematical disposition.