This study aims to determine the effect of background factors on the lateral thinking skill of prospective mathematics teachers. Personal background factors include personal identity (characteristics of gender, age, experience in math competitions, and knowledge of lateral thinking) and personal ability assessed as mathematical content ability, and pedagogical ability. This research combines quantitative and qualitative research methods. To determine the effect of Personal background on lateral thinking skill, multiple regression tests were used. To then see the effect of mathematical content ability and pedagogical ability on mathematical lateral thinking skills, a qualitative approach was used. The research subjects were twenty-six students of sixth semester undergraduate mathematics education study program. Data were collected through student GPAs, tests of ten lateral thinking mathematics questions, and interviews. Simultaneously, the background of students does not significantly affect the ability to think mathematics laterally, but individually several factors that have a positive impact include gender, experience in participating in mathematical competitions, mathematical abilities, and pedagogical abilities. The correlation between mathematical ability and pedagogical ability to lateral thinking ability was in the low category. The results of the qualitative analysis reveal that there were three levels of mathematical lateral thinking skills with a high level description able to solve problems correctly and generate new ideas, the middle level is able to understand the dominant idea correctly, and the lower level cannot understand the dominant idea. Most of students stated that they still do not know about lateral thinking and after knowing about mathematical lateral thinking, the majority of them stated that this ability is important to teach students. [ABSTRACT FROM AUTHOR]