The purpose of this study is to identify the teaching styles and problems faced by teachers as they attempt to cultivate higher-order thinking skills (HOTS) in the topic of quadratic equations. This study used a qualitative approach via structured interview involving four participants who are experienced mathematics teachers from three districts in Malaysia. Data obtained were analysed using the ATLAS.ti 8 software by dividing the transcripts into small codes based on thematic analysis. The results revealed that Malaysian teachers have limited and general understanding about higher-order thinking skills for the topic of quadratic equations. The interview results also found that existing teaching styles mainly involve teacher-centred strategies that emphasise on the memorisation of procedures or facts as well as steps to solve quadratic equation problems. Among the challenges faced by teachers were stated as students' acceptance, lack of teaching aids, teaching strategies in the classroom, and students' thinking skills. The findings of this study can help to refine and improve several shortcomings and weak students can be exposed to the learning of higher-order thinking skills in quadratic equations via real-life projects. It is proposed for future research to focus on integrating digital literacy, such as Desmos Graphing Calculator, in cultivating higher-order thinking skills for quadratic equations.