Research in science education is to discover the truth which involves the combination of reasoning and experiences. In order to find out appropriate teaching methods that are necessary for teaching science students problem-solving skills, different research approaches are used by educational researchers based on the data collection and analysis used at a given time. Though qualitative and quantitative research methods lies on separate continuum, they all aimed at identifying educational problems using different approach. This study critically examined the usefulness of both qualitative and quantitative approaches in researching problem-solving ability in science education curriculum. In doing this, six articles relating to problem-solving were examined to show the usefulness of both qualitative and quantitative research approaches to educational research. Advantages, disadvantages, strengths and weaknesses of both methods were discussed. Ethical consideration in relation to research in problem-solving instructions were discussed as well as suggestion for future research.