Both qualitative and quantitative research methodologies can be used to investigate the effectiveness of language teaching approaches and techniques. Qualitative research methods are suitable for investigating the experiences and perceptions of language learners and teachers, while quantitative research methods are suitable for measuring the effectiveness of specific teaching approaches or techniques. A mixed methods approach that combines both qualitative and quantitative methods can also be effective in investigating the effectiveness of language teaching approaches and techniques. Ultimately, the choice of research methodology would depend on the specific research questions and goals of the investigation.
Both qualitative and quantitative data collection instruments are appropriate depending on the emphasis of your study questions. You can utilize an observation in order to reveal the input and outputs of the process at first hand whereas a questionnary might be employed in order to reveal the perceptions of the methods from teachers and students views at second hand.