Merajsadat Malakouti I think you can go for both but I prefer qualitative because you can get more interesting insights, often more revealing than quantitative data but I think it also depends on your skills, your personality and what you want to examine.... Im in to psychology and Quantitative research is for me less rewarding since there are certain things you can not measure or you will struggle to find a method/methodology in order to measure...If I want to know the average height or shoe size of women I probably go for a quantitative study but if Im interested in the deeper questions I would most certainly go for qualitative. Within the research community there are people who are in favour of on or the other but try to find your own voice, your own style and also match it with what you want to examine. Good luck...best wishes :-)
I advise you to first make consultations with your supervisor because for a PhD, we like it or not, a lot will depend on which approach he/she prefers or is most accustomed to, as well. I assume you are a novice researcher like me by looking at this particular question. Therefore, you might need your supervisor to 'guide' you through your work more as compared to other experienced researchers. So, take him/her by your side and 'learn' the process of conducting research.
Having said that, in my opinion qualitative approach might suit better, as you stated 'motivation'. That will most likely involve some sort of interviewing or FGD where you will ask your participants of their views/perception on why they were motivated to participate in advocacy or civic engagements, their experiences etc.
For reference on qualitative approaches, you could look at this book or it's earlier versions by Creswell.
Creswell, J. W., & Poth, C. N. (2017). Qualitative inquiry and research design: choosing among five approaches. London, United Kingdom: Sage.
I do agree with Carole in recommending ‘Creswell (2014). Research Design: Qualitative, Quantitative and Mixed Methods Approaches’. It is one of the very useful textbooks to understand : qualitative, quantitative and mixed methods approaches. I previously used ‘a sequential explanatory mixed-method approach’ . The first phase used a self-administered questionnaire with a stratified random sample of the target population. The second phase applied semi-structured interviews with a purposive sample of questionnaire respondents to gather in-depth information on their views/ beliefs and other variables important to the research question. Or you can use an ‘exploratory sequential mixed method design’: starting the study with an exploratory, qualitative phase and then moving sequentially to a quantitative phase. The design depends on the background of the research topic and the study objectives.
Using a mixed-method approach can enrich the evaluation by ensuring that the limitations arise because of one type of data are balanced by the strengths of another.
You could use Concept Mapping, a mixed method participatory approach, developed by Trochim & Kane (2007). It combine qualitative data collection --braimstorming & sorting-- with quantitative analysis --MDS & HCA--to obtain various representations of how a group thinks about a topic. It is fast and fun.