The student movement is part of a social movement. Snapping Indonesian students are full of dynamics because it is always student movement changing characters and shapes on each era, from the early history of Indonesia is "generation 1908", " generation 1928 ", "generation 1945", "generation 1966" and " generation 1998". The student movement today is characterized by partial and sectoral policies in order to criticize the government not to depose the regime. The student movement Muhammadiyah University of Yogyakarta through the Student Executive Board (BEM) are often involved in the demonstrations to criticize the policies of the government of President Joko Widodo. The purpose of this study was to determine the issues become critical UMY student movement against the government of President Joko Widodo. Then to know the strategies of the student movement as well as to determine the contribution of the student movement against the social construction UMY. This study uses descriptive and qualitative research conducted at the campus of St. Louis, located in the Campus Integrated UMY Jl. Lingkar Selatan, Kasihan, Bantul, Yogyakarta 55183. Respondents there were 50 people who were taken from considering Faculty and programme study, consisting of members of the BEM and the regular student, also conducted several in-depth interviews with 4 members of the BEM. Data collection through questionnaires, interviews, observation, and documentation. Data analysis techniques used in qualitative research descriptive measures of data collection, data reduction, data presentation, and conclusion. The results of the study explained that the issues be a criticism of the student movement against the government UMY Jokowi is divided into four main issues, namely the price increases, domestic policy, foreign policy and monetary and fiscal policy. The most crucial issue is the issue of fuel price hike, foreign investment, especially in China and the issue of "Perpu Ormas". Strategies undertaken UMY student movement in criticism is through seminars, discussion, advocacy, and demonstrations. Strategy action done to accommodate the student movement in the container BEM UMY, has the goal of short-term (temporary) and long-term, to build awareness and ideological movement that it is still weak and build collectivity strong and manage strategic issues in actions that will be carried out. The contribution of the student movement in UMY against the social construction that is formed is to provide conceptual and operational discourse that is able to disseminate the issues to governments, communities, the demonstrators and the media. Social construction appears that the student movement UMY sought and seek to build a critique of government policy in order to better Jokowi and misery to the people.