The purpose of this research is to identify which aspects of the communication skills and mathematics connections of the prospective mathematics teacher that need to be improved. The subjects of the research were 34 fourth-semester students of Mathematics Education Study Program, State University of Yogyakarta, Indonesia, who took Discrete Mathematics course from February to May 2012. The identifications are done through 6 times by quizzes/tests. The aspect of mathematical communication that had been studied was the ability of students in: (1) writing the statements, reasons, or explanations, and (2) using terms, notations, tables, diagrams, charts, drawings, illustrations, mathematical models, or formulas. While the aspect of mathematical connections that had been examined was the ability of students in: (1) stating the relationship between facts, concepts, or mathematics principles, (2) developing a mathematical model of the daily life problems, and (3) mentioning the concept underlying the solution from the given mathematical problems. Results shows that the students tend to be weak in: (1) writing down the reasons, (2) using charts, pictures, and illustrations, and (3) developing a mathematical model.