This study investigated students' successes, strategies, and common errors in their answers to questions that involved the electron-pushing (curved arrow) formalism (EPF), part of organic chemistry's language. We analyzed students' answers to two question types on midterms and final exams: (1) draw the electron-pushing arrows of a reaction step, given the starting materials and products; and (2) draw the products of a reaction step, given the starting materials and electron-pushing arrows. For both question types, students were given unfamiliar reactions. The goal was for students to gain proficiency--or fluency--using and interpreting the EPF. By first becoming fluent, students should have lower cognitive load demands when learning subsequent concepts and reactions, positioning them to learn more deeply. Students did not typically draw reversed or illogical arrows, but there were many other error types. Scores on arrows questions were significantly higher than on products questions. Four factors correlated with lower question scores, including: compounds bearing implicit atoms, intramolecular reactions, assessment year, and the conformation of reactants drawn on the page. We found little evidence of analysis strategies such as expanding or mapping structures. We also found a new error type that we describe as picking up electrons and setting them down on a different atom. These errors revealed the difficulties that arose even before the students had to consider the chemical meaning and implications of the reactions. Herein, we describe our complete findings and suggestions for instruction, including videos that we created to teach the EPF.