Are more students cheating on assessment tasks in higher education? Despite ongoing media speculation concerning increased "copying and pasting" and ghostwritten assignments produced by "paper mills", few studies have charted historical trends in rates and types of plagiarism. Additionally, there has been little comment from researchers as to the best way to assess changes in plagiarism over time. In this paper, we discuss the relative strengths and weaknesses of research designs for assessing changes in plagiarism over time, namely cross-sectional, longitudinal, and time-lag. We also report the results of our own time-lag study of plagiarism. We assessed self-reported engagement in, awareness of, and attitudes towards plagiarism in three comparable groups of students at the same university on three occasions, each separated by five years (2004, 2009, and 2014). The data from our study paint an encouraging picture of increased understanding and reduced occurrence of several forms of plagiarism, with no upward trend in verbatim copying or ghostwriting. We suggest that technological and educational initiatives are counteracting the potential for increased plagiarism from online sources.