This study investigated how lecturers of Technical Writing and Academic Literacy assessed their students at a science and technology university in Botswana. The data for the study were obtained from the past test, assignment and examination papers administered to year one, year two and year three students enrolled in various programmes under the College of Sciences (including the Department of Information Communication and Technology), and the College of Engineering and Technology at the said university. In addition, a focus group of six teaching staff was interviewed to triangulate the data and to get in-depth information on how they set the assessment pieces. The data obtained from the assessment pieces were analysed qualitatively to determine the nature and the level of questions used. The data from the interview held with the teaching staff were also analysed qualitatively to determine what informed the way they set questions. The results from the study showed that the students were mainly tested for knowledge application; and many of the questions were from the low-level category as per Bloom's Taxonomy (1956) revised for the 21st Century Learners (The University of Utah's Centre for Teaching and Learning Excellence, 2001). The results also showed that lecturers did not take into account the level at which the students were studying. University students should be required to analyse, synthesise and evaluate information before them in order to demonstrate deeper understanding. It is recommended that lecturers should apply Bloom's Taxonomy when setting assessment tasks, taking into consideration the level at which the students were studying. It is hoped that the results from the study will sensitise the teaching staff at this university and other tertiary institutions on the importance of applying Bloom's Taxonomy when assessing their students.