Assessment is an evaluation tool in learning adjusted to the times. The criteria that must be included in the assessment are indicators in the cognitive domain and critical thinking. Therefore, this study intends to explore teaching assessments prepared by lecturers in assessing students’ cognitive shutter and critical thinking abilities. The data taken in the pandemic period of Covid-19. The subjects of this study were 269 lecturers who were teaching in English education departments in some private universities in South Sulawesi, Indonesia. There were 25 items of questionnaires arranged to analyze the teacher assessment in cognitive aspects. The results showed the dominant lecturer measured the ability of students on the C1-C2 scale even though some lecturers had been on the C5-C6 scale. The lecturers’ assessment of teaching has implemented indicators of critical thinking skills. This study recommends future researchers to develop assessment of teaching, especially for English Department and assessment mapping in facing the fourth industrial revolution era.