Still another type of writing to learn that builds on assigned readings is the response paper. Unlike the summary, the response paper specifically asks students to react to assigned readings. Students might write responses that analyze specified features of a reading (the quality of data, the focus of research reported, the validity of research design, the effectiveness of logical argument). Or they might write counter-arguments.
To extend these response papers (which can be any length the instructor sets), consider combining them into another assignment--a position paper or a research-based writing assignment.