My assessment strategies have evolved over the years but I think the principle that I've tried to stick to is carefully aligning the assessments with the course's learning objectives and outcomes.
For weekly quizzes and exercises I use multiple-choice and fill-in-the-blank questions, but not ones that are easily answered verbatim from the text. For example, an image may show a type of volcano they're asked to identify or a graph from which they're asked to estimate a river's flood recurrence interval. These questions include both computational (e.g., plate motion rates or radiometric ages) and non-computational (e.g., relative dating of sequences of events) problem solving as well.
I also include two writing assignments in which students write outlines and then abstracts of two recent topical journal articles (typically, from Scientific American). These assignments enable me to assess my students' abilities to think critically about how data and conclusions are linked in a scientific paper and to write concise, grammatically-correct narratives. I use a rubric to assess both the outlines and abstracts, and provide lots of written feedback.
This issue of assessment is something I would like to hear more folks weigh in on because I suspect there are lots of different strategies that work well for assessment.
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