Worksheets are an effective tool in ongoing efforts encouraging our students to engage their brains during class. Worksheets used in class can also help direct students' learning out-of-class. The following list, with links to discussion and illustrative examples, gives examples of goals that can be addressed by using worksheets.

 

 Helping students focus on an underlying ?big picture?

Bridging the gap between watching and doing

 Focusing students? attention in class

 Delivering and/or summarizing content efficiently

 Encouraging students to communicate their mathematical ideas

 Teaching students how to learn from their textbooks

Connecting new material to previously-covered material

One obvious disadvantage to incorporating worksheets into one?s teaching is the extra time that must go into creating them. However, I find that an imperfect worksheet often serves a particular purpose almost as well as a ?perfect? one ? a finding that relieves the pressure of finding sufficient time to create the perfect worksheet. And of course, worksheets can be revised and improved in subsequent semesters when repeating a particular class. But even better, worksheets ? as with many teaching innovations ? can be shared with and improved by colleagues. Mathematics faculty at my institution habitually share their course materials with colleagues, explicitly giving each other the right to revise and reuse worksheets. I often return to a course after an absence of a few years to find that my colleagues have substantially improved some worksheets that I initially created. Joint authorship, both simultaneous and asynchronous, brings additional benefits. Sharing worksheets often spurs conversation about teaching ? for instance, about course goals and how best to achieve them. Additionally, using another?s worksheet and attributing credit properly provides our students a subtle model of how to work together in an academic setting.

A less obvious drawback to using worksheets pertains to class time. It's all too easy to underestimate the time students will need to thoughtfully work their way through a worksheet ? and this is our valuable class time! Often the process reveals underlying problems: gaps in knowledge or skills that I assumed they already had. (Of course, identifying such knowledge/ skill gaps provides any instructor some useful information.) This time-related drawback is alleviated as I gain experience. Getting students comfortable with the idea that they won't always finish a worksheet also helps: I often have "straight-forward" and "more-involved" sections on one worksheet, and tell the students that I expect them to work through the former, then move on to the latter as time allows. This strategy also serves to keep the more advanced students from becoming disengaged while they wait for their classmates to finish. (Example: integration strategies)

These two costs of using worksheets are both mitigated over time, and are outweighed by the benefits. Students? benefits can be inferred from the list above. Students seem to appreciate the extra effort that goes into creating worksheets: our student evaluations typically mention worksheets in a highly positive manner. And faculty benefit too: from enhanced faculty interaction (as we share our worksheets), from becoming more informed as to what students are ?getting,? and from that same positive feedback on evaluations. Of course, our real benefit comes from the professional satisfaction in knowing we're doing all we can to help our students learn mathematics.

Acknowledgment

 Many thanks go to Karrolyne Fogel of California Lutheran University for helpful conversations, fruitful worksheet swaps, and for always keeping the focus on student learning.