This past semester I had worked these students hard. They were responsible for and graded on:
- Reading Reflections (three times per week, reading the section and answering questions about the material before we discussed it in class).
- Two sets of homework each week (about 12 fairly straightforward questions on WeBWorK due on Thursdays and three challenging multi-part problems due on Mondays).
- Seven short projects developed by Tevian Dray and Corinne Manogue as part of their Bridge Project (see http://www.math.oregonstate.edu/bridge/). These were started in groups of three or four, but each student was responsible for writing his or her own three to five page report of the solution. For the first report, I required a first draft that was critiqued and returned for revision and resubmission.
- A major project based on the Hydro-Turbine Optimization chapter in Applications of Calculus . The project was started in groups. Each student was responsible for an 8–12 page paper explaining the solution. The papers were turned in, critiqued, and returned for revision and resubmission. LaTeX and pdf files of my version of this project are available here.
- Two examinations during the semester and a final exam. After each exam during the semester, students were required to write about the problems they had missed points on, explain what they did wrong, and explain how to do it correctly. They could earn back half the points they had lost. For the final exam, they had to explain what they were doing to solve the problems, not just give an answer.
I was available to my students every afternoon, and I also had a great undergraduate preceptor (teaching assistant) who held help sessions Sunday and Thursday evenings, before the homework assignments were due. By the end of the semester, over half the class was coming to each of these, and so she organized them into groups working with each other on the homework while she circulated to help the groups that were stuck.
Not surprisingly, in the end of semester course evaluations my students wrote about how much work they had done for this course. And yet, when asked specifically whether or not they agreed with the statement, “The general workload was appropriate for this level course,” only five of my 33 students disagreed. One student comment that summarized the tenor of the end of course evaluations stated, “I would say that the course is difficult and a lot of work, but very rewarding, because if you put in a lot of time and effort then you can see yourself understand the material and do well. Although the course can be really hard at times, there is always somewhere to go for help.”
The second thing that happened this past week was my discovery of How Learning Works: 7 Research-Based Principles for Smart Teaching . This collaborative effort, published in 2010, translates what has been learned by those engaged in research in undergraduate education into practical guidance for those of us in the classroom. What the authors call principles, I see more as facets of teaching to which I need to pay attention. This is my own paraphrasing of these principles or facets:
- The need to understand the variety of prior knowledge that my students bring to my class and how it helps or hinders them.
- The importance of how students organize the knowledge they are acquiring and the need for me to understand common misalignments and to help them make the necessary connections.
- The critical role of student motivation and my responsibility to strengthen it.
- The need to develop automaticity in basic skills and the fact that learning how to integrate and apply these skills requires guidance and directed practice from me.
- How important it is that I provide useful feedback that is targeted at improving performance.
- The role of the social, emotional, and intellectual climate in my classroom.
- The need for me to guide students in practicing metacognition, monitoring what they are doing and why.
The book discusses the relevant research, but is also full of examples of traps we can fall into and strategies for dealing with these principles or facets in order to improve our teaching.
One trap discussed under #3 describes the teacher who, with the intent of spurring his students to work hard, warned them at the start of the course that they could expect that a third of them would not pass. This had exactly the opposite effect. With the expectation that they would not do well regardless of how much effort they put into the course, a large proportion of the students directed their time and energy to other courses.
The issue here is motivation, getting the students to put in the effort needed to learn the material. I believe that I did succeed particularly well this past semester in motivating most of my multivariable calculus students. How Learning Works identifies three levers that motivate students to work hard. The first is value. They have to believe that what I want them to learn will be of value to them. Personal enthusiasm on my part goes a long way toward building this sense of value. The second is a supportive environment. They have to believe that the course is structured in such a way as to help them be successful, rather than throwing up obstacles to their success. Starting the projects and encouraging them to share their understanding of homework problems within groups, providing feedback and multiple opportunities to demonstrate understanding (as with WeBWorK and the chance to earn back points lost on exams), and the availability of myself and my preceptor build the sense of support. The third is self-efficacy, belief that one is capable of achieving success.
This last is the main reason I will never again grade on a curve. The message sent by grading on a curve is that the proportion of failures has been determined in advance, regardless of how much work students are prepared to invest in the course. It is also why I am disturbed that in our national survey of calculus, faculty at the start of the term were able to predict, almost perfectly, what their grade distributions would be at the end of the term (see the last bullet under Instructor Attitudes in The Calculus I Instructor, Launchings, June 2011). Going into this course, I would never have predicted 67% A’s. I am delighted that what I did worked so well with so many of my students. 
Which brings me back to the issue of grade inflation. Grade inflation is a red herring because it misdirects our attention from what should be our true concerns: What do our grades mean in terms of expectation of student achievement and understanding? And how can we support as many students as possible to meet our highest expectations?
 Straffin, P. D., Jr. 1996. Hydro-Turbine Optimization. Pages 240–250 in Applications of Calculus. P.D. Straffin, Jr., editor. Classroom Resource Materials. MAA.
 Ambrose, S. A., M. W. Bridges, M. DiPietro, M. C. Lovett, M. K. Norman. 2010. How Learning Works: 7 Research-Based Principles for Smart Teaching. Jossey-Bass.
 Not all my students did well. The class GPA was 3.5. What was important was that I had explicit expectations of what would constitute A work, that I clearly communicated what was required to meet those expectations, that students saw them as challenging but achievable, and that my students really were graded according to these expectations.