## Monday, September 03, 2018

### 2018 calculus syllabus

In my last post, I explained a bit about how I feel like my syllabus is a work-in-progress, even though the semester has started and I’m already using it. In this post I’ll give some more details and even more history. I’ll quote extensively from my syllabus verbatim; here is a link to the entire thing for anyone who is interested.

Revising my syllabus for this semester really began last fall. I wasn’t entirely blind to the faults that were starting to show. One major change was in restructuring the exam schedule. When I switched to standards-based grading in calculus 1, I also started weekly quizzes (which students took on their own time outside of class) and had three midterm exams plus a final. The quizzes functioned as a sort of preliminary assessment for most of the standards. Each test covered about eight standards. After the third test, there were a couple more standards we covered in class, which were only assessed on a quiz and the final exam. Even with three midterms, however, I had often felt like students were rushed in completing them. I also began to question the value of the out-of-class quizzes. So I turned the quizzes into “labs” that students were free to collaborate on, and I switched from three midterm exams to five, which would formally assess every standard before the final.

I really liked how having five midterms broke up the material. Each test became more coherent in the material it included. Exam 1 covered limits. Exam 2, definition and interpretation of derivatives. Exam 3, rules for differentiation. Exam 4, applications of derivatives. Exam 5, definition of integrals and the Fundamental Theorem of Calculus. Especially helpful was splitting up the applications of derivatives (l'Hospital's rule, optimization, related rates, and so on) from the introduction to integrals; these topics had usually been all jumbled together in the last midterm, compounding the difficulty already created by it being late in the sester. Also, by dedicating one test just to derivative rules, I was moving towards having a Differentiation Gateway Exam, as several of my colleagues at Pepperdine use. And paired with that move was an awareness that I was gravitating towards a specifications framework.

This fall, I decided to maintain the five-midterm structure and get rid of the quizzes/labs, to be replaced by an occasional more substantial homework exercise that will be used in class. I collected seven standards into the Gateway Exam, which will form the bulk of the third midterm. I split the remaining standards into 45 “tasks”, which is a term I hope will be clearer than “standards”; each standard split into approximately two tasks. The idea of tasks goes back in my mind to the list of problems Kate Owens shared from her Ph.D. advisor George McNulty. That is, a task is a specific type of problem that students will show they know how to solve. Here is the new introduction to the “Goals and Assessment” section of my syllabus:

Change is present all around us, and understanding it is an essential component of many fields of study. Calculus is fundamentally a set of tools for measuring, quantifying, estimating, and interpreting change in a variety of contexts. In this course, we will delve into some of the most profound ideas in mathematics, whose roots are from ancient times and which began to develop fully in the 17th century; they continue to form the basis for much of modern science. My hope is that this class will develop your analytical ability and deepen your appreciation for the power and elegance of mathematics.

The skills you should acquire are related to the Learning Outcomes stated on the first page of this syllabus. Your mastery of the course content will be assessed through your performance on a collection of definite tasks. A complete list of tasks is on the last two pages of this syllabus. These tasks, rather than points or percentages, will be the primary basis for grading. The following sections provide details on how the tasks will be assessed and what you should accomplish in order to earn your final grade.

My hope is that this method of assessment, called standards-based grading or mastery grading, will keep you clearly informed as to the expectations of the class and how well you are meeting them, while also removing the (often distracting) elements of linear grading that uses letters or total points. Learning is not always a straightforward process, and one of my goals is to give you as many opportunities as possible to demonstrate your understanding. I will be glad to do everything I can to help you towards your goal of mastery. If you have questions or concerns at any time, please feel free to discuss them with me.

Another potential source of confusion from my SBG system in the past was the levels of ranking. I really liked that we were using the vocabulary of mastery / proficiency / basic ability / novice to talk about students’ progress, but it was rare that a student could rate their own work with one of these levels. So this fall I opted, as many others have, for a simple pass/fail approach on tasks. I don’t like the pass/fail language, however, so I chose successful for a task completed satisfactorily and progressing or incomplete for work that has major mistakes or is absent. I also wanted to handle small mistakes through a faster revision process, an idea I picked up from MathFest; for these situations, I added a revisions needed category. Here is how I describe the rating system in my syllabus:

A task is a problem or a collection of similar problems that should be solved using calculus tools. Your progress in the class will be measured in terms of the number of tasks that you accomplish. Partial credit is not given; a task must be fully successful in order to count towards your final grade. Whenever a task is included on an exam, your work will receive one of four ratings:
Ssuccessful Solution is complete and correct.
Rminor revisions needed Solution is correct except for small errors.
Pprogressing Partial understanding is evident, but solution contains substantial errors.
Iincomplete Not enough evidence is available to provide an assessment.
A task marked “S” has been completed; you can check it off the list at the end of the syllabus.
A task marked “R” can have a small mistake such as an arithmetic error or a miscopied value. You will have 48 hours (or over the weekend if the work is returned on a Friday) to complete a Revision Form that explains how to correct the mistakes, and to submit the form along with your original work, in order to earn a successful rating.
A task marked “P” demonstrates progress in mastering the topic, but reassessment is necessary in order to successfully accomplish the task.
A task marked “I” shows little or no relevant work. Reassessment is necessary.
To show mastery of a task after it has received a rating of P or I, see the section entitled “Reassessment” on the next page.
Hopefully this simplified rating system will also make it easier for me to track student progress over the duration of the semester and analyze trends afterwards. (I agree with Kate that Drew’s “A tale of two students” chart was a moment of clear inspiration at MathFest.)

In order to help students know what is expected to prepare for reassessment, and to help me schedule them more effectively, I have introduced Reassessment Tickets:

After a task has been assessed on an exam, you may schedule a reassessment if you did not successfully complete the task. This is a two-step process:
• First, pick up a Reassessment Ticket from my door or download and print one from the Courses site. Complete the form and return it to me at least 24 hours before you want a reassessment.
• Second, once a meeting is scheduled, come to my office and I will give you a new opportunity to demonstrate mastery of the task. If possible, I will grade your work immediately; otherwise, I will let you know the result by the following day.
I will reassess up to two tasks per student per week. In addition, you can use exam days as opportunities for reassessment of up to three tasks, provided you let me know 48 hours in advance which ones.
I plan to use one or two class days at the end of the semester for reassessment alongside review, as well.

Another element I introduced was subcategories of tasks: “core”, “modeling”, and “additional“ (not a great name, I’ll try to find a better one in the future). Again, lots of other people are already doing this, and I like what many of them are doing, which is to require two demonstrations of mastery for core skills and only one for the rest. I couldn’t figure out how to make that work with my system, so I made the following distinction: core tasks are the ones that could appear on the final exam. There are 14 of them, and I will choose seven to go on the final. (The final exam will also include a reflection essay, and a period of time for additional reassessment.) I also set higher expectations for how many core vs. additional tasks needed to be successful at each grade level.

What I learned from creating a list of tasks is that, because I state exactly what types of questions I will include on the tests, there is less wiggle room than with standards, which could always be applied to new sorts of problems. (This is the distinction between activity and ability I talked about in my last post.) I don’t know if my list of tasks, or the categorizing thereof, is ideal, but it is certainly enough to guarantee that a student who succeeds at all of them will have mastered calculus 1. (I used Robert’s classification of “core” and “supplemental” learning targets as a reference while I was sorting, but our lists don’t match up exactly.)

After all the work that goes into getting away from letter grades in a standards-based system, it’s always a bit dispiriting to turn back to them. So I start my section on “Final letter grades” with a bit of reluctance (not to say snark).

At the end of the semester, I am required to submit to the university a letter grade reflecting your achievement in this class. Here is how that grade will be determined.

To earn an A: in addition to passing the Gateway Exam and completing the Final Reflection,
• Submit 20 homework reports.
• Complete all modeling tasks.
• Complete all core tasks.
• Complete 6 core tasks on the final exam (minor errors are acceptable).
To earn an B: in addition to passing the Gateway Exam and completing the Final Reflection,
• Submit 15 homework reports.
• Complete 2 modeling tasks.
• Complete 12 core tasks.
• Complete 5 core tasks on the final exam (minor errors are acceptable).
Passing the Gateway Exam is required to earn a final grade of B– or higher.

To earn an C: in addition to completing the Final Reflection,
• Submit 10 homework reports.
• Complete 1 modeling task.
• Complete 10 core tasks.
• Complete 17 additional tasks OR pass the Gateway Exam and complete 14 additional tasks.
• Complete 4 core tasks on the final exam (minor errors are acceptable).
Failure to complete a Final Reflection will result in a grade of D or F.

To earn a D:
• Submit 5 homework reports.
• Complete any 30 tasks from C.1–C.14, A.1–A.28, M.1–M.3 OR pass the Gateway Exam and complete any 23 tasks.
• Complete 3 core tasks on the final exam (minor errors are acceptable).
Plusses and minuses will be assigned as follows: if all criteria for a letter grade are met as well as two or three of those for a higher letter grade, then a plus will be added. If all but one or two criteria for a letter grade are met, and the remaining items meet the criterion for one letter grade lower, then the higher letter will be given with a minus added.

I will use my discretion to assign a final letter grade in cases where a different set of conditions is met.

So there it is. My syllabus for calculus this semester. I’m sure by December, or even October, I’ll have a much better notion of what changes I should have made. I’ll let you know how it goes.

(I should also have given more attribution in this post to the people I stole ideas from, especially at MathFest, but I don’t have those notes on hand right now. So a general word of thanks goes out to this very sharing community.)