Adventures in Corequisite Calculus: Laying the Groundwork with Pre-Semester Preparations



Students working at whiteboards in groups of three

Last semester, I had the opportunity to teach my college’s first supported calculus course in response to AB 1705. As someone deeply involved in the development of our department’s supported classes, I eagerly volunteered to lead one of the sections. I had recently taught calculus both in-person and as a hybrid (with 40% of instructional hours asynchronous online), so this was another opportunity to adjust my existing calculus course into a new modality–a supported version.


The San Diego Mesa Corequisite Model: Supported (corequisite) courses in my department are linked courses where the transfer-level course (in this case, a 5-unit calculus course) is paired with a 1-unit lab (3 contact hours). All students are enrolled in both sections which are taught by the same instructor. Since the students and instructor are the same for both, we can use the additional time fluidly – for instance, in my course, the lab hours are scheduled on Fridays in a 3-hour block, but in reality, support is woven into each class instead of occurring on one day. In addition to the extra contact time with students, we have lower class caps on our supported sections (36 v. 46), so we can provide additional support to individual students.

Heading into the semester, I was excited about the possibilities. Because the supported calculus class is open access, I knew I would have students who had not completed precalculus previously, but I was not worried. I felt I had already encountered similar students in my regular calculus course. Most calculus instructors have had students who didn’t know how to graph a parabola, needed help with factoring, or had trouble with trigonometry. But this time I’d be armed with a smaller class cap and an extra 3 hours a week to provide support. Haven’t you ever had a class and thought, “If I just had fewer students, I could reach out more intentionally” or “If I had an extra hour, I could do this activity”? That was going to be me!

It turns out my optimism and excitement were not misplaced – last fall was the most fun I’ve had teaching in 14 years, and at the end of the semester, my course had a similar pass rate to my last two semesters teaching a traditional calculus course: 31 of my 39 (79.5%) students passed the course, compared to our campus pass rate of 60%.

As I attempt to describe the instructional moves that made my supported calculus class a success – both in terms of student outcomes and in terms of the joy that attending class each day brought me, it’s crucial to recognize the foundational role of the planning work that happens before the semester begins. This pre-semester work is made visible to our students through our syllabi and welcome emails – what we are communicating, how we are communicating, and our policies set the stage for the learning experiences that unfold during the semester. In this first blog post, I will highlight some features of my supported calculus class through a discussion of my syllabus. You’re welcome to poke around in my syllabus and lift anything that is useful to you.

Creating our Classroom Community

While most of my efforts to foster belonging and create community happen in the classroom, which I will discuss in future blog posts, I try to foster a sense of community before class even begins through my syllabus by humanizing myself and by building my students’ trust in my commitment to them and to their learning.

Humanize yourself: I always think of Rita Piersen’s quote: “Kids don’t learn from people they don’t like.” This is true for all learners, and I humanize myself in my syllabus to help students find a reason to like me. I probably overshare about myself – my interests, pictures of me with my soccer buddies, even a video of me speed-puzzling! By sharing these silly details about my life (including an invitation to help me earn a Peloton swarm badge!), I hope that students will see me as approachable, as someone they will be able to relate to. Initiating this human connection is the first step in establishing a learning partnership before we’ve even met.

Build your students’ trust in your commitment to them and their learning. I communicate throughout my syllabus that I’ve designed my course for all students to be successful, especially for those who have traditionally struggled in mathematics. For example, in the first paragraphs of the syllabus, I emphasize that in this supported course there is time to learn the skills necessary for success in calculus, and that I have taken steps to make the course accessible to students who may have some skill gaps:

The Welcome statement from my syllabus: If you’ve made it here, you should be signed up for my Calculus class. This is the first semester of offering a Math 150 without requiring 141 and I’m stoked (that’s geriatric millennial for excited) to have you in class. The idea of this course is that we will use the extra time to learn the algebra, trig, and precalculus skills necessary to be successful in calculus as we go.

One of the ways I’m hoping to make this class accessible to students who may be missing some skills is by using standards-based grading. This means that each week, we will focus on a given topic and you will have a few ways to demonstrate your understanding. If you need a bit more time to learn that material, you can retake quizzes or redo other assignments until you’ve got it down. My hope is that I’ve designed the course in a way that lets you focus on learning the skills necessary to be successful in future courses.

Another example from the first page of my syllabus is the ‘My Commitment to Us’ section. Instead of diving into late policies and other do’s and don’ts, I try to lay the foundation for a learning partnership that celebrates what each of us bring to the class, acknowledges the need for flexibility in course policies when life gets in the way, and sets up expectations for preparing for class by completing assignments that will allow us to “challenge each other and have good conversations.”  

Of course, my syllabus also contains the usual stuff. But the list of learning objectives and course overview full of scary math terms are all hidden away on a ‘required syllabus stuff’ page – instead, the structure of the syllabus directs students to pages that communicate that we’re about to embark on something different and that we will do it together. 

Focusing on Growth

 “My course is built on the idea that we aren’t perfect the first time we do something, and those mistakes are how we improve and learn.” This is a central organizing principle of my course design as I describe it in the My Philosophy section of my syllabus.

In a future blog, I will discuss the ways in which I normalize mistakes and highlight the learning process at every class meeting, but this focus on growth is also embedded in my grading policies which are an important part of any syllabus. 

In the discussion of grading in my syllabus, I have a bold heading: “Learning from Mistakes – My Mantra.” And I uphold that mantra by using standard-based grading. Most assignments (pre-class Delta Math problems, quizzes, and a portfolio) are treated as formative assessments. Instead of averaging scores, students get feedback on their work and can resubmit work on a similar assignment until they receive a perfect score or hit the deadline. This way no one is penalized for a slow start or for a gap in their algebra skills, and instead learning is rewarded. By exam time, most students have learned the material and do well, but I also allow one exam retake during the final exam period. I don’t grade homework or classwork, and I don’t use fluff points for attendance or compliance-based effort points. A student’s grade is based solely on what they have learned. I find that my students are motivated by the opportunity to improve their scores and demonstrate their learning–attendance in my class last fall was nearly perfect.

With the switch to grading for understanding and allowing reassessments, I don’t have to have a late work policy and I don’t have to judge students’ reasons for late work. I also avoid the inequities that can arise when there is some sort of unwritten exception to a late policy that is granted only to students who have the courage to ask. 

This growth-oriented approach to grading is particularly important in a supported course so that students are not penalized for their incoming preparation.

Communicating Support

Finally, we know students need to seek support when they struggle. However, students face many barriers when it comes to seeking support: fear of judgment, lack of awareness, accessibility or cultural barriers, and a belief they should be able to handle those challenges on their own. We can start breaking down those barriers by normalizing help-seeking in our syllabus. 

In the Student Support section, I deconstruct what it means when I say, “ I am your first contact for the help you may need in this course,” and my messaging is designed to encourage students to reach out for help. Some of these are simple changes, like rebranding “Office Hours” as “Student Visiting Hours.” I’ve previously taken this even further by adapting the approach given by Viji Sathy for providing additional context to office hours such as in this meeting menu approach. I’m lucky to have an embedded tutor who attends class and holds a class session each week, and both of our contact information and hours are on our homepage for the course. I also break down the additional places for tutoring in my orientation module in our learning management system by having students take a syllabus quiz that includes matching our different tutoring options to what they are. My syllabus also has resources for basic needs, counseling, and technology help. In a later blog post, I will discuss ways to normalize help-seeking behaviors throughout the semester to encourage students to use the resources available to them.

Many of the pre-semester practices mentioned above align with the findings of a recent study, Counting on Math Faculty. This study of 22,827 California community college students in 704 transfer-level math classes found that who a student had as their instructor was twice as important as the student’s academic preparation in predicting whether a student passed the transfer-level math course. The study also identified instructional practices associated with more equitable outcomes that resonate with the ideas discussed in this blog. 

As AB 1705 opens doors for students into classrooms that will be challenging for them, it’s crucial we adjust our course design so that students feel supported and welcome and that they have the opportunity to succeed without being penalized for their prior math preparation. There are fears that AB 1705 will exacerbate the racial disparities in STEM, and I think those fears are well founded if we teach a supported calculus class in a traditional lecture format with the ‘weed out’ culture that is so prevalent in STEM. I’m hopeful that together we can create supported calculus classes that meet the needs of all of our students who aspire to learn calculus, and I want this blog series to contribute to that effort.  

As I head into my second semester teaching supported STEM calculus, I committed to write this blog with several goals in mind:  


      • To make visible my choices and experiences– both what has worked and what hasn’t, in the spirit of improving my supported calculus course.

      • To share ideas and resources that have worked for me with the hope that other calculus instructors will find something useful.

      • To start conversations about how to best support STEM students in light of AB 1705.

    I’d love to connect with anyone also on this adventure! I’ll be hosting community hours on Thursdays from 12-1pm in a Coreq Calc Discussions Zoom Room every week until May 23rd. Please join me. I am happy to chat or answer any questions via email (kspoon@ My other roles involve a lot of work in professional learning, course design, assessment, zero textbook cost, statistics education, and online teaching, so I love connecting with faculty with similar interests.

    Until our next journey together, 

    Kelly Spoon

    Kelly Spoon is a Professor of Mathematics at San Diego Mesa College in the San Diego Community College District. She has been at the forefront of her institution’s response to AB705 and AB1705, playing a key role in coordinating Mesa’s corequisite classes for Intermediate Algebra, Statistics, and, most recently, Calculus.

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