Online Introductory Math
Colleges and universities are not factories, but they are institutions made up of a web of policy, practice, and procedure. These systems regulate almost every facet of institutional life, including the ways in which students move through their academic programs, movement which has substantial implications not only for the students themselves, but also for the faculty providing instruction, the physical and technological resources used in instruction, and the expenses and revenues associated with that instruction. Increasing efficiency, then, is about reducing the time, effort, and cost of providing instruction so that more students are able to progress more quickly through their academic programs. One corollary of this approach to efficiency is that increasing rates of student success is an essential part of the paradigm.
Time to degree is an important indicator of overall institutional efficiency and also an essential factor for individual students – and their families – making decisions about their academic careers. One of the main drags on student degree advancement can be a lack of progress through or success in required introductory courses. This problem is most notable in introductory math, which has often been criticized for slowing or stopping students’ academic progress, particularly for those students least prepared for college success.
There is a wealth of research as to why introductory math courses have become the obstacle they are in students’ timely academic progress, as well as a number of suggestions for how to ameliorate the problem. The local institutional context, such as the nature of the student body, the composition of the faculty, and the specific academic programs all must be considered when attempting to leverage introductory math courses as means of shortening time to degree. However, increasing the quality of instruction in line with the dimensions delineated above can go a long way towards keeping students enrolled and on track towards graduation.
In addition to students enrolling only to fail or drop out, the prerequisite nature of many introductory math courses can create an academic choke point if there are not enough seats available in classes to meet the demand from students. Increasing the number of seats available in any given course is one possible solution, but may be difficult or impossible with the constraints of the physical classroom spaces available. Online courses, however, are more flexible in this regard and can be an effective way to increase access to introductory math courses, thereby eliminating a potential obstacle to students’ academic progress.
Another structural way that the curriculum can reduce time to degree is to move what might have otherwise been prerequisite courses to co-requisite courses. In this model, students in need of additional introduction or reinforcement of foundational concepts and skills take a course aimed at providing that content in tandem with the routine introductory math course. Co-requisite courses have already proven successful in helping students successfully complete gateway math courses and there are emerging examples of this model working in online environments as well.
Of course, suggestions of accommodating more students may cause the eyebrows of faculty and administrators to arch suspiciously. Instructors will naturally begin calculating increased time for correcting homework assignments or answering student questions while the academic administrators will inevitably think of rising faculty loads as course sections multiply. The strategic introduction of technology into the learning environment, however, can mitigate the proliferation of grading time and course sections, among other common consequences of increasing student enrollment.
Helping instructors teach and facilitate learning more effectively via novel technologies can free up faculty time and attention for the activities and interactions only a “live” instructor can lead.
Helping instructors teach and facilitate learning more effectively via novel technologies can free up faculty time and attention for the activities and interactions only a “live” instructor can lead. These technologies can accommodate or automate many of the routine, mundane, and time-consuming elements of the teaching and learning process, enabling faculty to attend to the most important, impactful interactions with students. The essential balance is to leave to technology what it is best equipped to handle to ensure that faculty time is always well spent.
For example, the automated grading tools embedded in most learning management systems or even available through Google Forms are able to provide almost instantaneous ‘right or wrong’ to students on their responses to some kinds of quizzes or tests. Even newer technologies are now available that can build on that system of automated grading and supplement it with specific, “just in time” learning resources and feedback to correct the misunderstanding. These new capabilities can speed up the provision of corrective feedback to students with no greater effort on the part of the instructor.
Whether or not it is formally calculated or used in curricular decision-making, there is a cost-per-student amount for the offering of every course. By increasing the number of students being taught using the same human and institutional resources, the effective cost-per-student will be reduced. However, it is not simply a matter of adding more students to existing courses, the level of instructional quality must be maintained – or even increased. As more students enroll in any given course, an ever-increasing number will need resource-consuming additional support or will simply drop, fail, or withdraw, meaning they will need to return the course in future terms.
Similarly, increasing instructional quality for the same number of students will lower the overall cost-per-student because fewer students will need assistance from instructors, teaching assistants, or tutors, and fewer will drop, fail, or withdraw from required courses, removing the need to re-enroll. The academic progress these students can make is certainly a boon for them, if costs can be controlled, but also for the institution as a whole as retention and graduation rates eventually rise, bolstered by students whose academic paths have not been disrupted by lack of success in introductory math courses.
Institutions may find a synergy for lowering costs by both reducing effort and shortening time through the transition of introductory math courses from face-to-face and on ground to fully online learning. The automations, scalability, and vast array of digital learning tools available in an intentionally designed online learning environment can free up faculty time and attention to focus on student interaction and relationship-building, key elements of effective instruction and long-associated with student success.
Departments and institutions should ensure that the benefits accrued by these efficiencies are shared with the faculty doing the instructional work. Rather than eliminating or limiting faculty lines, it will be important to engender faculty buy-in for there to be demonstrable efforts at reducing teaching loads, carving out additional time for research, or adjusting service expectations for tenured and tenure-track faculty. Non-monetary benefits for adjunct instructors may be less obvious, but should also be pursued. For example, greater predictability in contracting or a certification to teach certain courses or content could be offered.
- Elli J. Theobald et. al., “Active Learning Narrows Achievement Gaps for Underrepresented Students in Undergraduate Science, Technology, Engineering, and Math,” Proceedings of the National Academy of Sciences, 117 (12), 2020, https://www.pnas.org/content/117/12/6476. ↑
- Elizabeth Zachry Rutschow et. al., “Gaining Ground: Findings from the Dana Center Mathematics Pathways Impact Study,” Center for the Analysis of Postsecondary Readiness (CAPR), November 2019, https://postsecondaryreadiness.org/wp-content/uploads/2019/11/gaining-ground-dana-center-mathematics-pathways.pdf. ↑
- Florence Xiaotao Ran and Yuxin Lin, “The Effects of Corequisite Remediation: Evidence from a Statewide Reform in Tennessee,” CCRC Working Paper No. 115, Community College Research Center, Teachers College, Columbia University, 2019, https://ccrc.tc.columbia.edu/media/k2/attachments/effects-corequisite-remediation-tennessee.pdf. ↑
- Dana Center’s Webinar on “Transitioning Corequisite Math Courses to the Online Environment,” https://www.utdanacenter.org/blog/free-webinar-transitioning-co-requisite-math-courses-online-environment. ↑
- In their recent white paper, Jessie Brown and Martin Kurzweil make a case that improvement in instruction can lead to improvement in student outcomes which in turn lead to increases in marginal institutional revenue that are larger than the marginal costs of improving instruction and of serving a large student population. See Jessie Brown & Martin Kurzweil, “Instructional Quality, Student Outcomes, and Institutional Finances, American Council of Education, 2018, https://www.acenet.edu/Documents/Instructional-Quality-Student-Outcomes-and-Institutional-Finances.pdf; Also see https://www.acenet.edu/Documents/Estimating-ROI-Instructional-Improvement-Ithaka-Step-by-Step.pdf. ↑
- For example, see Every Learner Everywhere, https://www.everylearnereverywhere.org/resources/. ↑