Meeting the Challenge of Online Learning in Mathematics
By: David Bressoud @dbressoud
David Bressoud is DeWitt Wallace Professor Emeritus at Macalester College and Director of the Conference Board of the Mathematical Sciences
This month’s column highlights a recent report of Ithaka S+R and TPSEMath, How to Support and Lead the Urgent Transition to Quality Online Learning in Intro Math (Fried and Joo, 2020). By “intro math” they are referring to the courses usually taken in the first year—college algebra though calculus and introductory statistics—although there is nothing in this report that is specific to any one of these courses. This paper focuses on attention to the issues that must be addressed as students encounter their first mathematics course at university, especially when this course is being taught either wholly or partially online. It concludes with some specific strategies for building quality online courses.
Most of the recommendations in this paper are relevant for these courses whether taught in-person or online. But this is a particularly opportune moment to bring these up. Going online or adding online components is forcing us to reconceptualize our courses. Furthermore, as faculty become familiar and comfortable with online modalities of instruction and assessment, they inevitably will become a greater component of instruction.
Simply putting lectures online perpetuates and accentuates the deficiencies of these courses as they have been taught. Making the changes that are needed cannot be done by individuals. As the report emphasizes, course design must be “a collaborative endeavor that is integrated within a larger system, with a shared focus on equity in access, opportunity, and outcomes for all students.” The report highlights two overarching concerns, quality and efficiency, that should be the focus of attention.
What I find particularly interesting are what this report sees as the components of quality. The first is equity. In an opening sentence that beautifully summarizes what we mean by equity, the authors state that
Not all students come to higher education with same academic and life experiences, making it incumbent on their colleges and universities, as well as individual instructors to design learning experiences that minimize or mitigate these differences.
This goes well beyond ensuring that all students have access to technology and the internet. It means paying attention to students’ preparation for online learning, course design and the quality of instruction, student perceptions of the course and the instructor, and the social component, ensuring connection to peers. This last is one of the hardest to foster in an online environment, but I am certain that the lack of connection to peers is one of the reasons MOOCs failed to meet their potential. Serious attention must be paid to facilitating these ties.
An emphasis on equity requires continual program assessment. Summative assessments such as DFW rates are useful, but they are retrospective. It is essential, especially as we move into these new modes of instruction, that extensive formative assessment be built in so that we know which students are having difficulty with which aspects of the course in a timely manner that enables mid-course correction and additional supports.
The second component of quality is conceptual understanding and quantitative reasoning. It was never enough for students in these courses to simply learn how to solve the kinds of problems demonstrated in class. Too much online instruction never rises above this level. Serious attention needs to be paid to how this will be accomplished in an online environment. Fortunately, it is difficult to securely administer online tests that rely on multiple choice or short answer questions. This forces greater attention to the use of alternative assessments that can also play a formative role, exploring student conceptualizations and understandings.
Conceptual understanding and quantitative reasoning are tied to the third component, alignment of learning goals and outcomes. Quality requires an assurance that the skills and knowledge gathered in one class adequately prepare students for the next. This requires attention to the articulation of the goals of successive courses. As the report states,
A change in the curriculum as impactful as moving introductory math online is an important opportunity to establish—or reestablish—the explicit and direct connection between the introductory math courses and the learning required for success in later courses.
The fourth component is intellectual challenge. This means constantly challenging students with mathematics that is within reach but beyond their current level of achievement. It also means providing structures that assist them as needed. Nothing engages students more effectively than success in solving problems that had seemed beyond their reach. In my own experience, this is one of the most challenging aspects of teaching: providing the scaffolding that facilitates success without being so prescriptive that any sense of self-agency disappears.
The fifth and final component is quality in online learning environments. Here they point to Quality Matters, a consortium of universities, publishers, course vendors, and others working to “promote and improve the quality of online education and student learning through the use of a quality assurance system and professional development.” It offers research, rubrics and standards, quality certification, professional development, and access to a community of those working to bring courses online.
Within this component, the report repeatedly emphasizes the importance of not assuming that all students know how to access the materials and use the technologies that are needed. Part of teaching in an online environment is ensuring that all students are able to access and use all of the components of the course.
The other overarching concern is efficiency. There are significant opportunities that come from moving courses online or adding online components. These include shortening the time to course or degree completion by making it possible for students to self-pace, reducing instructor effort by automating certain tasks such as the grading of routine assignments, and lowering costs by increasing the number of students in a class. This last can be dangerous. It can operate against maintaining quality. Quality is paramount. But the report argues that it is possible to maintain or increase quality as courses are redesigned to move partially or wholly online.
The report concludes with descriptions of general strategies. For each of these it includes examples, considerations for implementation, and recommended readings. These strategies include the production of course shells that reduce variability in course quality and delivery, jointly designed courses to leverage collective faculty expertise and enhance instructional quality, and outsourcing instruction to address internal capacity issues and quickly meet student needs.
This time of COVID-19 presents us with an unprecedented crisis. It would be a shame to let it go to waste.
Download the list of all past Launchings columns, dating back to 2005, with links to each column.