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IMPACTful Discussion/Blog - Linear Algebra

By Robert Cappetta posted 01-02-2024 21:06:59


In several discussions with members of the Math Intensive Academic Network, we have identified several challenges with the linear algebra courses taught at two-year colleges.  These include prerequisite courses, curriculum design and transfer issues.  Additionally, advances in technology provide opportunities that were previously unavailable.


Some two-year colleges require an advanced prerequisite like multivariate calculus (Parkland College, Monroe Community College), others integral calculus (College of DuPage, College of Southern Nevada, Miami Dade College), and still others differential calculus (Bucks College, Community College of Baltimore County, John A. Logan).  There is very little knowledge of calculus required to be successful in linear algebra, so there may be schools with even lesser requirements.  In an attempt to grow enrollment in linear algebra, it will be tempting to lower the prerequisite level. 


Another concern is the curriculum.  Is the course a matrix arithmetic course needed for students majoring in fields other than mathematics, should it be a concept and proof-based course designed for math majors, or should it be a course focused on applications?  Might  linear algebra for business majors be an option? Given the increased importance of fields like data science and computer science, which topics should be highlighted, and which could be de-emphasized?  Can a two-year college with relatively few advanced students offer multiple versions of the course to students with differing interests?  Of course, two-year colleges must be certain that local universities will continue to accept the course.


So, not surprisingly, the next issue is transfer.  Many schools that offer a traditional concept proof-based course have been having difficulty with transferring it to local institutions.  Universities may categorize such a course as an advanced one typically taught in the third or fourth year, thus making it unable to transfer from a two-year college.  In my experience, students trying to transfer such a course may be required to take a competency exam. 


The emerging use of technology in linear algebra provides students opportunities to examine applications that were previously not accessible.  The tools taught in this course can be used to examine many real-world problems.  Ideally good experiences in a linear algebra may encourage more students to study STEM fields, and particularly mathematics.


Sadly, many two-year colleges choose not to offer a course in linear algebra.  I hope this discussion can help us identify strategies to address some of these concerns and hopefully we can encourage more students to take linear algebra at our institutions. I invite all interested people to participate in this month’s conversation on the challenges and opportunities regarding teaching linear algebra in the two-year college.