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Changing perspectives: Reframing Mathematics for Life Sciences Students

Alan Garfinkel

Professor Alan Garfinkel

David Geffen School of Medicine, UCLA

In this interview Alan Garfinkel talks about the motivation behind his different approach to teaching calculus to biology students, along with the impact his course, book and accompanying videos have had on UCLA’s Life Sciences students. We also asked him how he is adapting to new teaching practices, what kind of results these are delivering, and how he wants to continue to change the way math is taught to make it more relevant, practical and enjoyable for students of other subjects. 

Read about Professor Garfinkel

Alan Garfinkel is Professor at the David Geffen School of Medicine, UCLA, where he studies cardiac arrhythmias from the point of view of nonlinear dynamics, and pattern formation in physiology and pathophysiology. In 2013, Professor Garfinkel was approached about changing the way mathematics was taught to students of Life Sciences at UCLA, with the aim of more closely applying it to the diverse range of biological systems.  He designed a specialised curriculum  - Mathematics for Life Sciences - to help his students better understand the dynamics of biological systems. Garfinkel’s curriculum had been running for four years at UCLA, with consistent year-on-year improvement in results, when his book: Modeling Life was published.

One of the aims of this textbook was to expand on the course material Professor Garfinkel had developed and rolled out at UCLA, and inspire broader adoption of this new approach. He wanted to give his own students (and those studying life sciences at other institutions) a practical tool to help them master and apply the mathematical foundations needed to develop models of dynamical processes in physiology and ecology. Using examples from neural, ecological and immune system dynamics, Modeling Life applies math to show how complex feedback relationships and counter-intuitive responses are common in systems found in nature. UCLA has seen a positive response from students of Garfinkel’s course, with 1600 successfully completing it in 2018. And engagement has been further boosted by a series of videos based on several chapters in the book. To date, chapter downloads of the eBook have exceeded 450,000.

Various professional bodies have made recommendations about training for students in the biomedical sciences. How does Modeling Life bring mathematics and the life sciences together to meet these guidelines for best practice?

“In 2009, two of the most prominent US medical institutions, HHMI (Howard Hughes Medical Institute) and AAMC (Association of American Medical Colleges) defined a new list of standard ‘undergraduate competencies’ required for future physicians. ‘Quantifying and interpreting changes in dynamical systems’ was at the top of this list. Two years later, the NSF and AAAS reinforced this, stating: “Studying biological dynamics requires a greater emphasis on modeling, computation, and data analysis tools.” At that time however, this list of competencies - which included knowledge of dynamic modeling of neural networks and ecological systems - was untouched by traditional freshmen calculus courses.” 

“Up until 2013, mathematics curricula - both at UCLA and across the US – were relatively  disconnected from Life Sciences programs, which meant that biology and medical students often struggled to apply the math they learnt from traditional calculus courses to their primary disciplines. We really needed to find a way of making Life Sciences students more comfortable and confident with the math content in their courses. Mathematics is an essential element of any life sciences program but, when taught in abstract, it loses its significance for undergraduate students, which has a knock-on effect on overall success rates. So at UCLA, we wanted to come up with a workable proposal for an integrated, applied mathematics curriculum that would better support our Life Sciences students during their course, and beyond into their professional lives. In 2018, just a few years on from the launch of the program, 1600 students completed the course with impressive results. During that time, I have talked to several institutions throughout the US about our course at UCLA and the organisational and teaching changes needed to successfully implement it.”    

Could you describe the impact your textbook Modeling Life has had on student behavior and achievement? How have you seen life sciences students attitudes towards mathematics change in this time?

“By the time Modeling Life was published, the Life Sciences Mathematics course (LS30A) had been running at UCLA for four years and it was this curriculum that really defined the structure and content of the book. The results we were seeing by that point were pretty remarkable. The level of engagement with Math from Biology students before and after the course were reflected in grade distributions. When compared with students of the traditional Math calculus course (Math 3A), we saw a stark difference in performance from the LS30A students who were earning an A or A+ in Physics at twice the rate of Math 3 students. The structure and content of LS30A was not only impacting performance in Life Sciences, it was also positively impacting students of related subject areas such as Physics and Chemistry. The difference stemmed from how we were teaching math to these same students - as an integral part of biological systems, rather than in abstract.

What we wanted to do with this course, and later with the book, was to carefully design and weave in a mathematics curriculum to the fabric of a biology course so that two subjects were no longer taught in isolation. What this achieved was shifting the perception of biology students in relation to mathematics. Amongst some of the outcomes we measured were: 

  • A supermajority of LS30 students (75% of science students and 80% of math students) felt that the course increased their confidence in their math and science abilities.
  • After completing LS30, 94% of the students saw the relevance of the course.
  • 67% of students who completed LS30 strongly agreed with the statement: “I saw the real-life application or relevance of what I learned”. 

The book, Modeling Life, was inspired by the LS30 curriculum, but also solidified it as an established method of teaching math to Life Sciences students at UCLA and beyond. The book and the course work in combination with one another, and have also paved the way for another teaching tool – recorded video tutorials - that we’re seeing increase student engagement even more.”

Which institutions and mathematics programs have shown interest in the book since its publication?

“The publication of Modeling Life has led to wider exposure of the Life Sciences Mathematics course, which is now being taught in the Math departments at Cornell University, University of Arizona and is being developed at the University of California, Santa Cruz. At least two Math vice-chairs have said: “we don’t want to be left behind”, so I have been visiting campuses and working  with them to implement it.

By starting with some of the most fundamental applications of math in subjects like Biology, we have been able to encourage teaching staff in other departments at UCLA, and beyond, to include applied math content in their courses. For there to be a sea change in this area it’s important to have teaching resources that support a fully integrated, interdisciplinary approach. The book offers instructors in both math and life sciences departments an opportunity to bring this approach to their classrooms. 

And responsibility for this new way of teaching math shouldn’t start and end with universities. I want to see this change taking hold earlier in education, and I’ve given a number of lectures on the subject at High Schools. Progress is very much in its infancy at this stage of education, with many students still locked into the calculus system. There’s a long way to go to make applied mathematics more relevant throughout the broader education system and that is what Modeling Life and the Life Sciences Mathematics course have been designed to support.”

How are you seeing students interact with Modeling Life in print and online and what role has SpringerLink played in this?

“There have been over 440,000 chapter downloads since the book was first made available for download on SpringerLink - equating to around 63,000 downloads of the whole book - so it’s clear that online accessibility of the title has been extremely important to students and teaching staff both at UCLA, and more broadly. 

The chapters in Modeling Life mirror the modules designed for the original course. Not long after the publication of the book I was having conversations with other academics and teaching and learning professionals about the continued effectiveness of a traditional lecture format. Out of those discussions came the suggestion that I experiment with new styles of teaching, including the flipped classroom model. I agreed to try this out and the series of videos we’d produced as an additional teaching aid seemed to be the ideal way of facilitating that. 
We ran a pilot where, for the first few weeks of the course, students watched the videos prior to class and came ready to discuss them. The content of the video and their analysis of it was what formed the basis of each session. This experiment began last fall and I was amazed by the results. Engagement with the videos by students was much higher than I had expected, and it’s transformed my perception of this style of teaching. What we’ve found is that by asking students to assimilate video content prior to class and discuss it during class, they are building and solidifying knowledge in this area more effectively than listening to a lecture for an hour (and referring to the book afterwards). We’re working on more videos this summer to support chapters 3, 4 and 5 of Modeling Life and we’ll be incorporating these into next year’s course. All of the videos we’ve produced so far are publicly available and can be freely used by other institutions who are looking to integrate mathematics modules with Life Sciences courses.” 

How do you see teaching practices in the Life Sciences evolving over the next 5-10 years, and what are your priorities as an academic and teacher in this field?

“Since running the flipped classroom pilot, I’m a firm believer in the benefits of this model for Life Sciences students and the impact it can have on their learning. The pilot really came about by chance, but I’m now considering developing a flipped version of the entire course, taking the structure and results of the pilot as a basis. It’s really encouraging to hear that University of California, Santa Cruz is piloting the Life Sciences Mathematics course and that others are planning to follow in their footsteps. The flipped version of the course, combined with the videos and book, make it possible to expand and replicate this style of teaching across the US and beyond.”

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