More stats, less calc

Standard

The times have changed, and our curriculum is not keeping up.

In the various majors offered by our Department of Biology, I’m convinced we’re not providing our students the most useful set of quantitative skills. After browsing the catalogs of a variety of other universities, I think we’re not alone.

Our curriculum has shortcomings when it comes to statistics, experimental design, and data visualization, interpretation, and management. I would guess that most of our faculty teaching upper division undergraduate courses would say that that things would be a lot better if our lower division students were provided with more opportunities to increase statistical, experimental, and data literacy.

We can’t add more units to our major, because reasons*. To add coursework related to data literacy, we’d have to cut something. I’d be all up for cutting calculus.

Our majors need to complete a semester of calculus, and some take it in semester right before they graduate. They also need to complete a year of physics, though nearly everybody takes the physics sequence without a calculus prerequisite. So, even though they need calculus to get a B.S. in Biology, they aren’t expected to apply it to anything in biology. I’m betting that most students aren’t using calculus much after they graduate.

I think it’s fair to say that, after graduation, many of our students would be using statistical and data science skills up the wazoo. With calculus, for a lot of them, not so much.

The irony here is that all of our majors do take a required course in statistics, taught by the math department. I am sure the students in this class are learning statistical theory and are getting three units’ worth of education out of the experience. Though in our biology curriculum, using this class as a prerequisite doesn’t change how we can teach our upper division courses. We’ve discussed collaborating with the math department to make sure that this course meets the needs of our students better (including, perhaps, sections designed just for our majors). However, I don’t think a single 3-unit class is going to give our majors all of the data science skills that they should be getting to go with a bachelor’s degree nowadays. We’ve got to do a lot more. (We have been having these discussions, but since I’m away on sabbatical, for all I know things are already happening, I’m just making a point to not pay attention. Whatever we do, it shouldn’t come without deliberative planning.)

I don’t want to jump on a “everybody must code!” bandwagon, but if I had to choose between requiring students to know basic differential and integral calculus, and being familiar with statistics and familiarity with (say) R, I vote for the latter. I do think that understanding calculus is fundamental to a contemporary understanding of how the natural world works. But I think understanding statistics is even more fundamental.

Has your department upped its game with data science? If so, how much of it is in your own department, how much of it involves courses/faculty from math or computer science? Did this come at a cost to other parts of the curriculum, and if so, which parts?

Update 28 March 2017: One year ago, I read and enjoyed a post by Stephen Heard, on nearly the same topic. It was so good, it was absorbed into my subconscious, so much that I was compelled to write this here blog post. But he said it first, and I think might have said it better. (After all, he did write a book on writing.) He had to point this out in the comments here, which shouldn’t have been necessary! I’m sorry, Steve.


*(We used to require an introductory computer science class, but when the chancellor’s office was asking departments to shed units from their majors, we removed this one. (It might sound like a loss, but students didn’t noticeably emerge from the course with new skills.)

19 thoughts on “More stats, less calc

  1. I wish there had been more stats and programming during my undergraduate degree , but I can also see lots of positive change in terms of stats curriculum development at the University of Edinburgh since I graduated (last year, so not that long ago). In addition to stats and programming being taught earlier on in the programme, myself and a few PhDs and PIs have started Coding Club, where we organise weekly workshops on data vis, version control, data management, efficient data manipulation, modelling, etc. We invite undergrads, postgrads and academic staff to attend, there is no obligation to come to all workshops, and in general we are trying to make things more fun and relaxed. The workshops are lead by myself, another recent graduate, and PhD students. I’ve loved teaching stats and R coding, and it’s so great to see people become more confident in quantitative analysis. We are also posting all the workshop materials online https://ourcodingclub.github.io/
    It’s all a work in progress and those of us are all still very much learning (I’m starting my PhD in Sept), but so far our initiative has been a success. So perhaps if there is no “room” for more stats and programming in the formal curriculum, there could be other ways to gain those skills.

  2. Steve, I’m sorry I didn’t link to your post! I now do recall this (and probably why I wrote this, subconsciously).

  3. We have largely pre-med aspiring biology majors and calculus is needed for the MCAT and perhaps other professional aptitude tests. So…we keep it required

  4. Andrea, that’s probably a common reason. One of our majors targets this audience.
    Although now the new MCAT requires biochemistry, I heard, and I don’t think people are changing majors to require biochem?

  5. Oh, interesting.

    I have no data on this beyond my own experience in learning + teaching, and since my undergraduate degree was a double-major in math and evolutionary biology, I’m, like, straight-up the wrong person to ask. So mostly I’m commenting to say “+1 for starting/continuing this conversation, I’d love to hear others’ thoughts.”

    But that disclaimer aside, I think that not knowing calculus closes a lot of doors, in a way that lacking few other skills does. You say that most of your students take a physics course that doesn’t require calculus, but I…don’t really get how one can understand physics without a basic understanding of calculus. (Also, for that matter, microeconomics.) One can’t get very far in statistics without calculus, nevermind ecological modelling. I did my PhD in the UK, where calculus isn’t part of the undergraduate biological curriculum; one of my year-mates had to teach himself some linear algebra for his research, and trying to teach yourself linear algebra without calculus is, it turns out, incredibly difficult. Also, from watching my British peers struggle, it seems that it’s much harder to teach oneself calculus than it is to teach oneself to code, or about ichthyology, or otherwise making up some deficit in one’s undergraduate education.

    Between a semester of stats and a semester of calculus, I’d go for the semester of stats, no question. But maybe there’s another trade-off? My evolutionary biology degree technically required a year of physics and a year and a half of chemistry (plus lab) — are those really more relevant to your typical ecologist/evo-biologist than a really good data science class? Perhaps flexibility, rather than prescriptivism, is the key? I’d love to see that conversation.

  6. I’m with Catherine. Statistics needs calculus. Most p-values are actually integrals, right? Perhaps there could be a midway point, where you learn just the calculus that is important for statistics, but I think if you are going to prioritize quantitative skills, it should not be at the expense of other quantitative skills.

    I’ve noticed a big trend for a version of “data science” which is really just running a lot of software packages without much insight into the statistics. I’m not sure the demand for those skills is going to be as big long-term as people are hyping right now.

  7. Excellent post highlighting one of the central curricular issues we are facing in biology. The field has become so diverse that there is really not a “core” of additional science courses that makes sense for all of our majors.

    I am really intrigued by the “flexibility” criteria that Catherine mentions above. Rather than 2 physics, 3 chem, 1 calc, and 1 stats, how about 7 courses from a menu of courses outside the department (maybe in two different fields?) that supports the particular pathway of the student in biology?

    In terms of trade-offs – what about trading stats at the expense of physics rather than calculus? What does no-calc physics do for biology majors other than MCAT prep? Don’t get me wrong – I love physics, but to me calc might be more essential for biologists if we have to make a simple either-or choice.

  8. I completely agree that we need more statistics training. While calculus underlies statistics, being able to use statistics in practice does not require a deep knowledge of calculus. Students would be better off being proficient at choosing the right tests, understanding assumptions/limitations, designing robust experiments, and being able to interpret the biology behind results. I believe this would help students better understand and conduct good science.

    I would like to see more emphasis on data visualization. This is a step that so many students do not do. Ben Bolker made this point in a a great interview https://cesess.wordpress.com/2015/08/03/on-the-appropriate-use-of-statistics-in-ecology-an-interview-with-ben-bolker/

    We even noted that a grounding in probability theory is not all that necessary for using statistics.

  9. Semi-related: a suggested math curriculum for ecologists, very different than (though overlapping a bit with) the usual calculus sequence:

    https://dynamicecology.wordpress.com/2014/10/20/what-math-should-ecologists-teach/

    I agree that more stats and coding would be more useful to most ecology students than the usual calculus sequence. And I think the same is true for biology students more broadly. But would it be more useful than the math curriculum suggested in the linked post? That’s debatable, I think. Thoughts?

    Also, well done Terry for not just saying that biology students should learn more stats/coding, but also saying what they should learn less of to free up time for them to learn more stats/coding. It really bugs me when people say that ecologists (or any group of students) should learn more of X without saying what should be chucked to free up time for more of X. Online discussions of curricula are the ultimate illustration that everybody wants to go to heaven but nobody wants to die.

    https://dynamicecology.wordpress.com/2014/10/08/what-should-ecologists-learn-less-of/

    In an old poll I asked readers what ecology students (as opposed to biology students more broadly) should learn more of, and less of. The most popular option for what ecologists should learn more of was stats/coding, though it only got a plurality of the votes. Opinion on what ecologists should learn less of were widely split. The most popular options for what they should learn less of were physics/chemistry, the wimpy cop-out “it depends”, and “other” (which was the option that you had to choose if you wanted ecologists to learn less calculus). There were also lots of votes for various things that ecologists probably aren’t actually spending any time learning in the first place. Once again illustrating that everybody wants to go to heaven but nobody wants to die when it comes to curriculum reform.

    https://dynamicecology.wordpress.com/2014/10/09/poll-results-what-should-ecologists-learn-less-of/

  10. It’s odd to think Sputnik is responsible for so much of our curriculum, but the same quandary exists in quantitative groundwater science: stick with cold-war-style calculus-based deterministic models (PDEs)? Or use a probabilistic method? The first is still popular, but estimating uncertainty is possible in modern methods, and almost always more useful. I like Stephan Heard’s descriptions!

  11. Hi Terry,

    Thank you for the article.

    I am in my second year of a four year Science/Arts double degree at Monash University (Australia), majoring in Physiology and Journalism. I am currently enrolled in a first year ‘Statistical Methods for Science’ unit. Monash offers several options to ‘tick off’ the maths requirement for science students and this subject is the second level up I think, for students who have completed medium to higher difficulty maths in high school.

    I must say I am enjoying it more than I thought I would! It covers useful topics such as regression, distributions, inference, hypothesis tests, chi-squared tests and ANOVA, all under the watchful eyes of the scientific method. We don’t use R or any such programs (although I would like to try them) – just good old Excel and the Data Analysis add-on.

    Anyway, just thought I would add in my thoughts as a student.

    Best Wishes,

    David

  12. Hi Terry,

    Here at Carleton University in Biology, we just made this kind of a switch by introducing a brand new mandatory introductory course in experimental design and statistics for biologists (that I will be teaching in the fall), and making room for this using the “flexibility” criteria that Catherine mentioned, requiring a minumum courses from a menu of sciency courses outside the department. Our switch is just underway, and we will see how the first class succeeds as they move through the program over the next few years. Our switch met with some resistance, but not as much as I had thought it might.

    We put this new introductory statistics and experimental design course in place by relaxing our requirements for some of the other sciency courses. Students now have a choice to take courses between a wide array of sciency subjects such as math, computer science, physics, etc.

  13. Ditto – here @ Tufts Biology we also switched to a more flexible quantitative requirement including but not limited to calculus – it also includes bioinformatics & statistics. In a visionary move two decades ago, Tufts hired me to teach undergraduate Biology majors introductory statistics & experimental design.

    It’s been a popular course not just for pre-meds (inclusion of statistics on the new MCAT promises to make this even more so), but also for our many students doing independent research projects in our labs.

  14. Interesting thoughts from everyone. While I see the argument in favour, being a quantitative ecologist who wishes he knew more calculus, I have a different view. For starters, it seems odd to me to drop one of the foundations of a skill set and discipline in an attempt to teach more of that discipline, calculus of course being “integral” to stats (sorry about that). I also think it’s risky to drop calculus in favour of more stats because that encourages an approach to stats as data analysis only rather than, what I see as more useful in ecology, as a tool for modelling.

    Really good science and experimental design often means you can use fairly straightforward stats techniques that don’t require a deep understanding of calculus. That’s the ideal in my view – I’m not an advocate for fancy methods for their own sake. If you can design your research question and data collection so that comparatively simple stats are all that is required, that’s ideal. But for observational studies that are so common, crunching numbers via t-tests, basic linear models and GLMS etc, will only get you so far. If you want to quantify multiple processes that might influence your response variable, more complex models can become necessary and using and interpreting them is really helped by knowing a bit of calculus – particularly if you need to do some of your own programming to make things work.

    We can learn by rote (in this situation use this type of model), but the deeper we understand maths and in particular, calculus, the better we will be able to apply and interpret research results I think.

  15. If I had to do it all over again as an undergrad, I would have ABSOLUTELY chosen less calculus and more statistics.

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