Mathematics as a Barrier to STEM Access-Part 2

Recently I wrote an essay about how Career Technical Education – what was once called Voc Ed – can contribute useful teaching approaches to all academic programs.? Then I wrote about how mathematics remains the major barrier to students entering STEM fields.? Let me now combine and reconcile the two thoughts.?

I emphasize to students the extraordinary usefulness of mathematics.? You can’t do science without math.? And you cannot learn the truth about the natural world without math.? It offers an extraordinary tool to separate truth from… nonsense.??

I was a math minor and considered it as a major – along with physics and engineering – so I’ve always gotten the appeal.? I loved theoretical math proofs and I especially liked the satisfaction of ending with the traditional pencil-stroke of QED.? But I recognize that not everyone does, and that that part of mathematics creates a barrier for STEM entry.? As I wrote, there is a disconnect between mathematics courses and the application of math as merely a useful tool rather than the [and read this in an ethereal tone] “the beautiful language of nature.”

In every Cell and Molecular Biology class that I’ve ever taught I began the semester by having students measure their body temperature over the course of the day (and night).? Everyone comes in a puts their data on the board and I ask the question, “does body temperature vary over the course of the day?”? There always seems to be a trend, but it is slight – is this signal or is this noise?? “Is this a real biological phenomenon or an illusion?”? I first argue that it looks like body temperature goes up during the day and drops at night.? Once I have everyone convince of it, I try to talk them out of it by arguing that the slight change looks like it’s within the uncertainties of measurement.? And then I say, “luckily we have an entire field of mathematics – statistics – that provides tools to tell you exactly this – whether this phenomenon is real.”? They graph body temperatures from the high point and the low point – the histograms pretty clearly show two different data sets.? They perform a T-test to definitively prove that this is indeed one of the most important physiological reactions in the body.? Wow - the power of statistics.? It is VERY common for a student to say, “You know, I took an entire semester of statistics in the Math department.? I could do all of the problems at the end of the Chapter.? I earned an A.? It never made sense until today.”?

Statistics is emerging as THE mathematics track that provides an alternate pathway from the algebra-trigonometry-calculus STEM pathway.? And I’m a convert to this point of view.? But…. Everytime I look at a statistics book I ask, “how many Greek letters and obscure equations do you really need in this field?”? Or alternatively I asked, “could you have muddied the delivery of these concepts or could you have made a discipline any less accessible if you had intentionally set out to design a field that you wanted to live in obscurity?”???

Math faculty do their best, but the discipline of statistics is saddled with traditional and archaic symbols,? jargon, and nomenclature.?? Again, if you set out to intentionally design an approach to an extraordinarily useful system to minimize the number of people who could understand it, you could not have done a better job – it’s as if it was designed with that purpose.?

There is a solution.

CTE programs, on the other hand, wrestle the teaching of mathematics from the mathematicians and teach it themselves in a conceptual way.? In colleges where this is tolerated by the mathematicians (and that isn’t every college), the subject area faculty teach Mathematics for Electronics, Mathematics for Water and Wastewater, or Mathematics for [fill in the blank.]. Math is taught as a tool rather than as the beautiful language of nature that everyone should inherently appreciate.? And the success rates are high and graduates know the mathematics that they need for their career.? They haven’t been exposed to mathematics that they will never use, and they frankly don’t miss it.? In biotechnology (again a CTE program) we teach laboratory calculations.? Many colleges require their post-baccalaureate students to take the course, and they require the students with earned doctorates (in biotech there’s usually one or two per semester) to take the course.? No one complains.?

After all, a carpenter does math?– and must immediately make a thousand snap calculations every day.? But not THAT math.? Water/ Wastewater programs match it to the certification tests that their workers must pass to start and to advance.?

In some colleges the discipline specific faculty have grabbed statistics.? They teach courses in “Statistics for the Social Sciences” or “Statistics for Biology” or “Statistics for Biotechnology” – these courses are much more applied, taught in the context of the needs of the discipline.? And at other schools the culture means that the Math faculty will oppose such a course out of principle – professors not trained in pure Mathematics should not teach Mathematics.? I advocate that statistics should be mandatory, but that the current approach should be discarded and it should be taught using Design of Experiments.? MiraCosta College’s Biomanufacturing Bachelors of Science degree teaches its own statistics this way and their success rate is off the charts – they have lost only two students since 2017.?

I read a paper that argued that statistics should be taught through the use of “Design of Experiments.”? I think that this is a good idea.?

This will remain a huge academic culture barrier to overcome.? The charges of “dumbing down” or “lowering the bar” will come fast and furious.?

But it isn’t.?

For years City College of San Francisco offered a very effective program called Bridge to Bioscience.? And they offered it in Hunter’s Point, one of the poorest neighborhoods in San Francisco.? This was a learning community that combined a class in laboratory techniques with a math class and an English class.? Students gathered data in the laboratory class and were sent to the math class to analyze it and then sent to the English class to learn how to write a lab report.? The contextualization led to a high success rate and a high articulation rate into their Biotech program.?

Math is a barrier to success.? And it’s a barrier to access.? It’s easy to argue that this field is THE barrier.? The question remains, is it important enough to be retained as a barrier to overcome or is it an artificial barrier?? To me the success of contextualized math approaches settles that argument in a pretty convincing way.? Again, here I think that academic courses can learn from CTE:? have the discipline faculty teach the math needed for the discipline

The two cultures are just different.? Over a decade ago one of the best Math teachers at my school approached me to say, “I’ve developed a math class specifically for Nursing majors, would you take a look at the text that I’ve devised?”? I told him, “be careful what you wish for since I live with a red pen in my hand.”? He said, “that’s OK.”? So he handed me his proposed text and I took out my red pen and bloodied every page.? Right off the bat on the first page was “identify the degree of the following polynomials” and I put a big red X through the problems and wrote “why would I, or a Nurse, need to know this?” Later on he wrote 3(10)6 and I crossed it out and wrote, “we never write it this way.? We write it 3 X 106.”?? Later I went by the bookstore to look at the final version and he hadn’t included a single one of my suggestions.? The cultures are just different.??

You really don’t need much of the math built into the requirements to succeed in multiple fields that require it. Now, I’m open to the argument that advanced math classes cultivate a math fluency that is very useful.?

Having settled that issue, let’s move on to chemistry.? How much chemistry does a biology major really need?? Oh, that’s a subject for a different time.?