Are STEM Students Born or Made? The STEM student paradox

A couple of things are causing me to think again about STEM students in developmental mathematics. First, we have local data showing that over half of our pre-calculus students came from the developmental math program … about 24% start in intermediate algebra, about 23% start in beginning algebra (or math literacy), and about 5% started in a pre-algebra course. Since we no longer have the pre-algebra course, those students will now take a math literacy course (raising the 23% to about 28%).

The other event was a student in one of my intermediate algebra classes. One of the things we always do on the first day of the class is to have students record what their college program is (either on a class sheet or on an individual form). This particular student recorded her program as “religious studies”. She had taken our beginning algebra course the prior semester, so being in this class was not a surprise.

However, this week, as we talked about a test in the course she told me that she was thinking of changing her major to mathematics. Of course, we shared a “how cool is that!” moment; we then talked about what math course she would take next semester. That was a good day!

Since then, I’ve been thinking about what led to the student’s statement about changing majors. This particular class uses a “Lab” approach … class time is used for doing some of the homework, getting help, and taking tests individually. We’ve had this format for about 50 years; although the method has been through many changes, the basic concepts have remained. One of my mottoes for the method is “get out of the student’s way!” We have pass rates that are just below that of traditional ‘lecture’ classes.

My impression of this student is that she got to really like the process of working through problems on her own. If she had to listen to me lecture … or if she had to work in a group to deal with math problems … I don’t think she would have had the meaningful experience which led to a ‘change major’ state.

Here is the STEM student paradox:

A focus on getting more students through a math course can lead to conditions that never inspire students to make a commitment to a STEM major.

Now, I am not saying that continuous lecturing will inspire a student. Continuous lecturing has no defense, and can be considered educational malpractice.

The issue here is that many of the processes we are using, combined with a limited symbolic formality based on contextualizing most topics (especially in developmental mathematics), tends to create a social focus for the learning while minimizing the symbolic complexity of the problems. More students might learn the course outcomes at the cost of seldom inspiring students to select a STEM major.

Of course, like pretty much any generality, this one has plenty of exceptions. I’m talking about the directionality of math classes, not about absolute location.

I would like to have a conversation with my student to see if she can articulate a reason, or even a description of the experience that led to a change. I might get some feedback concerning my assessment, which might support the hypotheses stated her (or might not).

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Math curriculum in general | Jack Rotman | November 5, 2016 4:03 pm

7 Comments

By schremmer, November 6, 2016 @ 8:18 pm

Re. the STEM student paradox:
Come on, not a paradox at all and you know it:

A focus on getting more students through a math course must lead to conditions that never inspire students to make a commitment to a STEM major.
(My change of “can” to “must”!)

Re. Continuous lecturing. I agree of course. But “continuous activities” is terrible too. (I think you would agree.) And it is a fact that one can ad lib on an issue that just came up in class with some effect but that one cannot put it into a book: I used to think one could and wrote monsters which it then took me several years to cut down to something readable.

Re. minimizing the symbolic complexity Ah, but being able to show off one’s superb control of “symbolic complexity” makes one feel sooo superior.

Re. changing her major to mathematics Given the students’ experience of mathematics (essentially null), I am always leery of students who decide that they want to get into mathematics.
By Jack Rotman, November 7, 2016 @ 7:36 am

I wouldn’t say “leery” … that implies a risk to mathematics. I do have some worries that the student does not understand the nature of mathematics that she is going to encounter on her journey. However, starting a journey with enthusiasm might result in her finding a set of subjects that she finds worthy of a life effort.
By schremmer, November 6, 2016 @ 8:44 pm

… and, not least, re. a less formal content, I do not see how the amount of “formalism” has anything to do here. What I want my students to learn are things like coping with new concepts, recycling old concepts to fit somewhat new situations, being able to formulate questions when in doubt, being able to see how likely a particular route towards some wanted result is actually going to get us there, what “obstruction”, if any, might there be, etc, etc.

The amount of formalism is dictated by the situation being faced, the rule of thumb being “If you don’t tell me unambiguously what you are doing or want to do, how am I supposed to have any idea of what you are doing or want to do.” So, rather than a priori formalism, what is primordial is to accept rewording until the meaning is successfully conveyed. The only answer to “You know what I mean” is “No”.
By Jack Rotman, November 7, 2016 @ 7:39 am

Thanks for pointing this out … I’ve edited the post to reflect (more accurately) what the perceived problem is. Your statement about the amount of formalism seems very useful to me, and reflects my core objection to some of the latest curricular efforts which favor context over mathematics (thereby distorting the natural connections between the two).
By Eric, November 7, 2016 @ 2:59 pm

I sympathize with A. Schremmer’s leeriness viz this student’s expectations because of my own personal experience. I suspect most math majors have no idea what they’re getting themselves into, whether they start their college career in Calc I or Elementary Algebra. But even if this student decides that Analysis and Topology are not really her thing, an A.S. in math is a pretty good stepping stone to lots of other paths that an A.S. in religious studies wouldn’t prepare her for. Even if her current inspiration only gets her through Calc I, I’d call it a win.

The larger pedagogical/structural question of throughput vs. inspiration is related to short-term vs. long-term goals. It may be that focusing our administrators’ gaze on graduation rates rather than course pass rates will help. I certainly know our tutors are shooting our students in the foot every time they say “just remember, __.”, which does help students get that one exam question right but is counter-productive to their ability to learn later concepts.
By Jack Rotman, November 12, 2016 @ 3:40 pm

Good points, Eric.
I think we need to remind everybody (our colleagues, as well) is that the only goals are the long-term goals. When a system works well, the ‘short term’ goals are supportive of the long-term goals. It’s natural to think of short- and long-term as opposing forces, but that is not a professional approach. The ‘just remember’ tutoring/helping message is a bit like an MD telling a patient that it’s fine to cope with the migraine by taking a pain med: the goal is to identify the causes and work towards avoiding migraines.
By schremmer, November 19, 2016 @ 8:30 pm

I have never encouraged students “to go into mathematics”. What I occasionally do is to suggest something along the lines of “Maybe you ought to consider doing a bit more mathematics, if only to get past the point of “show and tell.” Given that I was the first of their teachers not to show and tell, some students begin indeed to think about considering my suggestion and some in fact keep on going but almost invariably with engineering in mind.

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