What Mathematicians Do in Collaboration

Okay, the subject for this post is just a hint about the content; don’t expect news of a large-scale project involving multiple R1 institutions.  I’m talking about a very specific collaboration in a small zone within our work.  Namely … dealing with frustrating flaws in student reasoning in mathematics.

So, here is the context … After a recent test, I felt a need for the stress relief (aka “therapy”) due to a specific flaw in reasoning which was seen from a number of students in the class.  The particular problem begins with a context dealing with the terminal velocity of a falling object.  The problem provides a formula, which (upon substitution of values) leads to this equation:

30 =  √(64h)        [30 equals the square root of 64h]

Our office area includes several collaboration spaces, and one of them is adjacent to my office.  In that space, I posted this (as part of my stress relief):

I was disturbed by the number of students who lost their algebraic reasoning when dealing with radical equations, and decided that eliminating a coefficient was best done by subtraction (perhaps just because the result is ‘nicer’ than the correct process).

A couple of days later, one of my colleagues (who has not yet confessed) posted this response:

Of course, my first reaction involved two components.  First, that’s creative … why didn’t I think of that?  Second, this is hilarious but probably not the reasoning my students had in mind.

Adjacent to this, the “perpetrator” posted this rationale for declaring “yes! … mod 73”.

I’m still bothered by the students’ use of the ’22’ step (and they heard about that in class the next day).  However, my colleagues contribution did help me by showing a role for creativity and humor among mathematicians.

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Algebra Lament

Woe, my name is algebra.

I help people communicate about important relationships; people use me to predict future conditions.

Woe, my name is algebra.

I have been shunned and made fun of.  The fault is not mine; no, the fault is almost entirely that of ‘algebra courses’ taught without a focus on understanding, without attention to communication about the world.  The quadratic formula is not my fault!!

Woe, my name is algebra.

People think that I am another name for right answers to meaningless questions, that I am the effort to emulate some perfect series of steps to solve those meaningless questions.  I am not some worthless set of dance steps, steps being marketed in the absence of music or creativity.  Just because I can’t carry a tune doesn’t mean that I lack creativity!

Woe, my name is algebra.

I am the written language to communicate about matters quantitative.  Rejecting me is the rejection of the basic goals of education in the modern era.  For, how can people understand the world when all they can do is vaguely describe the qualitative traits … or calculate values for a few specific cases?  I may have faults, but ‘lack of clarity’ is not one of them!

Woe, my name is algebra.

My properties allow people to transition from a sum to a product, and to discover the almost magical explosion of options for working with expressions.  My properties allow people to express functions of variables in ways which uncover critical features of the relationships.  Instead of this beauty, most people are told that overly complicated trivial work is ‘algebra’.

Woe, my name is algebra.

I live in the core of science and society, despised solely for the company I’ve kept.  Did I have any say in that company?  Is it my fault that school mathematics is often taught in poor ways and with ‘outcomes’ which add no value for the learner?

Woe, my name is algebra.

My reputation has been ruined by others.  I am like a poor citizen who needs to be represented by public defenders who do not see my value.  The public defenders have good intentions about our students, but represent me in such a negative fashion that the majority of students conclude that I am worthless … and that they (the students) can never understand me.  My remote cousin with a similar name, ‘linear algebra’, has much better respect and cred.

Woe, my name is algebra.

I have been placed in two boxes.  One box is labeled “use only enough to get an answer”, perhaps to questions students might care about.  The other box is labeled “recipes for right answers to artificial questions”.  Does anybody put geometry in these boxes?  Does anybody put statistics in these boxes?  I can tell you that I seldom have any company in these boxes, and never for very long.  Let me out of the box!!

Woe, my name is algebra.

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“Mathematica Rex” — Present on YOUR Campus??

One of the items I read recently is called “A Field Guide to American Higher-Ed Reformers”, by Steven Ward.  See http://chronicle.com/blogs/conversation/2015/04/06/a-field-guide-to-american-higher-ed-reformers

This is a humorous (to me!!) catalog of current players in higher education and reform efforts.  One of the entries — ‘mathematica rex’ — was especially interesting, given the title.  The people with this ‘label’ are “Technocratic education managers and administrators”; in other words, administrators who depend upon technology and data even when such tools are not supported by understanding and vision.  I have some members of this species on my campus now, and perhaps you do as well.

You might read this field guide for humor, as I did.  You might also read it with an eye for identifying the most dangerous of the species.  I find it difficult to say which of two species is the more dangerous: Benevolentia disrumpo or Pecunia cogitans.

By the way, most of the people who read (or write) blogs like this are on the field guide.

Enjoy!

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Best Wrong Answer Ever!! How to not graph a function

I never laugh at a student, though I often try to laugh with a student.

Today, we had our first test in our intermediate algebra class.  In this class, I like to extend the very simplistic work the textbook does with graphing functions; we cover this in class, and students have a small set of practice problems.

Well, on one student’s test, I see this:

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