I feel like my MA in theoretical mathematics has given me an appreciation of
the beauty and precision of mathematics and its language. This helps
immensely in teaching all levels of mathematics. Skills, however, that a
teacher of developmental mathematics needs involve listening closely to what
students are saying and trying to determine what they hear (not what we
say). I am not sure we have developed a good way to train that skill. For
me, the best training I did for teaching developmental mathematics was a few
years I spent earning my living as a math tutor and as a musician. As a
musician, I am constantly in contact with people on a personal, social basis
who do not do well in mathematics and I hear their perspective in a way that
my students can never tell me.
As a math tutor, I learned to ask the students to verbalize their
understanding. I realized that students who do not do well at mathematics
seldom have the language to communicate mathematics or the concepts on which
to build the vocabulary. For example, we define "variable" to students who
have no concept of a variable that "a variable is a letter which represents
a number." Without the concept of a variable, that definition makes no
sense, so we get the response, "then why not just use the number instead?"
In developmental mathematics, we need to find ways to build concepts while
at the same time introducing the very sophistocated vocabulary and symbols
of mathematics. Our "drill and kill, skill, follow a recipe" model leaves
the student largely in the dark on concepts as well as mathematical
language.
Whatever credentials are adopted for hiring developmental mathematics
instructors, the interview should be carefully constructed. Here is my view
of a good interview question: "A student is asked to factor, 3x^2 + 2x - 1.
In their first step, they get (3x - 1)(x + 1), then they give a final answer
of x = 1/3 or x = -1." How would you work with a student (or class) to
understand the misconception?"
At the heart of being a good developmental instructor is the ability to
recognize misconceptions (as opposed to silly mistakes) and to guide the
student beyond the process to the concept.
Martha
-----Original Message-----
From: Dr. Frank Pecchioni <fpecchio@pop.jcc.uky.edu>
To: mathedcc@archives.math.utk.edu <mathedcc@archives.math.utk.edu>
Date: Wednesday, September 16, 1998 4:07 PM
Subject: Re: [MATHEDCC] Who should teach developmental courses?
>In response to Gideon Weinstein's recent message:
>
>>
>>In the best of all possible worlds, only those who WANT to would teach
>>developmental courses. I would certainly hope no-one who looks upon those
>>students as undeserving of being in college would be permitted to teach
them.
>>
>
>That point should go without saying -- but experience shows it needs to be
said.
>
>>
>>My reaction is a shudder and a grimace. With the awful job market, you'll
get
>>plenty of people desperate for jobs applying for the position, but how
many
>>people go for a Ph.D. in pure mathematics in order to teach such courses?
And
>>what kind of professional training and development would they have
received in
>>their doctoral program to prepare them for this kind of teaching and
>>leadership in curriculum development? CLEARLY, YOU NEED TO HIRE A PH.D.
IN
>>MATHEMATICS EDUCATION to have a real chance of getting the kind of person
who
>>would thrive in this job. They're already cognizant of many of the
>>educational issues and solutions that have been tried, and they are
already
>>trained to do the kind of education-related scholarship and professional
>>development that should be coming from someone who is immersed in a
>>developmental education program. At the very least, open the job to both
>>mathematicians and mathematics educators. I would also put in two very
>>important incentives: 1) 3 credits release each year, for curriculum
>>development and administrative duties, and 2) option to teach one calculus
(or
>>other non-developmental) course per year, for the change of pace and
feeling
>>of being less "walled off" and segregated from the other faculty.
>>
>
>There are other degrees and backgrounds that suit one for this kind of
work.
>
>While I have an MS in mathematics, my PhD is in Philosophy of Science. I
>worked mostly on formal systems and their use to codify empirical and
>mathematical theories. Most of the philosophical course work was squarely
>in the analytic tradition; that is, we relied heavily on linguistic
>analysis and sought to solve problems through 'logical reconstruction' of
>their background. We took clear expression as a sign of clear thought.
>
>While writing my dissertation, I took a job (and kept it) teaching
>developmental mathematics. It turned out that analytic philosophy was an
>excellent preparation for attacking some of the problems of developmental
>education.
>
>What developmental students need most (at least those I have taught) are
>much stronger language skills, writing and speaking as well as reading and
>listening. What developmental educators need most is clear thought and
>very careful expression. Most textbooks are poorly written, their
>explanations are hopelessly vague, and some of the problems are ambiguous.
>The field is in serious need of analysis and reconstruction.
>
>My life's work turned out to be making foundational mathematics more
>accessible to the victims of very poor educational backgrounds. The
>monetary awards have been rather slim, but the psychic rewards are
>fantastic. Academic honors have been equally slim (I was recently denied
>promotion; one objection raised against me was "he teaches [sneer]
>developmental"); but my students' appreciation for my efforts has been, as
>they say, phat.
>
>Mathematical competence, of course, is the sine qua non of a math teacher.
>There are many fields, though, with mathematically competent practitioners
>who might find the challenges of developmental math professionally
>rewarding. Off the top of my head, I would expect psychologists with an
>interest in learning theory to find in the experience a strong stimulus
>toward their own development. Developmental math would also benefit, I
>feel, from a more inclusive search for new teachers with widely differing
>backgrounds who could contribute new insights into the task we have chosen
>to perform.
>
>Road's in front o' me,
>Nothin' to do but walk.
>Langston Hughes
>
>
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