op watokal

Tell me now,
Me I be Fela, I be Black Power Man
Me I be Fela, I be Black Power Man
I go bend my yansh I go shit
I go commot away from the shit
The shit go be the last thing wey I go like to see
Not be so for some fools way I know
Not be so for some stupid people I know
Not be so for some fools wey I know
People wey go like to quench your soul
People wey go like to quench your soul
Them go use your shit to put you for jail
And don tell my shit too expensive shit
My shit no exhibit, it must not cost you
And don tell my shit too expensive shit
My shit na exhibit it must not cost you

unfinished essay (2001/2 vintage)

RESEARCH SKILL DEVELOPMENT PROGRAM

KEY POINTS.

THE POINT.

This is an effort at understanding how research skills in the
mathematical sciences can be acquired by students.

WHO WE ARE.

We are students at a state-funded liberal arts college based in
Sarasota, Florida. Our school is called New College. The
emphasis of the program at New College is self-directed learning.

SELF-DIRECTED LEARNING.

Since people have free will and learn from experience, self-directed
learning could be said to take place wherever people engage in
any activity. However, this view is unfounded, and the implication
is false. Unstructured learning is more accurately undirected.
If learning is structured, say by a teacher, this does not imply
that it is self-directed, even given the free will of the learner
to participate. The choice to participate in learning is not the
same as directing the learning. Structure can impose the direction
on a (passive) learner. This does not mean that the presence of a
teacher or a system to learn implies that the student's learning
is not self-directed. The criterion we are looking for is that the
student have an active, ongoing and purposive role in deciding the
structure of his/her/its [e.g. in the case of computer programs]
learning environment. A teacher must be informed by and responsive
to the student's feedback, or the learning the student does under
that teacher's instruction is not self-directed.

INTEGRATION OF RESEARCH AND EDUCATION.

In deciding upon a course of study, it behooves the student,
as he/she/it examines a potential activity, to consider questions
such as these, with the utmost care:

* What is the intellectual merit of the proposed activity?
* Is there sufficient access to resources?
* How well-conceived and organized is the proposed activity?
* To what extent does the proposed activity suggest and
explore creative and original concepts?
* To what extent will it enhance possibilities for future work?
* What are the broader impacts of the proposed activity?
* What is the product?

If these questions are addressed well, the student will enter
upon a focused program and will have already at the beginning
devised a coherent plan for its satisfactory completion.
Furthermore, the product is likely to be a net benefit to society.
The idea of traditional education is that it is the student,
with an increased knowledge and skill base, who constitutes
the product. His/her/its knowledge and skills (upon exiting
the educational program) are valued by society, and he/she/it
is willing to put forth during the program a commensurate amount
of blood, sweat, and tears (not to mention tuition and time) to
extract the valuable knowledge and skills. In scientific fields,
one of these skills is supposed to be the ability to do research.
The idea that "the best proof of someone's research ability is
the research they have done" has played a significant role in the
way scientific education, and the scientific enterprise, has
been run in recent years. Research experience at the undergraduate
level is one of the top criteria considered by graduate programs
in science when they decide which candidates to admit. It is not
without reason, then, that national programs for undergraduate
researchers (most notably, the National Science Foundation's
Research Experiences for Undergraduates (REU) summer programs)
are highly competitive, taking only the best qualified applicants
nationwide. Many technical and land-grant universities have
internally- or industry-funded Undergraduate Research Opportunities
Programs (UROP) which offer financial awards to undergraduate
students, which enable them to collaborate with faculty on
specialized research projects in their joint field of interest,
or to do original work on their won. These programs make it
possible for students to make research a part of their background.
In particular, such programs give students a chance to see what it
is like to work on open problems (usually the problems devised
by the program administrator or principal investigator; occasionally
on questions proposed by the student researchers themselves). It
goes without saying that such experiences are typically only part
of the curriculum. The NSF's vision of integrating research and
education is to have individuals concurrently assume responsibilities
as researchers, educators, and students, where all engage in joint
efforts that infuse education with the excitement of discovery and
enrich research through the diversity of learning perspectives.
The benefits of such a system are manifold. It is however very
difficult to implement in most educational contexts. A place
like New College, where the culture already is disposed towards
student self-direction, may be unique in its ability to foster
an undergraduate scientific curriculum based primarily on research.
The questions listed at the beginning of this section are the
questions a research must answer when initiating a research program
for undergraduates. (They were lifted from the NSF's summary of how
they review REU proposals.) By pointing out here that the same
questions are the natural questions for a student to ask when
considering how to invest his/her/its time and energy, we mean
to point to the unique possibility afforded the self-directed
learner, namely: he/she/it can act as a researcher, an educator,
and a student concurretnly, and, to a degree that is possible for
very few, harmoniously.

RESEARCH AS A WAY OF LIFE (ADDITIONAL REVIEW CRITERIA SPECIFIC TO REU).

There are other criteria considered by the NSF, for example, the
qualifications of the person who proposes the research project.
This is prima facia difficult for undergraduates to fulfil
satisfactorily.

Additional criteria:

* The appropriateness and value of the educational experience for teh
student participants, particularly the appropriateness of the research
project(s) for undergraduate involvement and the nature of student
participation in these activities.

* The quality of the research environment, including the record of the
mentor(s) with undergraduate research participation, the facilities,
and the professional development opportunities.

* Appropriateness of the student recruitment and selection plan,
including plans for involving students from underrepresented groups
and from institutions with limited research opportunities.

* Quality of plans for student preparation and follow-through designed
to promote continuation of student interest and involvement in
research.

* For REU sites, effectiveness of institutional commitment and of plans
for managing the project and evaluating outcomes.

ELEMENTS OF MATHEMATICS

* sets
* logic
* algorithms
* probability
* groups
* rings
* fields
* vector spaces and linear maps
* functions
* series
* topology
* calculus and applications (ODE, PDE, differential geometry)

HELPFUL (SOME WOULD SAY NECESSARY) SUPPLEMENTS

* physical science
* writing skills
* computer skills
* some semblance of background in philosophy and/or literature

INTEGRATING DIVERSITY INTO NSF PROGRAMS, PROJECTS, AND ACTIVITIES

Broadening opportunities and enabling the participation of all
citizens -- women and men, underrepresented minorities, and
persons with disabilities -- is essential to the health
and vitality of science and engineering.