The morning of the 17th

The morning, Friday the 17th, has produced a couple of pleasant rewards. 

In the statistic class one of the students had been deeply reading and studying the nature of data distributions, in particular the bi-nominal distribution.  Various students in various classes are at different places in their understanding of the demand side theory and the specific curriculum under study.  This student, somewhat unexpectedly, displayed a type of Eureka <*> experience in class. 



In my presentation this morning I addressed what data distributions are, how they are related to data sets and statistical studies.  I showed that each distribution had means and variances, measures of dispersion and central tendency, that creates a family of distributions.  Having introduced these very advanced concepts in a clear fashion, understood at least in the moment by all sixteen students, I started to talk about Pascal's triangle and the family of bi-nominal distributions. 

She immediately begin to respond in a clear minded fashion, talking about her understanding that the normal distribution was a limit of other distributions. I started a topical presentation on the relationship between the family of bi-nominal distributions and the normal distribution.  The student was so excited that all other students were soon drawn into a common experience.  The moments within this particular classroom experience were rich in potential and supported deep learning, largely because the experience was driven not by the professor but by the student.  She accepted the challenge of presenting a theorem on limiting distributions for next Wednesday.  Several other students also identified favorite topics that they would start to introduce to the class and then, once the topic was well defined, would develop either written or in class presentations.  Remember we are studying the entire curriculum every day, with focus driven by student demands.  The origin of discussions regarding what was going to be a "term project" was the students themselves.

This type of experience is a reminder that the demand side theory is based on what I have considered to be solid scientific evidence. The conjecture I developed, starting in 1985, was that due to poor and slow learning experiences during middle school, the great majority of all students develop an acquired learning disability.  The underlying work was published in my PhD dissertation on mathematical models of biological systems exhibiting learning (1988, University of Texas at Arlington).  The conjectured disability syndrome was both cognitive in nature and affecting one's ability to shift focus in how one sees oneself; e.g. self efficacy.  The remediation strategy was also derived from biological research literatures.  This strategy involves the use of what I now call the demand side theory of education, a theory derived from models of economic exchanges. 

Clearly, on her own she had found the textbook material on this topic interesting and worked with the relevant concepts.  Her past "acquired" discomfort with mathematics was simply absent. 

During this week my students, from the other classes, are also turning in excellent exercise sets, where each student selects ten exercises from anywhere in the text, over all chapters covered or to be covered.  This selection is for the purpose of demonstrating that individual's command of the material, and is presented in the form of a blank paper experience.  The experience occurs when the "test" is not regarded as a test, but rather a positive learning experience.  As we just passed the midterm, some students are already moving into the next semester's content. 

Now back to the social and political reality that I faced at the college. 

The Meeting at 11 AM

(see private log for longer detailed meeting minutes) <*>

The purpose of the Study on Rural College Practices, Prueitt in progress, is to examine common practices by administration and faculty and various trends in American Culture. The Study was under taken in order to bring a number of issues forward into the public light, issues dealing not only with HBCUs and Minority Serving Institutions but also all community colleges and colleges, as well of most universities. Funding is supported by a private foundation. 

My hopes were high, on this morning in October.  I had hoped that one more year of teaching would lead to a series of scholarly publications, and that I might take one more step in developing the foundational principles under which a review of national educational practice might be undertaken.  Part of these principles are derived from systems theory. 

What was to happen later this morning was surprising in the precision in which prediction based on systems theory suggests.  It appears that the college may have been passing though students even when they had not attended classes.  My efforts were bringing this fact into the light at the same time that the college was under federal funding pressure to demonstrate that graduating students had elementary understandings of college level mathematics. 

A faculty meeting may reasonably be considered typical of many and has common roots in culture and is discussed, in general terms, in the research notes for Rural College Practices.  All college and university practices provide a context for Rural College Practices.  The core problem we must consider is how to properly reveal these issues without incurring unwanted consequences. 

On the particular and the universal

The concept of universals and particulars is a vital concept in any demand side teaching activity.  Part of what is missing in the knowledge shared by text books and teachers is that knowledge from the foundations and philosophy of mathematics, in particular the nature of how natural language, sign systems and mathematics (as well as all academic disciplines) arise in the mind of one person, and as a cultural heritage. 

As I have addressed in many of my technical and scientific works, Western philosophy has focused on this question,


My students this year often are presented with class notes where the relationship between the past, the present and the future is discussed in the context of this central question.  Two purposes are served. 

The first is to bring each student's own particular experience into the moment, and to then discuss the general issues with respect to what demand side theory says about non-attendance, means to work with each other to allow a higher degree of non-attendance with students whose daily lives simply demand too much.  The second purpose is to open access for the student to the foundational concepts of elementary mathematics. 

The particular purpose draws the students and the professor into a common reality, a issue that is addressed in the "Anatomy of the 11 AM Meeting".  <*> This document is constructed as a generalization for the purpose of examining a non personal set of issues having no particular referent.  The document is designed to be about a set of "universals" drawn from many instances, not about any particular instance.  My work on quasi axiomatic theory goes into greater detail about how generalization is used in certain type of (perhaps classified) intelligence systems.  <*>

The Anatomy is thus "fictional" in nature and by design. 

The president's assertion at this meeting included:


The question is thus raised as to whether a consistent pattern exist across some class of college institutions.  The evidence is that there is such a class, and that this class includes non HBCU institutions, including many rural community colleges. 

In our work on Rural College Practices we studying one rural community college where three full courses are being offered as a series of pre-college mathematics.  This work is justified by arguments coming from accreditation agency self studies and specifically Quality Enhancement Plans (QEP), where a specific plan is developed based on making all instruction follow the least common value and being tested by multiple choice tests.  In this community college, the least qualified instructors of mathematics, those having the least amount of actual knowledge about the nature of mathematics, are forcing all instructors to develop long periods of study over very simple material tested using multiple choice tests.  The justification is that the student are not able to learn the standardized current college level algebra curriculum. 

It may also be important to bring to the public awareness that faculty from other countries are hired only when there is a statement signed that no candidates exist for this position having American citizenship.  Given the systematic exclusion of instructors who are "over-qualified", this statement is technically true.  When the majority of mathematics faculty have a temporary status, the pressure documented in the "Anatomy" becomes a source of college governance error.  But why is this error made?  How did the American educational system devolve to this state of affairs? 

In summary

The deeper issue is simply this:

A viable alternative to focusing all of the faculty's effort on studying to the standardized tests is the demand side pedagogy.  A discussion of the comparison between demand side and supply side educational theory is addressed in a number of these indexed notes <*>  including Note 9.