7

The Student Experience

from *<*>

It is worth repeating what was said in the previous paragraphs. Entering freshman students have been so profoundly confused by the instruction in arithmetic that they do not know what they know. Some are prepared for a serious course in college mathematics, but most are not. The issues are not related only to linear preparation as commonly assumed, student knowledge is fractured and there is no sense of the coherence that mathematicians know about. There is no willingness to learn. The institutions at the bottom of our college and university system, as measured by the rate at which student learn academic materials, do not acknowledge the real deficit.

Repeatedly rehearsed topics and blank paper tests provides a means to establish a positive experiential grounding for individual students. When the program works, the pedagogy creates in internalization of real mathematics seen as synthesis, rather than temporary test passing skills. The re-teaching of arithmetic in a novel setting is one way to start this process of internalization. When the program has not worked, for example in the Fall 2008, we note substantial interference from administrative micro-management and from a specific social orientation. Two aspects to the social orientation are under-expectation and the fear that this under-expectation will be discovered. It is thus natural that behaviors of all those concerned are complex and often misunderstood.

By re-teaching arithmetic in bases other than ten, we have found a means to present very challenging material that does not have any pre-requisites. These challenges include adding two factions that are not in base ten, and using bases other than ten in finding the solution set for systems of linear equations. The theory was developed in the late 1980s. However, it was only last year (2007-2008) that the full methodology was used. During this academic year, more than two hundred under-prepared students were exposed to this material, and due to this experience the great majority, 85%, came to see mathematics in a new and positive light.

The full methodology could not be attempted during the Fall of 2008, due to administrative interference. Prueitt's background and proposals were carefully examined during an employment interview process. He was hired with some high expectations. However, a discomfort was expressed soon after classes started with the notion that students should separate topics in the curriculum into the two categories, not known well and known well. Prueitt, as well as the division and department chairs, were called into the academic vice president's office. The professor was scolded for using the "not" word in his publications. He was told that using the "not" word was the same as using the "N" word.

The re-teaching of arithmetic in bases other than ten was also not allowed, again because the opinion formed that it would somehow not be appropriate to identify what was not known by individual students. A few weeks later, the president came to a meeting of the mathematics faculty and accused Prueitt of "undermining the faculty", and threatened further action if there was any additional discussion about the issues. *<*>

Workshops for all students, to be based on the lifting strategy, were not allowed and were specifically forbidden, as were discussions about the strategy with other faculty. The extremity of the interference may only be understood when one knows the extent of chain of command, administrative authority typical of under-served colleges and universities.

One must remember that there is no oversight of this institutional behavior other than the college board and the accreditation agencies. The origins of this administrative behavior is cultural and may reflect some other-wise positive elements of the churches often closely affiliated with these colleges. This affiliation often justifies, in the mind of the administration, the formation of a master-slave relationship to the general faculty. The faculty are treated as children, and faculty hired and retained that allow this treatment.

The selection of this college was made with the belief that a full understanding of the theory of acquired learning disabilities as well as the principles of the lifting strategy were fully appreciated by the senior administration. This appreciation did remain at the mathematics department level and the level of the division of science and mathematics during the entire semester, and neither was given notice of the pending administrative action. The problem was at the academic vice president level, an administrator whose PhD is in music education and who is very uncomfortable with any arithmetic and algebraic concept.

The problem is cultural and perhaps completely understandable. However, the intent of the administration is to preserve as unchallenged a freshman mathematics program, producing no mathematics majors other than mathematics education majors, and a measure by CAAP standard exit tests ranking the college at 3%. 97% of all colleges scored higher on the 2008 exist tests in mathematics. This intent is not consistent with the public trust and with the expectations of students and parents who depend on this public trust. More than one of the HBCU colleges may be shown to have this particular challenge.

Before the beginning of the Spring of 2009. Prueitt was placed on involuntary administrative leave, with pay, without a hearing and without discussion, in spite of support from the chairs of mathematics and the division of science and mathematics. This was unfortunate. The issue that was an object of Prueitt's research was regarding the cultural aspects of education in the HBCU setting. These issues are extra ordinarily difficult, and in spite of careful selection by Prueitt, the administration of this HBCU utterly failed to support, and opposed in every way possible, what should have been a simple demonstration of a process carefully proto-typed.

The re-teaching of arithmetic in new bases opens the door to teaching within cultural contexts other than what might be called the mainstream. The technology described is consistent with the development of a sub-stratum generative interface language. As the sub-generative interface language is experimental we will delay a more complete discussion. *<*>

The issue now is in pedagogy and regarding curriculum and the cultural resistance by some institutions of higher learning. The abstract construction shared between the lifting strategy and the sub-stratum generative interface languages is a knowledge representation based on topic maps. The key feature to the particulars of this new curriculum is the existence of a set of methods for creating an inventory of topics known, topics that are not know or for which there is an uncomfortable feeling. This feature, e.g., topic inventories, creates the necessary personal foundation for a deep study of a few essential concepts.

The basis for the administrative leave action was fear that "what students did not know would become apparent". A system was in place that worked, with the result and 73% of entering freshman at the college graduated with degrees in four years. This asserted fact is used to recruit new students.

Students were uniformly placed into a first semester college algebra course, in spite of an average on the standard entrance exam of around 25 out of 100. This placement lead to the core issue that these classes had a mixed population, with most completely unmotivated and a few properly prepared. The eight or nine faculty were expected to pass most of these students, without proper chalk boards, without classroom supplies and without standard tutorial resources. Some investigation of the history reveals that failure to do so has regularly resulted in intimating email and notices of intent not to renew contracts. Attempts to find legal recourse are rare since these attempts place black marks on academic employment records.

Clearly a successful lifting strategy would need to differentiate and move students into class sections based on student need, as opposed to the desire by administration officials to pretend as if college algebra did not really need to be learned. At this college students learned, shortly after arrival on campus, that attendance is not required in order to pass these courses, that the president will change the grade if the professors have not conceded to the pressure by the academic vice president on faculty.

Students learned that classrooms may be disrupted based on a demand that no challenging material be presented. One student regularly stopped Professor Prueitt on campus and asked if he was going to get his "A". The professor responded that if he, the student, would attend class that this might occur. The student attended less than 20% of the classes and on the final wrote, "I did not learn anything this semester in this class, and I feel I should get an A for what I already knew before the class". The rest of the final was blank, simply blank.

In those cases where the lifting strategy has found success, the novelty of arithmetic in arbitrary bases creates an door leading to the awareness that arithmetic is both interesting and learnable. Once this awareness exists in a strong fashion, there is a possibility of shifting the self-image from one that knows that he or she cannot learn the freshman curriculum. The proper internalization of some deep part of mathematics is experienced as part of the student’s image of self. This line of reasoning leads to the essential concept of a mapping between structure and function, and this mapping creates the basis of both human intelligence and sub-stratum interface language generation. *<*>

The essential concepts in the traditional college mathematics courses include sets, the real numbers, an equation, the concept of a function and the solution set to equations and functions, as well as lines and parabolas. In addition to these concepts; the student becomes open to learning the foundations to discrete mathematics, computing and probability. All that is needed is the individual opportunity to shift deeply help viewpoints.

A strategy is necessary and a specific one is suggested by cognitive and immune theory (see Part Three). The strategy is to study what one knows, and NOT study what one does not know. The reason this strategy works is due to the acquired learning disability itself *<*>. Because of the nature of this disability, our students react to standardized material by becoming confused. The reaction is frustration and even anger.

The lifting strategy is common sense. Rehearsing what one knows is time-on-task, and time-on-task improves overall outcomes. The topic mapping strategy also has a specific effect related to the development of new viewpoints. By not studying things that are not understood, new orientations can be produced whereby the self-efficacy shifts. Then, and only then, is the student in a position to take advantage of the more advanced teaching methods. The strategy is constructivist in nature and can thus be described in the language used by the leading schools in educational thought.

The topic inventory strategy may be re-enforced using technology that supports facebook and other collaborative Internet and cell phone programs. In a quality college or university, student led collaboration sessions can lead to student collaboration outside of class.

It is not only the individual that has adopted specific efficacy. The situation can be clearly seen in this way. Students are so uncomfortable studying the traditional mathematics curriculum in the traditional way that their ability to perform is impacted. Only by relieving all of the students in a class, or even on a campus, of a fear of failure will the learning process be legitimized. In the academic year 2007-2008 this result was achieved, in the fall semester of 2008 this result was not achieved. The social structure is strong enough to hold all students to old expected behaviors, unless there is a consistent re-programming of expectations. *<*>

This is not to say that expectations are to be lowered. The opposite is true. The shift in pedagogy and curriculum comes to be seen by the student population, as a whole, as deserving of the considerable effort, e.g. positive time on task, that students must make. Once the shift has occurred, a new dynamic takes over where individual students begin to really excel in the standard curriculums.