Demand Side Learning

The lifting strategy is a comprehension program

Friday Oct 24th, 2008

The demand side theory suggests that a focus on comprehension rather that a focus on skill is necessary and sufficient.

It is easy to see that under prepared students have a deficit in background, and an active resentment about the nature of mathematics, as perceived by the students. <*> A result of this observation is a judgment that the many standardized remedial and developmental programs are not designed to address the actual problem that almost all students have on entering college. The actual problem is that they have gone tired of studying for skills based test over subjects that they culturally feel is not relevant to them personally or to those in their cultural status.

How has this deficit come about, and how is it maintained?

The central cause of the crisis in mathematics education may be the reliance on working and reworking exercises, without motivation and when no comprehension of the fundamental of mathematical reasoning. The over use of remediation is coupled with cultural indoctrination that methodologically removes a sense of empowerment. Under served students come to expect the same that is expected from them.

The current educational systems largely supports skill based, classroom and textbook, instruction where comprehension is often absent in most or all senses. It may be suggested that most K-12 teachers do not have the level of comprehension about the foundations of set theory, arithmetic and algebra thought to be necessary to conduct lifting strategy instruction. <*> This deficit is a result of specialized coursework in "mathematics education" that replaces core mathematics courses like topology, real analysis and abstract algebra. The result of K-12 instruction is conjectured by Prueitt to result in an acquired learning disability, a disability that may be removed using the lifting pedagogy. Once the disability is acquired, textbooks, no matter how large and how organized and illustrated, do not convey human type comprehension.

These two issues, the quality of teachers and textbooks, are important but less important that the contrast between demand side verses supply side approaches.

The two approaches are fundamentally inconsistent with each other. <*>

The movement to "technology" to address the crisis in mathematics and science education is also questioned based on demand side theory. Simply put, in spite of many iterations on software based tutoring systems, these systems are unlikely to ever engage unwilling students in comprehension based inquiry. The argument involves a discussion about the difference between natural intelligence and the behavior of a computer program. Yes, if handled well computer programs may help as refresher exercises, but comprehension involves the placement of the self into the topic and for most under served students this placement is contrary to cultural programing.

A review of the current literature shows that current incoming freshman students are not willing to learn the standard college algebra curriculums. A human touch is needed, a nurturing touch such as exists as some colleges.

However, if students are deeply uncomfortable with college algebra curriculum it is not nurturing to demand of all students to endure one more round of what they often see as abuse. The lifting strategy focus on fundamental topics like set theory and the beginnings of probability, as well as foundations of arithmetics seen deeply when studied in a base other than base ten. Once the learning disability is lifted, the standard curriculum may be learned far more easier.

So what is demand side theory, and why might demand side thinking explain the, partial, failure of technology and other failures in educational reform? I say "partial" because there are positive uses of computer technology in mathematics and science education. The point is that refocusing from skills to comprehension is not one of these uses.

One of the basic assertions of supply side theory is that comprehension arises from the repetition of skills. However, it is clearly observed that long term comprehension does not generally arise from the repetitive practice of skills. This observation is consistent with the assertion that supply side fails in educational theory, in a fashion similar to how pure supply side fails in economic theory.

The consequences of fundamentally changing the focus of mathematics training from skills to comprehension based, is discussed in the other foundational works on the lifting strategy. The point being made here is that the lifting strategy is NOT a remedial program or a developmental program in the classical sense.

The curriculum used last year was an advanced study of arithmetic in number bases other than ten, set theory and the properties of abstract algebra. This curriculum may be mastered in four weeks. A sample of this curriculum is at the link <*>