Demand Side Theory

Summary: A specific “demand side” strategy is to be used as part of a web based support infrastructure creating an enhancement of comprehension in arithmetic, algebra and set theory as well as an aid in recruitment of students into colleges. Institutions for a number of complex reasons, specifically resist comprehension-based strategy in favor of, so called, skills based strategy.

Theory: The underlying theory suggests that current educational practice fails to convey an understanding about the nature of mathematics. The theory is based on immune and cognitive mechanisms and suggests that an acquired learning disability is enforced by self-efficacy and social philosophy. Framed in the context of nature verses nurture debates, we suggest that poor performance by American students in pre-college mathematics is more consequent from how individuals are nurtured than from essential natures of these under-served populations.

Goal: Technology and pedagogical design has been under way for a number of years. The design may be prototyped and then proposed as a national infrastructure program. Critical to the next step is successful implementation in technology prototype. Primary interest is in the community college setting, and at four-year colleges.

Problem to be addressed: Many incoming freshman students have accommodated the viewpoint that mathematics is not for “them”. Our culture acknowledges a discomfort with even simple arithmetic, and often accommodates the viewpoint as arising from natural causes. In fact, this accommodation may have a great deal to due with social viewpoints reinforcing academic under-preparation for minority populations.

Target Population: Specific experience has developed regarding Native American educational systems, K-12 and colleges; Hispanic Serving Institutions, and Historically Black Colleges and Universities. In under-served communities; Native American, Hispanic and African American, the development of accommodation is expressed in specific common behavioral patterns. Equalizing effort is needed. This effort has political, sociological, pedagogical and technology dependencies.

The solution to be prototyped: A new model may replace developmental and remediation programs. Enhancement of the knowledge already understood is to be combined with student self-identification of where confusion exists due to poor past experiences. A specific "lifting strategy" would replace developmental programs. The enhancement program is demand side in the sense that the needs of the individual are to be understood and curriculum designed in the context of the individual’s known needs. The national program is to be shaped by this demand side educational theory.

The program will create new textbooks, new pedagogy and web-based support. The negative reflection by students on developmental and remedial programs is to be replaced with a positive program based on clear explanations about essential theory, notation and examples.

Over the past decade, we have studied standardization issues related to school, college and university governance and national educational policy. We use a knowledge management framework to map National Council of Teachers of Mathematics focus elements and the demand side learning theory. Recent experiences at two small rural HBCUs has sharpened our understanding of the role that under expectation plays in poor outcome metrics.

The pedagogy: The lifting pedagogy is a two-step process; engagement followed by acceleration. Engagement: Socratic and participatory pedagogy is used to help each individual construct a new view about his or her perception of a few topics, studied deeply. These topics might include: the nature of arithmetic in arbitrary bases, Boolean algebra, the concept of a function, the concept of a graph, and elementary probability. The strategy requires clear guidance to students who must understand what they know clearly and what is not understood clearly. Acceleration: The shift of a student’s viewpoint about his or her capability comes from engaging the mind in a deep way. Once this occurs, it is possible to teach the standard college materials and to do so at a deeper level of understanding.

Long-term social benefits: A web-based bridge program could, it is conjectured, address the problem of negative student self-efficacy and do so across the nation. The benefits are long term and fundamental to positive cultural transformation. The co-development of a set of standards for service support is envisioned. A specific service infrastructure supporting all aspects of education is defined. Service architecture and the lifting pedagogy are derived from a common grounding in demand side theory. This theory is seen as individual centric and relying on a more complete understanding of collaborative web environments.

Modules and platforms: The first modules we developed (1994-95 and 2007-2009) were about shifting the representation for numbers between number bases and then doing first arithmetic and then some matrix algebra; e.g., Cramer’s rule in arbitrary number bases. The arithmetic in arbitrary number bases provides one portal into a view of mathematics that is relevant to liberal arts students. This includes the concept of solution set, a plane or cross product, graphs and functions. A second module is being developed in set theory and probability. A third module is in statistics.