Mathematical Literacy and Abstraction in the 21st Century

Ed Dubinsky received his Ph.D. in mathematics from the University of Michigan in 1962 and for the next 25 years engaged in research in theoretical mathematics. In the mid‐80′s he became interested in mathematics education and has worked exclusively in the area since then. In his research, he tries to understand how a person's mind might be working when he or she tries to understand mathematical concepts at the postsecondary level. Based on this research, he has conducted large‐scale curriculum development projects in calculus, discrete mathematics, abstract algebra and cooperative learning. He has been editor or co‐editor of UME Trends, Research in Collegiate Mathematics Education, and the Journal of Computers in Mathematics and Science Teaching. He has held faculty positions at 8 universities in 5 countries on 3 continents: Fourah Bey College (Sierra Leone), University of Ghana, Tulane University, McMaster University, Polish Academy of Sciences, Clarkson University, Purdue University, and Georgia State University. Dr. Dubinsky is presently retired and consults with several universities on education matters.     

Investigations of quark fragmentation universality

We propose event cuts in deep inelastic scattering, suitable for an examination of quark fragmentation universality. We compare the current hemisphere of the Breit frame with the hemispheres in annihilation events, using Monte Carlo simulations. The agreement between the two processes is improved after the suggested event cuts are introduced. A method to study the scale evolution in the quark hemispheres using data from fixed-energy experiments is presented. This makes it possible to use the high statistics from LEP1 also at scales below the mass. We also discuss observables which are sensitive to the dynamics of regions closer to the remnant. The observables probe the relatively clean region on the current side of the hardest emission in the event, and can be used to distinguish between different assumptions about remnant effects and mechanisms for the parton evolution. Received: 3 November 1998 / Revised version: 25 January 1999 / Published online: 30 June 1999     

Meaning and Formalism in Mathematics

This essay is an exploration of possible sources (psychological, not mathematical) of mathematical ideas. After a short discussion of plationism and constructivism, there is a brief review of some suggestions for these sources that have been put forward by various researcher (including this author). These include: mental representations, deductive reasoning, metaphors, natural language, and writing computer programs.The problem is then recast in terms of the relation between meaning and formalism. On one hand, formalism can be seen as a tool for expressing meaning that is already present in an individual's mind. On the other hand, and the discussion of this point is the main contribution of this paper, it is not only possible, but a standard activity of mathematicians, to use formalism to construct meaning and this can also be a source of mathematical ideas.Although using formalism to construct meaning is a very difficult method for students to learn, it may be that this is the only route to learning large portions of mathematics at the upper high school and tertiary levels. The essay ends with an outline of a pedagogical strategy for helping students travel this route.This revised version was published online in September 2005 with corrections to the Cover Date.     

Ueber die Untersuchung von Balsamen und Harzen

Ohne Zusammenfassung     

Reduction von schwefliger S?ure zu Schwefelwasserstoff

Ohne ZusammenfassungBrünn am 2. April 1897.     

Formeln zur Berechnung bei indirecten Analysen

Ohne Zusammenfassung     

Mechanisms of catalytic biomass gasification

This paper discusses possible mechanisms for the pyrolytic reaction of biomass with steam in the presence of alkali carbonate and supported-nickel catalysts. In addition to catalyzing the carbon/steam reaction, the alkali carbonates alter the biomass pyrolysis reaction path-ways, producing gas and char at the expense of tars. Nickel catalyst, while quite effective for secondary tar and gas reactions, tend to lose activity over time; therefore, studies of these catalysts were directed toward identifying mechanisms of carbon deposition, the primary cause of catalyst deactivation.