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It’s Just Math: Research on Students’ Understanding of Chemistry and Mathematics

“Inadequate experience in mathematics is the greatest single handicap in the progress of chemistry in America” 1 – Dr. Farrington Daniels

The ability of students to transfer and meaningfully apply their mathematical knowledge in chemistry has been a concern in undergraduate chemistry for decades, as Dr. Farrington Daniels pointed out in 1929 1. One might ask, how did we get here and why did Daniels frame the lack of experience and knowledge of mathematics in this way?

The transformative rise of American science can be traced back to the decades between 1880–1930 2. Although different science fields grew and matured at different rates and under different influences, our focus will be on chemistry and mathematics. American chemists during these decades relied heavily on laboratory measurements and experiments and de-emphasized areas that were considered to be theoretical in nature that required an adept understanding of mathematics. Thus, at that time, the United States was a nation with more experimentalists than theorists. As Servos noted for chemists and educators, laboratory instruction was surrounded with a “special mystique”2.

“For many of them the laboratory was, first and foremost, a place to mold character, to inculcate in young men the virtues of honesty, perseverance, and fidelity in the little things, and to instill respect for painstaking manual labor”2 – J. W. Servos

Thus, there was a privileged position given to experimentalists who made their discoveries by laboring in the laboratory versus those who might discern how nature worked by using mathematical models to probe and reveal its secrets.That norm in American science scraped against the theories that had been developed by the 1880s to describe thermodynamics, electricity, and magnetism, all of which required an understanding of differential equations 3, 4, 5. By the early 1900s, kinetic molecular theory and statistical thermodynamics required more mathematical prowess. The early decades of the 20th century saw the development of quantum theory, and with it, a host of mathematical formalisms required to understand, explain, and predict how atoms and molecules behaved. Servos notes the educational systems in particular in Germany and France emphasized engagement in mathematics in what Americans would consider secondary school, undergraduate, and graduate programs 2. To the detriment of the growth of theoretical understandings of chemistry and physics, American school systems at the secondary, undergraduate, and graduate level simply did not provide the same level of rigorous preparation in mathematics.

For example, the Harvard University Catalogue in 1900 for the Lawrence Scientific School and Harvard College describes elementary studies in algebra through quadratic equations and plane geometry, and courses at the advanced level included logarithms and trigonometry, solid geometry, analytic geometry, and advanced algebra6). The requirement for advance study in chemistry was a course of at least 60 experiments performed at the school. There was no coursework in calculus at Harvard at that time, and calculus was not a requirement for chemistry majors at a majority of U.S. institutions in the early 20th century.

Two more examples by way of the career trajectories of prominent chemists serve to illustrate the standards in American universities. Nobel laureate Irving Langmuir received his undergraduate degree in metallurgy from the Columbia School of Mines in 1903 and went to Göttingen to study physical chemistry2. In letters to his family, he described his classroom experiences and frustration at his inability to meet the mathematical expectations of the coursework. He dropped a course in mechanics and theoretical physics at the midway point due to the challenging level of mathematics. He began work in Nernst’s laboratory on physical properties of electrolytes but was removed from the project due to his inadequate mathematical preparation 2.

Langmuir later won the Nobel Prize in 1932 for his discoveries and investigations in surface chemistry7, and he mastered a great deal of mathematics that was applied to his research endeavors. However, Servos notes that Langmuir preferred to work on problems guided by visual analysis and models that were more concrete in nature and not entirely mathematically based2.

Farrington Daniels, the author of our first quote, supplies another example. Daniels was a physical chemist who was a pioneer in kinetics and solar energy research. He was a leading chemical educator and received the 1957 James Flack Norris Award for Outstanding Achievement in Teaching Chemistry for his impact on undergraduate physical chemistry instruction via his publications, presentations, and textbooks8.

References

  1. Daniels F. Mathematical Requirements for Physical Chemistry J. Chem. Educ. 1929 6 254 258 [ACS Full Text], [CAS], [Google Scholar]
  2. Servos J. W. Mathematics and the Physical Sciences in America, 1880–1930 Isis 1986 77 611629 [Crossref], [Google Scholar]
  3. Partington, J. R. A History of Chemistry; MacMillan: New York, 1970. [Google Scholar]
  4. Segré, E. From Falling Bodies to Radio Waves: Classical Physicists and Their Discoveries; Dover: Mineola, NY, 2007. [Google Scholar]
  5. Segré, E. From X-Rays to Quarks: Modern Physicists and Their Discoveries; Dover: Mineola, NY, 2007. [Google Scholar]
  6. The Harvard University Catalogue, 1899–1900; Harvard University: Cambridge, MA, 1900. See pp 289– 295,303– 306. [Google Scholar]
  7. Irving Langmuir – Biographical. NobelPrize.org. Nobel Media AB 2018. https://www.nobelprize.org/prizes/chemistry/1932/langmuir/biographical (accessed Oct. 3, 2018). [Google Scholar]
  8. James Flack Norris Award for Outstanding Achievement in the Teaching of Chemistry Recipients. http://www.nesacs.org/awards/norris/awards_norris_recipients.html (accessed Oct. 3, 2018). [Google Scholar]

This post is an excerpt from It’s Just Math: Research on Students’ Understanding of Chemistry and Mathematics‘.

Editors: Marcy H. Towns, Kinsey Bain, Jon-Marc G. Rodriguez
Publication Date (Web): April 24, 2019
Copyright © 2019 American Chemical Society
Read a free sample chapter: How Did We Get Here? Using and Applying Mathematics in Chemistry

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