Student Research Guide WQ25/ Cognitive Effects of Numeral Systems

EBSCO DATABASE: Brückler, Franka Miriam, and Vladimir Stilinović. “The Tradition of Large Integers in Historical Arithmetical Textbooks.” Mathematics Enthusiast, vol. 21, no. 1/2, Feb. 2024, pp. 54–70. EBSCOhost, https://doi-org.skagit.idm.oclc.org/10.54870/1551-3440.1617.

• Franka Brückler is an assistant professor at the University of Zagreb with a PhD in mathematics. The paper highlights the historical practice of reading long numbers as a means to teach children the Hindu-Arabic numeral system. In the process, the paper details a timeline of the spread of Hindu-Arabic numerals through Europe and the development of arithmetic as a general skill.

JSTOR DATABASE: Buijsman, Stefan. “How Numerals Support New Cognitive Capacities.” Synthese, vol. 197, no. 9, 2020, pp. 3779–96. JSTOR, http://www.jstor.org/stable/45294958.

• Stefan Buijsman is an associate professor of philosophy at the Delft University of Technology. This paper discusses two theories of cognitive model for the brain's interpretation of numerals and acquisition of arithmetical ability. Evidence is presented that demonstrates the brain has both natural ability for numbers and is augmented with the acquisition of a numeral system.

EBSCO DATABASE: Ebersbach, Mirjam. “Development of Children’s Estimation Skills: The Ambiguous Role of Their Familiarity With Numerals.” Child Development Perspectives, vol. 10, no. 2, June 2016, pp. 116–21. EBSCOhost, https://doi-org.skagit.idm.oclc.org/10.1111/cdep.12172.

• Mirjam Ebersbach is a professor of developmental psychology at the University of Kassel. Learning numerals enhances a child's understanding of real life quantities. However, children may associate some numerals to be larger than they really are and make improper comparisons. This error decreases as children learn to correctly associate more numbers with actual amounts.

PRINT BOOK: Ifrah, Georges, and David Bellos. The Universal History of Numbers : From Prehistory to the Invention of the Computer. J. Wiley, 2000. https://sbctc-skagit.primo.exlibrisgroup.com/permalink/01STATEWA_SKAGIT/hsm5hs/alma991000272029702822

• Georges Ifrah was a mathematics historian. This book covers the history of numbers from the earliest known examples to the modern system that we now use. The chapters regarding the Greek and Roman numeral systems, the development of Hindu-Arabic numerals, and the introduction of the numerals into Europe are very relevant to this guide. The associated descriptions of people's interactions with these numeral systems are informative towards the impacts of numeral systems.

EBSCO DATABASE: Odic, Darko, and Ariel Starr. “An Introduction to the Approximate Number System.” Child Development Perspectives, vol. 12, no. 4, Dec. 2018, pp. 223-29. EBSCOhost, https://doi-org.skagit.idm.oclc.org/10.1111/cdep.12288.

• Darko Odic is an associate professor in the department of psychology at the University of British Columbia. The paper describes the approximate number system. The ANS is a function of the brain that gives an innate understanding of quantity but is inexact. The ANS is foundational for quantitative reasoning.

INTERNET PUBLICATION: OECD. “Do Adults Have the Skills They Need to Thrive in a Changing World?: Survey of Adult Skills 2023.” OECD Skills Studies, OECD Publishing, Paris, 10 Dec. 2024, https://doi.org/10.1787/b263dc5d-en.

• The Organization for Economic Cooperation and Development is a well established international organization that is, in part, known for its statistical publications. This publication is a statistical report on numeracy and literacy in OECD member countries. For this guide, the levels of numeracy, and the proportions thereof, take prominence. This establishes how far society has numerically advanced.

JSTOR DATABASE: Larvor, Brendan. “Why ‘Scaffolding’ is the Wrong Metaphor: The Cognitive Usefulness of Mathematical Representations.” Synthese, vol. 197, no. 9, 2020, pp. 3743–56. JSTOR, http://www.jstor.org/stable/45294956.

• Brendan Larvor is a reader of philosophy at the University of Hertfordshire. The paper argues that math is embodied in its notation and not merely supported by it. Written calculation with Hindu-Arabic numerals transfers much of the effort to features of the notation. The use of the notation advances the study of math and becomes a part of the subject itself.

ACADEMIC ENCYCLOPEDIA: "Numerals and Numeral Systems." Britannica Academic, Encyclopædia Britannica, 3 Apr. 2024. academic-eb-com.skagit.idm.oclc.org/levels/collegiate/article/numerals-and-numeral-systems/345278#233818.toc.

• Britannica Academic is a scholarly encyclopedia for use as a reference resource. This entry is credited to David Smith and William LeVeque. David Smith was a professor of mathematics at the Columbia University. William LeVeque was a professor of mathematics at Claremont Graduate School. The entry covers what numeral systems are, a few types of numeral systems, and a brief history of select numeral systems.

PROQUEST DATABASE: Throop, Liz C. "Thinking on Paper: Hindu-Arabic Numerals in European Typography." Visible Language, vol. 38, no. 3, 2004, pp. 290-303. ProQuest, https://skagit.idm.oclc.org/login?url=https://www.proquest.com/scholarly-journals/thinking-on-paper-hindu-arabic-numerals-european/docview/232933730/se-2.

• Liz Throop is a retired professor of Art and Design from Georgia State University. This paper covers the introduction of Hindu-Arabic numerals to Europe and various difficulties the adoption faced. Benefits and drawbacks of the system are discussed. The paper takes particular attention towards the development of the typeface for the numerals.

EBSCO DATABASE: Zhu, Yiwen. “How Were Western Written Calculations Introduced into China? An Analysis of the Tongwen Suanzhi (Arithmetic Guidance in the Common Language, 1613).” Centaurus: Journal of the European Society for the History of Science, vol. 60, no. 1/2, Feb. 2018, pp. 69-86. EBSCOhost, https://doi-org.skagit.idm.oclc.org/10.1111/1600-0498.12169.

• Yiwen Zhu is a professor of Philosophy at Sun Yat-sen University and researches the history of mathematics. This paper addresses the introduction of western calculation methods to China. A place value numeral system and calculation system utilizing Chinese characters was developed that eased the use of the abacus and was in some regards more efficient than Hindu-Arabic numerals.