Integer Number Lines in U.S. School Mathematics - Conclusion

John Wallis (1685), a British mathematician, may have been the first to offer a physical illustration of a number line (Núñez, 2017), although I would maintain his was an illustration of a relative number line. This article draws attention to the lag-time between the work of mathematicians like Wallis and the use of the number line with negative integers in U.S. school mathematics. The descriptions of how number lines have been used in different ways highlight a trend from absence to descriptions, to formality, to illustrations. In mathematics education, teachers and their students now talk about the number line in a wide range of contexts—anthropology, cognitive science, pedagogy, and history, to name just four. This article has, I hope, added a missing piece to this conversation, by examining the number line through the lens of school mathematics. Understanding and discussing the gaps between forms of pure and applied mathematics, on the one hand, and school mathematics, on the other, is an important development toward more robust, scholarly discussions—not only with respect to negative integers and number lines, but also to mathematics and mathematics education, in general.

Acknowledgments

The author would like to thank Dr. Nerida Ellerton and Dr. Ken Clements for access to their comprehensive collections and also for the personal communications about the texts. The author would also like to thank Dr. Janet Beery and the anonymous reviewers for the helpful feedback that made the revision process delightful. 

About the Author

Nicole M. Wessman-Enzinger, PhD, is an Assistant Professor in the School of Education at George Fox University. She teaches content and pedagogy mathematics courses for future teachers. Her main research interests are situated in children and prospective teachers' cognition about negative numbers. She views the history of mathematics education as a tool with which to make sense of students' thinking and contemporary issues.