Most and Least: Differences in Integer Comparisons Based on Temperature Comparison Language
- 111 Downloads
The language involved in de-contextualized integer comparisons poses challenges, as students may interpret “most” based on absolute values rather than on order. Using the context of temperature, we explored how students’ integer value comparisons differed based on question phrasing (which temperature is hottest, most hot, least hot, coldest, most cold, least cold) and on numbers presented (positive, negative, mixed). Participants included 88 second graders and 70 fourth graders from a rural school district in the Midwestern USA, and each student solved 36 integer comparisons. For comparisons with positive number choices, students had more difficulty with “coldest” than “hottest”; however, the results were reversed for comparisons with only negative number choices. When working with mixed comparisons, students often chose the least of the cold as opposed to the least cold, suggesting that they saw hot and cold as categorical opposites rather than opposites on a continuum, with zero as a boundary.
KeywordsIntegers Language Number comparisons Temperature
This research was supported by NSF CAREER award DRL-1350281. The authors would like to thank the schools, teachers, and students involved in the research for their participation and support. The authors give thanks especially to Mahtob Aqazade for her review of the paper.
- Bell, A. (1984). Short and long term learning—Experiments in diagnostic teaching design. In B. Southwell (Ed.), Proceedings of the Eighth International Conference for the Psychology of Mathematics Education (pp. 55–62). Sydney, Australia: International Group for the Psychology of Mathematics Education.Google Scholar
- Bofferding, L. & Hoffman, A. (2015). Comparing negative integers: Issues of language. In K. Beswick, T. Muir, & J. Wells (Eds.), Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, p. 150). Hobart, Australia: PME.Google Scholar
- Case, R. (1996). Introduction: Reconceptualizing the nature of children’s conceptual structures and their development in middle childhood. Monographs of the Society for Research in Child Development, 61(1–2), 1–26.Google Scholar
- Cheshire, J. (1998). Double negatives are illogical. In L. Bauer & P. Trudgill (Eds.), Language myths (pp. 113–122). New York, NY: Penguin Putnam, Inc..Google Scholar
- Donaldson, M., & Balfour, G. (1968). Less is more: A study of language comprehension in children. British Journal of Psychology, 59(4), 461–471. https://doi.org/10.1111/j.2044-8295.1968.tb01163.x CrossRefGoogle Scholar
- Dougherty, B. J. (2010). Developing essential understanding of number and numeration for teaching mathematics in prekindergarten–grade 2. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
- Murray, J. C. (1985). Children’s informal conceptions of integer arithmetic. In L. Streefland (Ed.), Proceedings of the Ninth Annual Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 147–153). Noordwijkerhout, The Netherlands: International Group for the Psychology of Mathematics Education.Google Scholar
- National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Retrieved from http://www.nctm.org/flipbooks/standards/pssm/index.html.
- National Governors Association Center for Best Practices & Council of Chief State School Officers (2010). Common core state standards for mathematics. Retrieved from http://www.corestandards.org/Math/Content/K/introduction
- National Research Council (2009). Mathematics learning in early childhood: Paths toward excellence and equity. Committee on Early Childhood Mathematics. In C.T. Cross, T.A. Woods & H. Schweingruber (Eds.), Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: The National Academies Press.Google Scholar
- Peled, I., Mukhoadhyay, S., & Resnick, L. (1989). Formal and informal sources of mental models for negative numbers. In G. Vergnaud, J. Rogalski, & M. Artique (Eds.), The international group for the psychology of mathematics education (Vol. 3, pp. 106–110). Paris: International Group for the Psychology of Mathematics Education.Google Scholar
- Pratt, D., & Simpson, A. (2004). McDonald’s vs Father Christmas. Australian Primary Mathematics Classroom, 9(3), 4–9.Google Scholar
- Siegler, R. S., & Robinson, M. (1982). The development of numerical understandings. In H. W. Reese & L. P. Lisitt (Eds.), Advances in child development and behavior (Vol. 16, pp. 242–312). New York, NY: Academic Press.Google Scholar
- Swanson, P. E. (2010). The intersection of language and mathematics. Mathematics Teaching in the Middle School, 15(9), 516–523.Google Scholar
- Vosniadou, S., Vamvakoussi, X., & Skopeliti, I. (2008). The framework theory approach to the problem of conceptual change. In S. Vosniadou (Ed.), International handbook of research on conceptual change (pp. 3–34). New York, NY: Routledge.Google Scholar
- Wessman-Enzinger, N. M., & Mooney, E. S. (2014). Making sense of integers through storytelling. Mathematics Teaching in the Middle School, 20(4), 202–205. https://doi.org/10.5951/mathteacmiddscho.20.4.0202 CrossRefGoogle Scholar
- Whitacre, I., Bishop, J. P., Philipp, R. A., Lamb, L. L., & Schappelle, B. P. (2015). Dollars & sense: Students’ integer perspectives. Mathematics Teaching in the Middle School, 20(2), 84–89. https://doi.org/10.5951/mathteacmiddscho.20.2.0084 CrossRefGoogle Scholar