Abstract
In this chapter, we explore various forms of reasoning employed by students as they work on another “non-existence” task given the available rods. The task, which was presented to the students towards the end of the second session and which does not have a correct solution using the rods that are included in the set, prompted the students to use multiple forms of reasoning to justify their claims. The arguments posed by the students were structured as both direct and indirect arguments.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Steencken, E. (2001). Tracing the growth in understanding of fraction ideas: A fourth grade case study (Unpublished doctoral dissertation). Rutgers, The State University of New Jersey, New Brunswick, NJ.
Yankelewitz, D. (2009). The development of mathematical reasoning in elementary school students exploration of fraction ideas (Unpublished doctoral dissertation). Rutgers, The State University of New Jersey, New Brunswick, NJ.
Yankelewitz, Y., Mueller, M., & Maher, C. A. (2010). A task that elicits reasoning: A dual analysis. Journal of Mathematical Behavior, 29, 76–85.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Sense Publishers
About this chapter
Cite this chapter
Winter, E., Yankelewitz, D. (2017). Reasoning by Cases While Exploring Fractions as Numbers. In: Maher, C.A., Yankelewitz, D. (eds) Children’s Reasoning While Building Fraction Ideas. Mathematics Teaching and Learning. SensePublishers, Rotterdam. https://doi.org/10.1007/978-94-6351-008-0_5
Download citation
DOI: https://doi.org/10.1007/978-94-6351-008-0_5
Publisher Name: SensePublishers, Rotterdam
Online ISBN: 978-94-6351-008-0
eBook Packages: EducationEducation (R0)