@article{22508f4f79ac4a99bf5800dd37bfafdf,
title = "Analysis of the argumentation of nine-year-olds engaged in discourse about comparing fraction models",
abstract = "In this paper we analyze the argumentation of nine-year-olds as they justify their reasoning for a fraction comparison problem. We illustrate how their proof-like arguments evolve in a class discussion and are backed by the rod models they produce, showing both valid and invalid arguments.",
keywords = "Argumentation, Argumentation diagrams, Cuisinaire rods, Fourth grade mathematics, Fractions, Modeling, Proof, RUanalytic, Reasoning, Teacher education, Toulmin, VMCAnalytic, Video Mosaic Collaborative",
author = "{Van Ness}, {Cheryl K.} and Maher, {Carolyn A.}",
note = "Funding Information: National Science Foundation grants: Synthesizing Video Data on Students{\textquoteright} Mathematical Reasoning (DRL-0723475, directed by Carolyn A. Maher); Cyber-Enabled Design Research to Enhance Teachers{\textquoteright} Critical Thinking Using a Major Video Collection (DRL-0822204, directed by Carolyn A. Maher) and A Three and One Half-Year Longitudinal Study of Children{\textquoteright}s Development of Mathematical Knowledge, (MDR-9053597, directed by Robert B. Davis and Carolyn A. Maher) and a grant from the New Jersey Department of Higher Education (93-992022-8001, directed by Carolyn A. Maher). This state and federally funded research project provided an innovative in-school mathematics enrichment program to one suburban, rural elementary school in central New Jersey (Colts Neck), USA. Funding Information: Research on children{\textquoteright}s mathematical learning was supported by three grants from the National Science Foundation: MDR-9053597 directed by R. B. Davis, C. A. Maher; REC-9814846 directed by C. A. Maher; and REC-0309062 directed by C. A. Maher, A. B. Powell, and K. Weber and a grant from the N.J. Department of Higher Education: 93-992022-8001. The Video Mosaic Collaborative is a research and development project sponsored by the National Science Foundation: DRL-0822204, directed by C. A. Maher with G. Agnew, C. E. Hmelo-Silver, and M. F. Palius. Publisher Copyright: {\textcopyright} 2018 Elsevier Inc. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.",
year = "2019",
month = mar,
doi = "10.1016/j.jmathb.2018.04.004",
language = "English (US)",
volume = "53",
pages = "13--41",
journal = "Journal of Mathematical Behavior",
issn = "0732-3123",
publisher = "Elsevier Inc.",
}