@inbook{c6ee1ede60584ce89b5273546b743b2d,
title = "Two Cases Studies of Fifth Grade Students Reasoning About Levers",
abstract = "The purpose of this teaching experiment was to give fifth grade students activities using simple machines to see how they would use proportional reasoning to mathematize those activities. We chose a series of activities using two types of levers, because of their experiences with seesaws and because this combined mathematics with science. We hoped that they would develop models of the lever. We also hoped that they would recognize the inverse multiplicative relationship between distance and weight. The students did demonstrate evidence of preliminary models about the relationship between weights and distances on a lever. On the final day, the students, in a thought experiment, were able to discover the multiplicative relationship between distance and weight, but they did not realize the inverse nature of this relationship.",
keywords = "Combined Mathematics, Fulcrum, Inverse Nature, Multiplicative Relationship, Seesaw",
author = "Paula Guerra and Linda Hern{\'a}ndez and Ahyoung Kim and Muhsin Menekse and James Middleton",
note = "Funding Information: Acknowledgment The research reported in this chapter was supported, in part, by grants from the National Science Foundation (#0337795). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the N. Publisher Copyright: {\textcopyright} 2013, Springer Science+Business Media Dordrecht.",
year = "2013",
doi = "10.1007/978-94-007-6271-8_26",
language = "English (US)",
series = "International Perspectives on the Teaching and Learning of Mathematical Modelling",
publisher = "Springer Science and Business Media B.V.",
pages = "301--312",
booktitle = "International Perspectives on the Teaching and Learning of Mathematical Modelling",
}