A1 Refereed original research article in a scientific journal

Early developmental trajectories towards the concept of rational numbers




AuthorsMikko Kainulainen, Jake McMullen, Erno Lehtinen

PublisherRoutlege Taylor & Francis Group

Publication year2017

JournalCognition and Instruction

Volume35

Issue1

First page 4

Last page19

Number of pages16

ISSN0737-0008

eISSN1532-690X

DOIhttps://doi.org/10.1080/07370008.2016.1251287

Web address http://www.tandfonline.com/doi/full/10.1080/07370008.2016.1251287


Abstract

Difficulties with rational numbers have been explained by a natural
number bias, where concepts of natural numbers are inappropriately
applied to rational numbers. Overcoming this difficulty may require a
radical restructuring of previous knowledge. In order to capture this
development, we examined third- to fifth-grade students' understanding
of the size of rational numbers across a 1-year period. On three
occasions, students answered a test about the size of decimals and
fractions. Latent transition analysis allowed profiling five different
rational number size concepts and mapping students' developmental
trajectories during the early learning of this topic. Development from
natural number-based reasoning to mathematically correct understanding
was almost nonexistent during this time period. Instead, students appear
to move through intermediary concepts. Locating these temporary and
mediating number concepts supports the idea of a slow and gradually
developing conceptual change in rational numbers.



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