2014
DOI: 10.1007/s10857-014-9295-2
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Investigating the improvement of prospective elementary teachers’ number sense in reasoning about fraction magnitude

Abstract: We report on interview results from a classroom teaching experiment in a Number and Operations course for prospective elementary teachers. Improving the number sense of this population is an important goal for mathematics teacher education, and researchers have found this goal to be difficult to accomplish. In earlier work, we devised a local instruction theory for the development of number sense, which focused on wholenumber mental computation. In this study, the local instruction theory was applied to the ra… Show more

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Cited by 21 publications
(23 citation statements)
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“…The theory includes three goals for developing number sense with whole numbers: "students will capitalize on opportunities to use number sensible strategies, will develop a repertoire of resource strategies, and will reason with models to understand and use new number sensible strategies" (p. 249). Building on their work with whole numbers and using Smith's (1995) framework, Whitacre & Nickerson (2016) extended their local instructional theory to rational numbers, particularly focusing on fraction magnitude. They developed a sequence of learning activities (hypothetical learning trajectory) based on prior work, and as the class moved through the learning activities, the researchers "conjectured that students' reasoning would develop from instructed to constructed strategies" (p. 65).…”
Section: Research Backgroundmentioning
confidence: 99%
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“…The theory includes three goals for developing number sense with whole numbers: "students will capitalize on opportunities to use number sensible strategies, will develop a repertoire of resource strategies, and will reason with models to understand and use new number sensible strategies" (p. 249). Building on their work with whole numbers and using Smith's (1995) framework, Whitacre & Nickerson (2016) extended their local instructional theory to rational numbers, particularly focusing on fraction magnitude. They developed a sequence of learning activities (hypothetical learning trajectory) based on prior work, and as the class moved through the learning activities, the researchers "conjectured that students' reasoning would develop from instructed to constructed strategies" (p. 65).…”
Section: Research Backgroundmentioning
confidence: 99%
“…One set of learning experiences involved explicit teaching of comparison strategies based on Whitacre & Nickerson's (2016) scheme for fraction comparison strategies. Teacher candidates were taught specific comparison strategies with the purpose of expanding their thinking beyond using common denominators.…”
Section: Description Of Direct Instruction Experiences On Fraction Comentioning
confidence: 99%
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“…Approaches for students to learn multiplication have been widely modelled, scaffolded and discussed. As a result there are many research studies on multiplication with different foci such as array representation (Barmby, Harries, Higgins, & Suggate, 2009;Young-Loveridge, 2005), classroom-based studies and rectangular areas which done by Izsák (2004), understanding among prospective teachers (Lo, Grant & Flowers, 2008;Thanheiser, 2010;Whitacre & Nickerson, 2016). An array is a rectangular arrangement of discrete objects in rows and columns.…”
Section: Multiplicationmentioning
confidence: 99%
“…Likewise, Larsson, Pettersson and Andrews (2017) stated that the way teachers introduce multiplication to students as repeated addition is a problematic instruction, particularly when multiplication is extended to multi-digits and decimals. Whitacre and Nickerson (2016) also pointed out that prospective teachers need to be able to make sense of mathematics and use their prior knowledge as a resource in learning. Jiew and Chin (in press) explored further by investigating how prior knowledge can support or impede the sense making of multiplication in new contexts.…”
Section: Multiplicationmentioning
confidence: 99%