Development of a Flexible Understanding of Place Value

Ladel, Silke; Kortenkamp, Ulrich

doi:10.1007/978-3-319-23935-4_16

Cited by 9 publications

(2 citation statements)

References 4 publications

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“…They provide concrete representations for the number bases . They model numbers with objects hinting at different dimensions (see Ladel and Kortenkamp 2015;Rottmann and Peter-Koop 2015). In spite of the diffusion, they have been criticised from an epistemological and cognitive perspective (Stacey et al 2001), suggesting, instead, of using Linear Arithmetic Blocks (LAB) that model numbers with length, showing the position of numbers on a number line.…”

Section: Multibase Arithmetic Blocksmentioning

confidence: 99%

Language and Cultural Issues in the Teaching and Learning of WNA

Sun

Bartolini

2018

New ICMI Study Series

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Il ne s'agit pas là de philosophie comparée, par mise en parallèle des conceptions; mais d'un dialogue philosophique, où chaque pensée, à la rencontre de l'autre, s'interroge sur son impensé ('This is not about comparative philosophy, about paralleling different conceptions, but about a philosophical dialogue in which every thought, when coming towards the other, questions itself about its own unthought' (Jullien 2006, p. vi)) 他山之石,可以攻玉 (tā shān zhī shí, kěyǐ gōng yù) ('The stone from another mountain can be used to polish one's own jade' (Xiao Ya, Shijing: He Ming, 1000 A. C.)

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Section: Multibase Arithmetic Blocksmentioning

confidence: 99%

Language and Cultural Issues in the Teaching and Learning of WNA

Sun

Bartolini

2018

New ICMI Study Series

View full text Add to dashboard Cite

show abstract

“…Understanding the place value system is one of the important competencies for the further development of arithmetic skills such as the development of multi-digit numbers and operations with them (Dietrich et al, 2016) as well as other basic numerical competencies (Lambert & Moeller, 2019) such as mentally representing the magnitudes of numbers. Similarly, children who understand the decimal structure of numbers flexibly (Ladel & Kortenkamp, 2016) are more likely to solve math problems and do basic operations successfully (Gebhardt et al, 2014). A profound understanding of the place value system also facilitates the expansion of the number systems into decimal fractions (Moloney & Stacey, 1997).…”

Section: Introductionmentioning

confidence: 99%

Validation of a Model of Sustainable Place Value Understanding in Turkey

Herzog¹,

Sarı²,

Olkun³

et al. 2021

INT ELECT J MATH ED

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Research has shown that a profound place value understanding is crucial for success in learning mathematics. At the same time, a substantial number of students struggles with developing a sustainable place value understanding. In this regard, two aspects of the place value system appear especially relevant: First, the knowledge of the decimal structure of numbers, and second, the relation between the bundling units. To support teaching place value understanding, a developmental model of place value understanding focusing on both aspects has been constructed and validated in Germany. The model comprises five levels of place value understanding that build upon each other hierarchically. This study aims at validating the level hierarchy in Turkey to prepare the usage of the developmental model as learning trajectory for Turkish primary schools. N=437 Turkish students from Grades 2 through 4 completed a translated version of the item collection of the German validation study as well as a Turkish place value test that is not based on a developmental model. In a Rasch analysis, most items of the translated item collection showed item difficulties as predicted by the model. In a regression analysis, item difficulties were well predicted by their allocation within the level hierarchy, while other item characteristics did not inform about the item difficulties. Substantial correlations between the translated item collection and the Turkish test underpin the claim that the model is appropriate to assess Turkish students' place value understanding as well as structuring place value instruction in Turkish primary schools.

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Artifact-Centric Activity Theory—A Framework for the Analysis of the Design and Use of Virtual Manipulatives

Ladel

Kortenkamp

2016

International Perspectives on Teaching and Learning Mathematics With Virtual Manipulatives

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Development of a Flexible Understanding of Place Value

Cited by 9 publications

References 4 publications

Language and Cultural Issues in the Teaching and Learning of WNA

Language and Cultural Issues in the Teaching and Learning of WNA

Validation of a Model of Sustainable Place Value Understanding in Turkey

Artifact-Centric Activity Theory—A Framework for the Analysis of the Design and Use of Virtual Manipulatives

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