@inbook {LadKor-EML-2014, title = {Number concepts {\textendash}- processes of internalization and externalization by the use of multi-touch technology Silke Ladel and Ulrich Kortenkamp}, booktitle = {Early Mathematics Learning}, year = {Submitted}, chapter = {3-3}, keywords = {ACAT}, author = {Silke Ladel and Ulrich Kortenkamp} } @book {KorBraBenKruLadVog-EML-2014, title = {Early Mathematics Learning}, year = {2014}, publisher = {Springer-Verlag}, organization = {Springer-Verlag}, keywords = {submitted}, isbn = {978-1-4614-4677-4}, url = {http://www.springer.com/education+\%26+language/mathematics+education/book/978-1-4614-4677-4}, editor = {Ulrich Kortenkamp and Birgit Brandt and Christiane Benz and G{\"o}tz Krummheuer and Silke Ladel and Rose Vogel} } @article {LadKor-AAMTEML-2012, title = {An activity-theoretic approach to multi-touch tools in early maths learning}, journal = {The International Journal for Technology in Mathematics Education}, volume = {20}, number = {1}, year = {2013}, abstract = {

In this article we present an activity theory based framework that can capture the complex situations that arise when modern technology like multi-touch devices are introduced in classroom situations. As these devices are able to cover more activities than traditional technologies, even computer-based, media, we have to accept that they now take a larger role in the model of interactions. We reflect this fact by moving the artefact into the centre of our observations, leading to an artefact-centric activity theory (ACAT). The theory was developed in the need of analysing learning environments for primary maths education.

}, keywords = {refereed}, url = {http://www.tech.plym.ac.uk/research/mathematics_education/field\%20of\%20work/ijtme/volume_20/number_one.html$\#$one}, author = {Ladel, Silke and Kortenkamp, Ulrich} } @inbook {LadKor-DTBLEPVUAAT-2013, title = {Designing a technology based learning environment for place value using artifact-centric activity theory}, booktitle = {Proceedings of the 37th conference of the International Group for the Psychology of Mathematics Education. Mathematics learning across the life span}, volume = {1}, year = {2013}, pages = {188-192}, keywords = {refereed}, author = {Silke Ladel and Ulrich Kortenkamp}, editor = {Anke M. Lindmeier and Aiso Heinze} } @conference {LadKor-EMWMAA-2012, title = {Early maths with multi-touch {\textendash} an activity-theoretic approach}, booktitle = {Proceedings of POEM 2012}, year = {2012}, keywords = {invited}, url = {http://cermat.org/poem2012/main/proceedings_files/Ladel-Kortenkamp-POEM2012.pdf}, author = {Ladel, Silke and Kortenkamp, Ulrich} } @conference {LadKor-AAMTEML-2011, title = {An activity-theoretic approach to multi-touch tools in early maths learning}, booktitle = {Proceedings of ATATEMLO 2011 in Paris}, year = {2011}, keywords = {refereed}, author = {Ladel, Silke and Kortenkamp, Ulrich} } @conference {LadKor-FMBUNO-2011, title = {Finger-Symbol-Sets and Multi-Touch for a better understanding of numbers and operations}, booktitle = {Proceedings of CERME 7, Rzeszow}, year = {2011}, abstract = {

Basic concepts of numbers and operations are fundamental for mathematical learning. Suitable materials for developing such basic concepts are hands and fingers. Among other things, this is because of their natural structure of 5 and 10. To support the development of concepts and the process of internalization a linking between different forms of representations by the computer can be helpful. To benefit of both, the advantages of the hands and fingers and the automatically linking, we suggest using multi-touch-technology, i.e. computer input devices that are able to recognize several touch gestures at the same time. Here, children can present numbers with their fingers that produce virtual objects. These objects can be automatically linked with the symbolic form of representation.

}, keywords = {refereed}, author = {Ladel, Silke and Kortenkamp, Ulrich} } @conference {LadKor-IMSFSS-2011, title = {Implementation of a multi-touch-environment supporting finger symbol sets}, booktitle = {Proceedings of CERME 7, Rzeszow}, year = {2011}, keywords = {refereed}, author = {Ladel, Silke and Kortenkamp, Ulrich} } @conference {LadKor-RMMERMMELREMS-2009, title = {Realisations of {MERS} (Multiple Extern Representations) and {MELRS} (Multiple Equivalent Linked Representations) in Elementary Mathematics Software}, booktitle = {Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education. January 28th - February 1st 2009, Lyon (France)}, year = {2009}, abstract = {

Assumptions of multiple mental representations lead to the presumption of an enhanced mathematical learning, especially of the process of internalization, due to MERs (Ainsworth 1999) and MELRs (Harrop 2003). So far, most educational software for mathematics at the primary level aims to help children to automatize mathematical operations, whereby symbolical representations are dominating. However, what is missing is software and principles for its design that support the process of internalization and the learning of external representations and their meaning themselves {\textendash} in primary school these are in particular symbols. This paper summarizes the current state of research and presents a prototype that aims to the above-mentioned purpose.

}, keywords = {refereed}, url = {http://www.inrp.fr/publications/edition-electronique/cerme6/wg7-01-ladel.pdf}, author = {Ladel, Silke and Kortenkamp, Ulrich}, editor = {Durand-Guerrier, Viviane and Soury-Lavergne, Sophie and Arzarello, Ferdinando} } @article {LadKor-VAGKF-2009, title = {Virtuell-enaktives Arbeiten mit der {\quotedblbase}Kraft der F{\"u}nf{\textquoteright}{\textquoteright}}, journal = {MNUprimar}, year = {2009}, abstract = {

Der {\"U}bergang von einem ordinalen Zahlkonzept zu einem strukturierten Zahlbegriff f{\"a}llt manchen Kindern schwer. Wir stellen vor, wie diesen Kindern mit Hilfe des Computers die {\guillemotright}Kraft der F{\"u}nf{\guillemotleft} n{\"a}hergebracht werden kann. Dabei stellt sich als entscheidender Vorteil heraus, dass die Kinder F{\"u}nferp{\"a}ckchen virtueller Pl{\"a}ttchen mit einem {\guillemotright}Griff{\guillemotleft} nehmen k{\"o}nnen, ohne die Pl{\"a}ttchen einzeln abz{\"a}hlen zu m{\"u}ssen, diese aber dennoch auch wieder einzeln gegriffen werden k{\"o}nnen.

}, keywords = {refereed}, author = {Ladel, Silke and Kortenkamp, Ulrich} }