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Erschienen in: Technology, Knowledge and Learning 1-2/2012

01.04.2012

Fostering Hooks and Shifts: Tutorial Tactics for Guided Mathematical Discovery

verfasst von: Dor Abrahamson, Jose Gutiérrez, Timothy Charoenying, Andrea Negrete, Engin Bumbacher

Erschienen in: Technology, Knowledge and Learning | Ausgabe 1-2/2012

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Abstract

How do instructors guide students to discover mathematical content? Are current explanatory models of pedagogical practice suitable to capture pragmatic essentials of discovery-based instruction? We examined videographed data from the implementation of a natural user interface design for proportions, so as to determine one constructivist tutor’s methodology for fostering expert visualization of learning materials. Our analysis applied professional-perception cognitive–anthropological frameworks. However, several types of tutorial tactics we observed appeared to “fall between the cracks” of these frameworks, due to the discovery-based, physical, and semantically complex nature of our design. We tabulate and exemplify an expanded framework that accommodates the observed tactics. The study complements our earlier focus on students’ agency in discovery (in Abrahamson et al., Technol Knowl Learn 16(1):55–85, 2011) by offering an empirically validated resource for researchers, instructors, and professional developers interested in preparing future teaching for future technology.

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1
The activity protocol then concludes with a hands-on activity that we do not treat in this paper. Therein, the control mechanism is changed from manual to numeral: we introduce a ratio table that students need to fill in, and then the computer “plays out” the number inputs by moving the cursors automatically from one number pair to the next and giving the appropriate color feedback. We enable students to go back and forth between these interaction modes.
 
2
That said, the particular embodied-interaction problems that we have implemented so far in the Mathematical Imagery Trainer perhaps do not demand of students to manage as much information as do inquiry tasks in biology, and, more generally, it is not unproblematic to compare design frameworks across STEM disciplines.
 
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Metadaten
Titel
Fostering Hooks and Shifts: Tutorial Tactics for Guided Mathematical Discovery
verfasst von
Dor Abrahamson
Jose Gutiérrez
Timothy Charoenying
Andrea Negrete
Engin Bumbacher
Publikationsdatum
01.04.2012
Verlag
Springer Netherlands
Erschienen in
Technology, Knowledge and Learning / Ausgabe 1-2/2012
Print ISSN: 2211-1662
Elektronische ISSN: 2211-1670
DOI
https://doi.org/10.1007/s10758-012-9192-7

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