The effects of representational format on learning combinatorics from an interactive computer simulation

Kollöffel, Bas Jan; Eysink, Tessa H.S.; Jong, Ton de; Wilhelm, Pascal

doi:10.1007/s11251-008-9056-7

Cited by 37 publications

(39 citation statements)

References 58 publications

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“…Other stijdies of combinatorics and probability learning have consistendy found that instmction based on formal representations alone is as effective as or more effective than grounded instmction (Belenky & Nokes, 2009;Kolloffel et al, 2009). This negative fmding was replicated in Experiment 2.…”

Section: Discussionmentioning

confidence: 67%

Integrating formal and grounded representations in combinatorics learning.

Braithwaite

Goldstone

2013

Journal of Educational Psychology

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The terms concreteness fading and progressive formalization have been used to describe instructional approaches to science and mathematics that use grounded representations to introduce concepts and later transition to more formal representations of the same concepts. There are both theoretical and empidcal reasons to believe that such an approach may improve leaming outcomes relative to instruction employing only grounded or only formal representations (Freudenthal, 1991;Goldstone & Son, 2005;McNeil & Fyfe, 2012; but see Kaminski, Sloutsky, & Heckler, 2008). Two experiments tested the effectiveness of this approach to instruction in the mathematical domain of combinatorics, using outcome listing and numerical calculation as examples of grounded and formal representations, respectively. The study employed a pretest-training, posttest design. Transfer performance, that is, participants' improvement from pretest to posttest, was used to assess the effectiveness of instruction received during training. In Experiment 1, transfer performance was compared for 4 types of instruction, which differed only in the types of representation they employed: pure listing (i.e., listing only), pure formalism (i.e., numerical calculation only), list fading (i.e., listing followed by numerical calculation), and formalism-first (i.e., listing introduced after numerical calculation). List fading instmction led to transfer performance on par with pure formalism instmction and higher than formalism-first and pure listing instruction. In Experiment 2, an enhanced version of list fading training was again compared to pure formalism. However, no difference in transfer performance due to training was found. The results suggest that combining grounded and formal representations can be an effective approach to combinatorics instruction but is not necessarily preferable to using formal representations alone. If both grounded and formal representations are employed, the former should precede rather than follow the latter in the instructional sequence.

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Section: Discussionmentioning

confidence: 67%

Integrating formal and grounded representations in combinatorics learning.

Braithwaite

Goldstone

2013

Journal of Educational Psychology

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“…The tests contained 12 and 26 items respectively. The sensitivity and reliability of the test items have been established in recent years in a number of studies performed across Germany and The Netherlands (see e.g., Berthold and Renkl 2009;Eysink et al 2009;Gerjets et al 2009;Kolloffel et al 2009;Wouters et al 2007). The pre-test was aimed at measuring (possible differences in) the prior knowledge of the students.…”

Section: Representational Toolsmentioning

confidence: 99%

Comparing the effects of representational tools in collaborative and individual inquiry learning

Kollöffel

Eysink

Jong

2011

Computer Supported Learning

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Constructing a representation in which students express their domain understanding can help them improve their knowledge. Many different representational formats can be used to express one's domain understanding (e.g., concept maps, textual summaries, mathematical equations). The format can direct students' attention to specific aspects of the subject matter. For example, creating a concept map can emphasize domain concepts and forming equations can stress arithmetical aspects. The focus of the current study was to examine the role of tools for constructing domain representations in collaborative inquiry learning. The study was driven by three questions. First, what are the effects of collaborative inquiry learning with representational tools on learning outcomes? Second, does format have differential effects on domain understanding? And third, does format have differential effects on students' inclination to construct a representation? A pre-test post-test design was applied with 61 dyads in a (face-to-face) collaborative learning setting and 95 students in an individual setting. The participants worked on a learning task in a simulationbased learning environment equipped with a representational tool. The format of the tool was either conceptual or arithmetical or textual. Our results show that collaborative learners outperform individuals, in particular with regard to intuitive knowledge and situational knowledge. In the case of individuals a positive relation was observed between constructing a representation and learning outcomes, in particular situational knowledge. In general, the effects of format could not be linked directly to learning outcomes, but marked differences were found regarding students' inclination to use or not use specific formats.

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“…Recent research on the use of multiple external representations for learning provides some further support for this view (e.g., Kolloffel, Eysink, de Jong, & Wilhelm, 2009). …”

Section: Generativitymentioning

confidence: 96%

Framing the Features of Good-Quality Knowledge for Teachers and Students

Lawson¹,

Askell–Williams²

2012

Enhancing the Quality of Learning

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In this paper we have two concerns. First we consider the features used to describe good quality learning actions and knowledge representations. Our second concern is the need to develop students' knowledge of how to act, during teachinglearning transactions, in order to generate good quality knowledge representations.There is a convergence of views, at a broad level, about the character of good quality knowledge. Although there are frequent specifications of the features of good quality learning these discussions mostly do not build on one another so that a coherent representation of such learning is built up. There is therefore a need to consider further the characteristics of learning that are regarded as being of good quality. For this purpose we set out a framework based around six dimensions of good quality knowledge, namely, extent, well-foundedness, structure, complexity, generativity, and variety of representational format. In the final section of the chapter we advance arguments that point to the need to attend to the state of students' and teachers' knowledge about how to act, in strategic cognitive and metacognitive ways, in order to generate good quality knowledge representations.

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The effects of representational format on learning combinatorics from an interactive computer simulation

Cited by 37 publications

References 58 publications

Integrating formal and grounded representations in combinatorics learning.

Integrating formal and grounded representations in combinatorics learning.

Comparing the effects of representational tools in collaborative and individual inquiry learning

Framing the Features of Good-Quality Knowledge for Teachers and Students

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