Mathematics Learning and Knowing: A Cognitive Process

Greenes, Carole

doi:10.1177/002205749517700105

Cited by 12 publications

(9 citation statements)

References 6 publications

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“…Possibly, the arithmetical format is more difficult to use to construct a domain representation. Another possibility is that students failed to view mathematical symbols as reflections of principles and structures, but rather perceived them as indicators of which operations need to be performed (Atkinson et al 2003;Cheng 1999;Greenes 1995;Nathan et al 1992;Niemi 1996;Ohlsson and Rees 1991). This would mean that the textual and the conceptual format are more close to the code in which students can explain the domain to themselves, or maybe students consider those formats more suited to express their knowledge to the outside world.…”

Section: Discussionmentioning

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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Section: Discussionmentioning

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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“…One needs to know, for example, the conceptual meaning of the multiplication sign. In arithmetical representations the underlying principle or concept is not as explicit as in diagrams and texts, and as a result most learners tend to view mathematical symbols (e.g., multiplication signs) purely as indicators of which operations to perform on adjacent numbers (Atkinson et al 2003;Cheng 1999;Greenes 1995;Nathan et al 1992;Niemi 1996;Ohlsson and Rees 1991).…”

Section: Representational Formatsmentioning

confidence: 99%

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

et al. 2008

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The current study investigated the effects of different external representational formats on learning combinatorics and probability theory in an inquiry based learning environment. Five conditions were compared in a pre-test post-test design: three conditions each using a single external representational format (Diagram, Arithmetic, or Text), and two conditions using multiple representations (Text + Arithmetic or Diagram + Arithmetic). The major finding of the study is that a format that combines text and arithmetics was most beneficial for learning, in particular with regard to procedural knowledge, that is the ability to execute action sequences to solve problems. Diagrams were found to negatively affect learning and to increase cognitive load. Combining diagrams with arithmetical representations reduced cognitive load, but did not improve learning outcomes.

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“…Most students tend to view mathematical symbols (e.g., multiplication signs) purely as indicators of which operations need to be performed on adjacent numbers, rather than reflections of principles and concepts underlying these procedures (Atkinson, Catrambone, & Merrill, 2003;Cheng, 1999;Greenes, 1995;Nathan, Kintsch, & Young, 1992;Niemi, 1996;Ohlsson & Rees, 1991). Therefore, they easily lose sight of the meaning of their actions.…”

Section: Representations In the Domain Of Mathematicsmentioning

confidence: 99%

“…One needs to know, for example, the conceptual meaning of the multiplication sign. In arithmetical representations the underlying principle or concept is not as explicit as in diagrams and texts, and as a result most students tend to view mathematical symbols (e.g., multiplication signs) purely as indicators of which operations to perform on adjacent numbers (Atkinson et al, 2003;Cheng, 1999;Greenes, 1995;Nathan et al, 1992;Niemi, 1996;Ohlsson & Rees, 1991).…”

Section: Representational Formatsmentioning

confidence: 99%

“…Some of the students' difficulties with mathematics are caused by the abstract and formal nature of arithmetical representations which do not explicitly show the underlying principles or concepts. Most students tend to view mathematical symbols (e.g., multiplication signs) purely as indicators of which operations need to be performed on adjacent numbers, rather than reflections of principles and concepts underlying these procedures (Atkinson et al, 2003;Cheng, 1999;Greenes, 1995;Nathan et al, 1992;Niemi, 1996;Ohlsson & Rees, 1991). Complicating factor is that combinatorial and probability problems and ideas often appear to conflict with conceptions and intuitions people have (Batanero & Sanchez, 2005;Fischbein, 1975;Garfield & Ahlgren, 1988;Greer, 2001;Kapadia, 1985).…”

Section: Introductionmentioning

confidence: 99%

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The role of external representations in simulation-based inquiry learning

Kollöffel¹

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Mathematics Learning and Knowing: A Cognitive Process

Cited by 12 publications

References 6 publications

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

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

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

The role of external representations in simulation-based inquiry learning

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