The development of a semantic model for the interpretation of mathematics including the use of technology

Michael Peters

Research output: Thesis › Doctoral Thesis

Abstract

The semantic model developed in this research was in response to the difficulty a group of mathematics learners had with conventional mathematical language and their interpretation of mathematical constructs. In order to develop the model ideas from linguistics, psycholinguistics, cognitive psychology, formal languages and natural language processing were investigated. This investigation led to the identification of four main processes: the parsing process, syntactic processing, semantic processing and conceptual processing. The model showed the complex interdependency between these four processes and provided a theoretical framework in which the behaviour of the mathematics learner could be analysed. The model was then extended to include the use of technological artefacts into the learning process. To facilitate this aspect of the research, the theory of instrumentation was incorporated into the semantic model. The conclusion of this research was that although the cognitive processes were interdependent, they could develop at different rates until mastery of a topic was achieved. It also found that the introduction of a technological artefact into the learning environment introduced another layer of complexity, both in terms of the learning process and the underlying relationship between the four cognitive processes.
Original languageEnglish
QualificationPh.D.
Awarding Institution
  • Plymouth University
Supervisors/Advisors
  • Graham, Edward, Supervisor, External person
Publication statusUnpublished - 2010

Fingerprint

semantics
mathematics
interpretation
learning process
artifact
psycholinguistics
language
learning environment
psychology
linguistics
Group

Keywords

  • mathematics education
  • instrumentation
  • technology
  • parsing mathematic constructs
  • conceptual reasoning
  • syntactic reasoning
  • semantic reasoning
  • semantic model

Cite this

Peters, Michael. / The development of a semantic model for the interpretation of mathematics including the use of technology. 2010.
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title = "The development of a semantic model for the interpretation of mathematics including the use of technology",
abstract = "The semantic model developed in this research was in response to the difficulty a group of mathematics learners had with conventional mathematical language and their interpretation of mathematical constructs. In order to develop the model ideas from linguistics, psycholinguistics, cognitive psychology, formal languages and natural language processing were investigated. This investigation led to the identification of four main processes: the parsing process, syntactic processing, semantic processing and conceptual processing. The model showed the complex interdependency between these four processes and provided a theoretical framework in which the behaviour of the mathematics learner could be analysed. The model was then extended to include the use of technological artefacts into the learning process. To facilitate this aspect of the research, the theory of instrumentation was incorporated into the semantic model. The conclusion of this research was that although the cognitive processes were interdependent, they could develop at different rates until mastery of a topic was achieved. It also found that the introduction of a technological artefact into the learning environment introduced another layer of complexity, both in terms of the learning process and the underlying relationship between the four cognitive processes.",
keywords = "mathematics education, instrumentation, technology, parsing mathematic constructs, conceptual reasoning, syntactic reasoning, semantic reasoning, semantic model",
author = "Michael Peters",
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}

Peters, M 2010, 'The development of a semantic model for the interpretation of mathematics including the use of technology', Ph.D., Plymouth University.

The development of a semantic model for the interpretation of mathematics including the use of technology. / Peters, Michael.

2010.

Research output: Thesis › Doctoral Thesis

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T1 - The development of a semantic model for the interpretation of mathematics including the use of technology

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N2 - The semantic model developed in this research was in response to the difficulty a group of mathematics learners had with conventional mathematical language and their interpretation of mathematical constructs. In order to develop the model ideas from linguistics, psycholinguistics, cognitive psychology, formal languages and natural language processing were investigated. This investigation led to the identification of four main processes: the parsing process, syntactic processing, semantic processing and conceptual processing. The model showed the complex interdependency between these four processes and provided a theoretical framework in which the behaviour of the mathematics learner could be analysed. The model was then extended to include the use of technological artefacts into the learning process. To facilitate this aspect of the research, the theory of instrumentation was incorporated into the semantic model. The conclusion of this research was that although the cognitive processes were interdependent, they could develop at different rates until mastery of a topic was achieved. It also found that the introduction of a technological artefact into the learning environment introduced another layer of complexity, both in terms of the learning process and the underlying relationship between the four cognitive processes.

AB - The semantic model developed in this research was in response to the difficulty a group of mathematics learners had with conventional mathematical language and their interpretation of mathematical constructs. In order to develop the model ideas from linguistics, psycholinguistics, cognitive psychology, formal languages and natural language processing were investigated. This investigation led to the identification of four main processes: the parsing process, syntactic processing, semantic processing and conceptual processing. The model showed the complex interdependency between these four processes and provided a theoretical framework in which the behaviour of the mathematics learner could be analysed. The model was then extended to include the use of technological artefacts into the learning process. To facilitate this aspect of the research, the theory of instrumentation was incorporated into the semantic model. The conclusion of this research was that although the cognitive processes were interdependent, they could develop at different rates until mastery of a topic was achieved. It also found that the introduction of a technological artefact into the learning environment introduced another layer of complexity, both in terms of the learning process and the underlying relationship between the four cognitive processes.

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KW - technology

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KW - conceptual reasoning

KW - syntactic reasoning

KW - semantic reasoning

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M3 - Doctoral Thesis

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Peters M. The development of a semantic model for the interpretation of mathematics including the use of technology. 2010.

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