The Role of Representation(s) in Developing Mathematical Understanding

Pape, Stephen J.; Tchoshanov, Mourat

doi:10.1207/s15430421tip4002_6

Cited by 215 publications

(145 citation statements)

References 10 publications

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“…Thus, pupils need to learn to work with representations using symbols and schemes. Pape and Tchoshanov (2001) propose that representations are an important feature of mathematics.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

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Schematising activities in early childhood education

Poland¹,

Oers²,

Terwel³

2009

Educational Research and Evaluation

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The purpose of this study was to determine the importance of introducing schematising to children in early childhood and to determine whether schematising can be taught to children. This was done using a longitudinal, quantitative study with a quasi-experimental design (N ¼ 133). In this study, the use of schematising was taught to an experimental group of children to determine if it is possible to realise significantly improved results in schematising tasks for an experimental group in comparison to a control group of children who were not taught schematising. Pupils in the experimental group demonstrated significantly better results on schematising, which cannot be explained by maturation. In our future research, we will investigate the mathematical performances of these experimental and control groups in the next grade of the primary school curriculum.

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“…Thus, pupils need to learn to work with representations using symbols and schemes. Pape and Tchoshanov (2001) propose that representations are an important feature of mathematics.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…Consequently, according to Pape and Tchoshanov (2001), in mathematics education, representations must be thought of as tools for reasoning, explaining, and justifying. Educators should teach children the function of these tools.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Schematising activities in early childhood education

Poland¹,

Oers²,

Terwel³

2009

Educational Research and Evaluation

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“…Presenting students with multiple representations of the same data recognizes different learning styles and allows a student several possible ways to connect initially with the information. A strong understanding of how the representations are related increases the robustness of students' understanding and their ability to transfer this learning to new situations [Pape and Tchoshanov, 2001]. Technology offers many new opportunities to visualize and manipulate data that can help students make connections between different representations.…”

Section: Strategies For Successful Quantitative Teachingmentioning

confidence: 99%

Making Undergraduate Geoscience Quantitative

et al. 2008

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Modern geoscience uses equations, models, and numbers in conjunction with observations, maps, and words as fundamental tools for investigating Earth. Yet the U.S. public persists in viewing the study of Earth processes as highly qualitative and, in many states, as a remedial science course that is not accepted as appropriate preparation for admission to U.S. colleges and universities. Geoscience teachers and faculty are working to change this perception by increasing the quantitative content of the geoscience curriculum. From the most mathematical of senior theses to the most basic of introductory courses, geoscience instructors can make these courses more reflective of the full range of tools used in the geosciences by including the quantitative content and methods that pervade geoscience. In addition to being provided with a more realistic perception of our science, college students whose major study is the Earth sciences will be better prepared for geoscience careers and all of our students will be more quantitatively literate.

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“…Thus, pupils need to learn to work with representations using symbols and schemes. Pape and Tchoshanov (2001) propose that representations are an important feature of mathematics. Consequently, according to them, in mathematics education, representations must be thought of as tools for reasoning, explaining and justifying.…”

Section: Why Learn To Schematise?mentioning

confidence: 99%