How high is the tramping track? Mathematising and applying in a calculus model-eliciting activity

Two complementary processes involved in mathematical modelling are mathematising a realistic situation and applying a mathematical technique to a given realistic situation. The authors present and analyse work from two undergraduate students and two secondary school teachers who engaged in both proc...

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Bibliographic Details
Published in:Mathematics education research journal 2010-09, Vol.22 (2), p.141-157
Main Authors: Yoon, Caroline, Dreyfus, Tommy, Thomas, Michael O. J.
Format: Article
Language:English
Subjects:
Calculus
Cognitive processes
College Mathematics
Data interpretation
Education
Educational Benefits
Foreign Countries
Individualized Instruction
Integrals (Mathematics)
Knowledge Level
Mathematical applications
Mathematical Concepts
Mathematical Models
Mathematical thinking
Mathematics
Mathematics Education
Mathematics Instruction
Methods
Modelling (Mathematics)
New Zealand
Pilot projects
Problem Solving
Secondary School Mathematics
Secondary School Teachers
Teaching Methods
Theoretical analysis
Undergraduate Students
Undergraduate study
University mathematics
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Summary:Two complementary processes involved in mathematical modelling are mathematising a realistic situation and applying a mathematical technique to a given realistic situation. The authors present and analyse work from two undergraduate students and two secondary school teachers who engaged in both processes during a mathematical modelling task that required them to find a graphical representation of an anti-derivative of a function. When determining the value of the anti-derivative as a measure of height, they mathematised the situation to develop a mathematical model, and attempted to apply their knowledge of integration that they had previously learned in class. However, the participants favoured their more primitive mathematised knowledge over the formal knowledge they tried to apply. The authors use these results to argue for calculus instruction to include more modelling activities that promote mathematising rather than the application of knowledge. [Author abstract, ed]
ISSN:1033-2170
2211-050X
DOI:10.1007/BF03217571