### Abstract

by increasingly powerful information technologies (IT), has lead, and leads to

increasingly widespread use of mathematical models. This development gives

rice to a democratic problem: How can ordinary people judge the conclusions

delivered by mathematical models? Are the conclusions to be believed, since

“mathematics do-not lye”? Or is it better to lean on the saying: “there are

lies, damned lies and statistics”?

In the paper, I will illustrate a crude distinction between mathematical models

derived from theories, and ad hoc mathematical models without reference to

more global theories.

The distinction cannot be used to evaluate, whether specific models are hiding

or guiding. Theory-derived models may be too idealized to be trusted. And ad

hoc models may be trustworthy due to their richness of input data.

The value of the distinction is that it makes it clear that some mathematical

models, the theory-derived models, besides of the possibility of evaluating

them by comparing with empirical data, also can be evaluated by theoretical

considerations. Evaluating ad hoc models are, in contrast, restricted to be

done by empirical control only.

Thus, the distinction between theory-derived models and ad-hoc models may

help ordinary people, not to distinguish between trustworthy and nontrustworthy models but to distinguish between the different qualities of the

evaluation processes behind different sorts of models.

Original language | English |
---|---|

Title of host publication | Mathematics as a Bridge Between the Disciplines : Proceedings of MACAS-2017 Symposium |

Editors | Claus Michelsen, Astrid Beckmann, Viktor Freiman, Uffe Thomas Jankvist |

Number of pages | 14 |

Place of Publication | Odense |

Publisher | Laboratorium for Sammenhængende Uddannelse og Læring |

Publication date | 2018 |

Pages | 15-28 |

ISBN (Electronic) | 978-87-92321-27-5 |

Publication status | Published - 2018 |

### Bibliographical note

Symposium held at Danish School of Education, Aarhus University, Copenhagen 27-29 juni, 2017### Cite this

*Mathematics as a Bridge Between the Disciplines: Proceedings of MACAS-2017 Symposium*(pp. 15-28). Odense: Laboratorium for Sammenhængende Uddannelse og Læring.

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*Mathematics as a Bridge Between the Disciplines: Proceedings of MACAS-2017 Symposium.*Laboratorium for Sammenhængende Uddannelse og Læring, Odense, pp. 15-28.

**Mathematical modelling - hiding or guiding?** / Jensen, Jens Højgaard.

Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review

TY - CHAP

T1 - Mathematical modelling - hiding or guiding?

AU - Jensen, Jens Højgaard

N1 - Symposium held at Danish School of Education, Aarhus University, Copenhagen 27-29 juni, 2017

PY - 2018

Y1 - 2018

N2 - The increasing scientific management of technology and society, supportedby increasingly powerful information technologies (IT), has lead, and leads toincreasingly widespread use of mathematical models. This development givesrice to a democratic problem: How can ordinary people judge the conclusionsdelivered by mathematical models? Are the conclusions to be believed, since“mathematics do-not lye”? Or is it better to lean on the saying: “there arelies, damned lies and statistics”?In the paper, I will illustrate a crude distinction between mathematical modelsderived from theories, and ad hoc mathematical models without reference tomore global theories.The distinction cannot be used to evaluate, whether specific models are hidingor guiding. Theory-derived models may be too idealized to be trusted. And adhoc models may be trustworthy due to their richness of input data.The value of the distinction is that it makes it clear that some mathematicalmodels, the theory-derived models, besides of the possibility of evaluatingthem by comparing with empirical data, also can be evaluated by theoreticalconsiderations. Evaluating ad hoc models are, in contrast, restricted to bedone by empirical control only.Thus, the distinction between theory-derived models and ad-hoc models mayhelp ordinary people, not to distinguish between trustworthy and nontrustworthy models but to distinguish between the different qualities of theevaluation processes behind different sorts of models.

AB - The increasing scientific management of technology and society, supportedby increasingly powerful information technologies (IT), has lead, and leads toincreasingly widespread use of mathematical models. This development givesrice to a democratic problem: How can ordinary people judge the conclusionsdelivered by mathematical models? Are the conclusions to be believed, since“mathematics do-not lye”? Or is it better to lean on the saying: “there arelies, damned lies and statistics”?In the paper, I will illustrate a crude distinction between mathematical modelsderived from theories, and ad hoc mathematical models without reference tomore global theories.The distinction cannot be used to evaluate, whether specific models are hidingor guiding. Theory-derived models may be too idealized to be trusted. And adhoc models may be trustworthy due to their richness of input data.The value of the distinction is that it makes it clear that some mathematicalmodels, the theory-derived models, besides of the possibility of evaluatingthem by comparing with empirical data, also can be evaluated by theoreticalconsiderations. Evaluating ad hoc models are, in contrast, restricted to bedone by empirical control only.Thus, the distinction between theory-derived models and ad-hoc models mayhelp ordinary people, not to distinguish between trustworthy and nontrustworthy models but to distinguish between the different qualities of theevaluation processes behind different sorts of models.

M3 - Book chapter

SP - 15

EP - 28

BT - Mathematics as a Bridge Between the Disciplines

A2 - Michelsen, Claus

A2 - Beckmann, Astrid

A2 - Freiman, Viktor

A2 - Jankvist, Uffe Thomas

PB - Laboratorium for Sammenhængende Uddannelse og Læring

CY - Odense

ER -