4. april 2018

How many people have ever lived? A study and research path

"How many people have ever lived? A study and research path" - [10Mb]

 IND's studenterserie nr. 60. Specialerapport. Matematik.

Lasse Damgaard Christensen, marts 2018. 

Vejleder: Carl Winsløw


This thesis describes the testing and analysis of a Study and Research Path (SRP) on a classical question from mathematical demography. The hypothesis of the study has been that an SRP on demography can give high school students an insight into how mathematical methods can be used to answer questions in the social sciences. Specifically the SRP concerned the generating question: “How many people have ever lived? ”.

The Anthropological Theory of Didactics (ATD) has been used as a theoretical framework for the study and an epistemological reference model (ERM) has been developed. We have first performed our own study and research of the question and found that it can be answered in multiple ways. The most prominent methods focused either on modelling yearly births as a function of time in order to calculate a definite integral or on modelling the population size as a function of time in order to calculate the integral and divide this with an estimate of an average life expectancy. We have then designed a teaching sequence and made an a priori analysis of it. In the a posteriori analysis we have focused on which questions the students developed, how students used media and students’ praxeologies regarding integration and interpolation.

We have found that students developed questions similar to those in the a priori analysis which could be divided into three branches: counting deaths, counting births and counting “person-years”. The students mainly studied media to gain information on the origins of man and to find demographic data. Only little media on the methods for calculating an answer was found and it was not studied in depth. A better study of such media might have given a greater variety in successful methods used by students. Regarding both interpolation and integration students almost exclusively used techniques involving CAS. We have found that students know the praxis parts well but that their knowledge of the theory on both regression and integration is lacking. Other studies have suggested that more focus on giving students an interpretation of the definite integral as a Riemann sum may alleviate the problem.