Mini-Workshop: Studying Original Sources in Mathematics Education
Authors: Furinghetti Fulvia , Jahnke Hans Niels , van Maanen Jan A. 
Published: December 2009

1. General background

In the last thirty years quite some initiatives evolved and much material was developed for using the history of mathematics in the teaching of mathematics at all levels. There is a growing consensus that historical work of pupils and students may contribute to further through:

Among the various possible activities by which historical aspects might be integrated into the teaching of mathematics, the study of an original source is the most demanding and the most time consuming. It requires a detailed and deep understanding of the mathematics in question, of the time when it was written and of the general context of ideas. The aspect of language becomes important in ways which are completely new compared with usual practices of mathematics teaching. Thus, reading a source is an especially ambitious enterprise, but rewarding and capable of substantially deepening the mathematical understanding.

In principle, the aims and effects which might be pursued through the study of an original source will not be different from those attained by other types of historical activities. However, there are some ideas which are specifically supported by reading mathematical sources.

2. Theoretical and practical orientations

The mini-workshop comprised sessions of different types. Most of the meetings were devoted to traditional presentations of papers. On the other hand, in some sessions the participants discussed the needs and aims of the future development of the field. As a result, research questions were identified which evolved from work in the past and might be helpful in orienting future work. They reflect central issues related to the integration of original sources from the history of mathematics into mathematics education. Each of the questions addresses both the learning of mathematics (by secondary school and university students and by prospective or in-service teachers) and the teaching of mathematics (at the secondary and university levels). In both cases, each of the questions retains its general formulation; however, each is approached differently by the authors according to the target population and their intended educational goals. Thus each question may have more than one answer.

Another issue that came up in the workshop was the problem of upscaling. There is no reason to believe that teaching which is done by an enthusiast with good results can easily and successfully be repeated by the average teacher. It is a welcome development that new materials are being published and that research is being done on projects where “average teachers” are doing the teaching.

In many countries mathematics education standards are in the process of being elaborated. These standards often appear as collections of mathematical problems. The approach of reading sources can be successful in the future only if the community will produce problems in a format adequate to be included among these standard problems. Some contributions during the meeting showed that this is in fact possible.

A related issue is the important role history of mathematics, particularly the reading of sources, might play in the training of teachers for all levels. Studying sources can provide awareness for subtleties in the meaning of mathematical concepts which cannot be afforded otherwise. Thus, the sensitivity of teachers in regard to content-related difficulties of their students might be considerably enhanced. The workshop showed that many activities are in place worldwide which try to take advantage of an approach which includes the study of sources.

3. The Workshop

Most of the contributions during the workshop were related to and inspired by one or more of the research questions outlined in the previous section.

The organizers thank the Institute staff for providing a comfortable environment to the participants.