Mathematical Wonders: Renaissance Thinkers & Their Impacts

This article is the fifteenth of an ongoing series from EuroClio providing teachers with ideas and practical resources for teaching a range of topics in their classrooms. You can find a wealth of additional resources including units, source collections and eLearning activities on the Historiana website and you can read the other articles in the series here.

Mathematics and Magic: Progress and limitations of mathematics and related sciences during the Renaissance
As part of our growing number of collections on the Renaissance period, Historiana has recently developed a new source collection entitled Mathematics and Magic. The collection examines continuity and change in ideas about mathematics with a focus on some of the most influential thinkers of the time. The collection begins with an examination of some of the Ancient Greeks from whom Renaissance mathematicians drew much of their knowledge and then proceeds to consider a number of mathematical innovations and innovators from the Renaissance. Importantly, the collection also explores some of the limitations of these innovative ideas, whether this was as a result of resistance to new ideas at the time or of the pervasiveness of occult beliefs (such as numerology) in mathematical thinking in this period.

Opportunities for Interdisciplinary Learning
Many schools are increasingly seeking opportunities for students to engage in interdisciplinary learning. Students’ ability to constructively assimilate knowledge, understanding and methods from multiple areas of study is viewed as an essential 21st century skill. This source collection provides an excellent opportunity for teachers from mathematics, science and history departments to work together to develop students’ understanding. The collection refers to several important innovations in mathematical understanding from the Ancient Greek and Renaissance periods. Students would be able to deepen their appreciation of these ideas and their significance with support from expert teachers in the relevant field(s). Team teaching, a coordinated sequence of lessons or even the sharing of mini video lessons could all facilitate such an interdisciplinary learning experience.

Philips Galle, Portrait of Niccolò Tartaglia, Antwerpen, 1572, Rijksmuseum via Europeana

Ideas for Teaching Historical Thinking with this Source Collection
In addition to the opportunities this collection presents for interdisciplinary learning, there are several ways in which it might be used to promote students’ historical thinking:

Continuity and Change: Examine the ideas that changes and those that persisted in the field of mathematics in the Renaissance period.
Perspective-taking: Investigate the perspectives of various groups in this period on particular mathematical ideas. For example: Perspectives of the mathematicians, the Catholic Church, European rulers, occult groups, and so on.
Significance: Draw conclusions about the relative significance of different mathematical ideas or the thinkers themselves.

Mathematician John Dee performing an experiment before Queen Elizabeth I, Henry Gillard Glindoni, Wellcome Collection via Europeana, L0083955 b1465819, ICV No 51391, Iconographic Collection, 47369i, j9xszjzn.

Mathematical Minds: A Combined Online/Offline Lesson on Significant Thinkers
The example eLearning Activity provided on Historiana entitled Mathematical Minds presents a lesson idea which combines online and offline modes of teaching and learning. The lesson aims to develop students’ skills in drawing justified conclusions about historical significance.

Students begin the lesson online. After a brief introduction, students begin by reading about five influential thinkers of the Renaissance period: Tartaglia, Descartes, Copernicus, Dee and Wilkins. As they read, students are asked to highlight parts of the text that refer to new ideas, the use of old ideas and the impacts of innovations in mathematical thinking. This task aims to familiarise the students with these key thinkers and draw their attention to the information that will be most relevant for the next part of the task.

Students are then divided into groups to prepare for a real-life (offline) balloon debate. Balloon debates require students to imagine the key individuals are in a hot air balloon that is sinking quickly. Students must vote to decide which individuals to evict from the balloon to lighten the load one at a time until only one person remains. Representatives of the individuals take turns to convince the audience of the reasons for which they deserve to stay in the balloon. In this task, students representing the mathematicians must convince their peers of the significance of that mathematician to keep their place in the balloon. The balloon debate activity can be adapted to include individuals, events or factors and different criteria (most important, best/worst, etc.) for all kinds of different topics.

After the balloon debate, students return for one last online component. They make their own final assessment of the relative significance of the thinkers which they then justify in a brief paragraph sent to their teacher.

As with all Historiana eLearning Activities, this activity can be saved to ‘My Historiana’ and then edited and adapted for use in your specific classroom context.


Historiana would not be possible without the efforts and generous contributions of historians and educators from Europe and beyondand the support of the Connecting Europe Facility of the European Union.


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