NNDK17000U  Diagrams in Mathematical Practice: Philosophical and Cognitive Perspectives

Volume 2017/2018

Various forms of diagrams play a central role in mathematical teaching and research, and yet the role played by diagrams in mathematics is not well understood; in fact, the very concept ’diagram’ does not even have a clear and universally accepted definition. In this course we will investigate the various roles diagrams play in mathematics. On the basis of cognitive and philosophical theories we will shed light on the functions diagrams play in mathematical research. We will explore cases of diagram use, and especially discuss and explore the cases taken from mathematics courses the participants are currently following. After taking this course, students will understand what they do when they use diagrams, and they should be well suited to enter the current debate about the future of diagram use in mathematics. 

Learning Outcome


At the end of the course the students will know contemporary philosohical and cognitive accounts of the role of external artifacts such as mathematical diagrams in human thinking.


At the end of the course students will be able to communicate and discuss meta-aspects of their mathematical practice to others in writing


At the ende of the course students will be able to: 

  • reflect upon his or her own use of diagrams in his or her own mathematical practice
  • analyze and critically assess the use of diagrams in mathematics
  • critically discuss the role diagrams play in contemporary mathematics research practice



A compendium of relevant literature will be used. See Absalon for specifications.

At least one year of mathematics at BSc-level.
Lectures, discussion classes, workshops.
Feedback by final exam (In addition to the grade)
Peer feedback (Students give each other feedback)
7,5 ECTS
Type of assessment
Written assignment
Writtenm assignment throughout the course.
Students must hand in a written essay by the end of the exam week. The essay must address the course literature and it must address philosophical and/or cognitive aspects of diagram use in mathematics. Apart from that students are free to chose their precise topic.
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examinator

Same as ordinary exam

Criteria for exam assesment

The evaluation of the essay will be based on the learning goals of the course. To get the highest mark the essay must demonstrate that the student masters all of the learning goals of the course. 

  • Category
  • Hours
  • Lectures
  • 14
  • Exercises
  • 14
  • Class Seminar
  • 14
  • Project work
  • 80
  • Preparation
  • 84
  • Total
  • 206