Tech in Teaching

Two Case Studies in Math Service Lectures

Dr. Andreas Steiger, D-MATH

Case 1:

Linear Algebra for INFK


  • Type: Mandatory first year service lecture
  • Size: 300 students in one well equipped lecture hall, plus exercise classes
  • Style: Traditionally taught by writing on the blackboard
  • Materials: Script available to everyone
  • Content: Abstract mathematics and algorithms; Need for high precision


Algorithms are introduced as baby versions and later extended. How to present such extensions without copying the whole basic algorithm to the blackboard again?

Typical solution: Use slides on the projector

Problem with that: No persistence. Unable to show the algorithm and a sample computation at the same time.

Solution: Use Black

Only use the upper part of the projector canvas, fill the lower part with black!




  • Which challenges do you encounter when presenting your material?
  • How do you use the classroom equipment, and why?


Discuss in pairs!

Case 2:

Analysis for MAVT & MATL


  • Type: Mandatory first year service lecture
  • Size: 650 students in one lecture hall and a live stream to a second hall, plus exercise classes
  • Style: Traditionally taught by writing on the blackboard
  • Materials: Script available for purchase
  • Content: Many theorems and computations by hand
  • Video podcast available to students (my choice)
  • Exercises already contain automatically graded MC questions


  • Lecture always at 8-10, students are tired or less likely to come
  • Little feedback on how the class is doing
  • Content is sometimes abstract, difficult to get an intuition
  • Using the blackboard is messy and takes time

Year 1: Introducing EduApp

Ask one MC question 25-30 minutes into each 45 minutes of lecture time

  • Wakes students up
  • Makes them to use the new material
  • Feedback for students and for me

Open a Feedback Channel in EduApp

  • Students can ask questions outside of classroom time
  • More feedback for everyone

Year 2: Introducing GeoGebra

GeoGebra is a free and easy to use software to visualize geometric objects in 2D and 3D while allowing algebraic manipulations

  • Large online repository of applets freely available
  • Did not have time to develop own applets, simply copied from others
  • Strongly helps students getting a grasp of what's going on in 3D analysis
  • No crappy blackboard drawings anymore

Year 3: Introducing Xournal

Switched from blackboard to digital notebook writing

  • Whole lecture now taught on projector, no more going back and forth
  • Digital notes are easy to edit, during and after class
  • PDF of my proof-read notes available to students
  • Drawing in Xournal is faster, easier and clearer than on blackboard

Year 3: Innovedum Grant for GeoGebra Applets

Hired a scientific assistant to create a complete set of GeoGebra applets for my whole course

  • Designing applets for classroom and student use, tailored to our standards
  • Writing new exercises involving the applets
  • Creating a style guide and best practices on how to use GeoGebra in this setting
  • Sharing applets with lecturers teaching similar classes

More advanced GeoGebra applet: Tangent planes and the total differential, requires NETHZ login

Also available for students on the web (mobile compatible!)

Lessons learned (General)

  • Take small steps, improve incrementally, polish the material from previous years
  • Every change takes preparation and practice
  • Have a fallback ready in case your tech breaks down
  • Keep an overview of how you teach and what your changes do
    • My case: Blackboard cleaning was an important mini-break for students. I now spend more time reviewing where we are and what we've done so far on that day

Lessons learned (Technical)

  • Cable internet is much more reliable than wireless
  • Prepare all digital media/browser tabs before class, bring your laptop ready to go
  • Set up your laptop distraction-free, e.g.:
    • Quit programs with notifications (e-mail etc.)
    • Use a different, clean browser in class than for your daily work
    • Use full screen modes whenever possible, also in browsers
    • Use virtual desktops/workspaces to switch seamlessly between content

What challenges did you face when using technology?