# Tech in Teaching

### Two Case Studies in Math Service Lectures

Dr. Andreas Steiger, D-MATH

## Linear Algebra for INFK

### Setting

• 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

### Challenge

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!

### Question

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

Discuss in pairs!

## Analysis for MAVT & MATL

### Setting

• 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)

### Challenges

• 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
• 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