Teaching Conformal Projections

I had a small revelation in class the other day while I was teaching projections. I have an inflatable globe I like to carry to reference an actual 3D representation of the earth when my powerpoints only show a flat sphere.

On my way to class, feeling like a geography professor.

Conformal projections preserve the shape and angles of the world, but distort sizes and distances. A tip-off that a projection is conformal is that the meridans and parallels (latitude and longitude lines) are perpendicular for the whole map. This forms a grid. It’s easy to say this out loud and believe that people will get it, but in reality, projections are rather abstract, adn there’s just not enough time in a class to have everyone do their own actual projection to tangibly connect the abstraction to reality.

On my inflatable globe (and on all other spheroid or ellipsoid representations of the earth), lines of longitude and latitude are always at right angles to each other. Just like in a conformal projection.

  1. Student assesses the ellipsoid globe, looking particularly at the meridians and parallels. Prompt: how would you describe the relationship between these lines? Is if the same for the whole world/ellipsoid? What relationships are the same and what are different?
  2. Look at a world-map projection in a specific format. What is the relationship between the meridians and parallels? Which relationships are consistent and what are not?

With little prompting, the fact that the lat/long line angles are always right angles in both conformal projections and on the globe gets “aha!” faces as the concept of round to flat clicks.

Another finding from bringing this see-through globe to class? Holding it in front of the projector makes azimuthal projections. Helpful for linking the round ellipsoid to the flat projection.

Observation of an Experienced Instructor

I observed Professor X (tenured faculty) teaching a 100-level geography class. I had not taken a class with them, but I had heard that they were engaging, and I had a friend who had previously benefited from observing them. I had seen the syllabus from a prior semester and was pleasantly surprised to see student-centric elements that I had learned about in CITL training about in-class engagement. I was intrigued to observe an instructor who had clearly studied instructing. Professor X did not disappoint! They gave me permission to observe their class and provided me with an updated syllabus, which was even more active, engaging, and learner-focused than the version I had seen previously.

About the Class

The class was a survey of human geography and GIS methods, using a unifying theme to introduce many sub-disciplines of human geography including economic geography, medical geography, and political geography. In my conversation with Professor X, they said that this course is usually a split between engineering seniors who need it as a social science elective and people pursuing a GIS minor, for whom this is a required course. This semester, there were more urban planners than they had seen in previous years. In general, the class is male-dominant (70/30), and is typically attended by traditional students, usually juniors and seniors. In further discussion, they mentioned that ideally, this class would target freshmen, to give them an introduction to human geography, but it serves a practically different purpose now.

Professor X said that their goal with this class session was for students to learn: 1) what kind of questions economic geographers ask and 2) how physical and human location matters to businesses. This lecture had a 15-minute mini-lecture, a 10-minute whole-class discussion activity, a 10-minute individual (group optional) brainstorm, and a 10 minute debrief and group analysis of the brainstorm. I learned after class that the professor had run out of time, and opted to do a longer discussion of the activities and not show a video they had planned.

Setting the Scene

I got to class early, so I could find a quiet spot to observe, out of the way. I asked Professor X where the front of the room was – their response was “This room doesn’t really have a front, but you can sit in that corner. People tend not to sit there.” The classroom for this course is an adaptive classroom, with whiteboards on all four walls, traditional hanging presentation screens on two of them, and airport-style monitors floating from the ceiling. From any seat, it would be impossible to not see a screen. The professor told me that the course had started the semester with a higher enrollment and that they had been using the whole room – they showed me that this room can adapt into three smaller rooms, if necessary. They had trimmed off one room, so the active space used for class was 2/3 of the largest space possible. This adaptive size worked – as the room filled up with students, my table was the only empty one.
Students sat at tables designed to seat 6 – one or two tables had only 3 or 4, and one table was entirely filled with latecomers. This scale seemed to promote student discussion, the room had a gentle murmur as classtime approached.

During the 10 minutes before class, Professor X set up class. First, they put up their intro slide for the day, which had a provocative map of which company has the highest profit in each state. At 10 o’clock on the nose, I heard an alarm clock ring, and saw the professor turn the alarm off on their phone. I have never seen someone have an alarm for class, but it is a lot easier than staring at the clock waiting for it to tick over to start time!

Professor X demonstrated many positive teaching qualities, but I will focus on the three from which I can learn the most: giving clear explanations, stimulating interest in the material, and encouraging discussion and interaction.

Clear Explanations

The class session I observed was the first class after spring break. At the beginning of class, Prof X mentioned this, then immediately went into a review of what the class had covered in the weeks prior to spring break. They used brief slides with only a couple of “subject words” and “topic words” expressing prior weeks’ subjects and topics within them. Most of the content they conveyed was verbal. I noticed that they would give a brief description, then a longer (and different) description, and finally would give an example of something relevant to the prior weeks’ review. Having not been in those classes, I found this beginning of the lecture very accessible and clear.

When they introduced the topic for the day, they were very clear about how much of the topic this class would cover (very little), that if students were interested, there was a whole class just on this topic they could take. One of the topics was about how the location of things matters for shipping – they gave very clear statements about why, for example, certain cities were warehouse hubs: “they are within a day’s drive of 80% of the country.” Using this concrete language helped explain why warehouses have different location requirements than say, a Starbucks, which should be closer to people at work or leisure, and not a long drive from a lot of places.

Stimulating Interest

At the beginning of class, and at the beginning of the lecture, Prof X displayed the map of most profitable companies in each state, and asked students to think about what patterns they saw, if they saw any surprises, and whether they saw particular patterns in the types of businesses or types of services provided. They walked around the classroom during this exercise, and many students participated, contributing their own view on the map. During the lecture part of the class, the professor talked about how their own research was related to the topic they were discussing. Finally, during the debrief of the final exercise, the professor gave a short anecdote or example about every answer that students volunteered. By not only affirming and recording responses but also demonstrating their value by adding their own to it, they kept the room engaged in the topic for the whole 50-minute class period.

Encouraging Discussion

The class was a quiet class (I observed another undergraduate class immediately after and was surprised at how much more the undergraduates talked an hour later and in a different layout room!). However, the class session was very interactive. Before class started, students engaged with the introductory image, and after reviewing the previous week’s topic, they were prompted to talk about it in a whole-class discussion. The professor helpfully linked peoples’ observations about the map to the topics they were about to lecture on.

The second activity was an individual activity, which the quieter tables seemed to be as engaged with as the louder tables. This activity asked students to apply a concept that the professor had just explained – brainstorming different industries that were in different sectors of the economy, then thinking about what location factors were most important to them (ie. Proximity to resources, proximity to many distribution locations, proximity to talent or capital). The professor circulated through the room while people completed the written portion. They encouraged them to talk with their tables and to ask questions.

The third activity was to write these industries and their location factors on different whiteboards (requiring the professor to move around the room). Then the professor had the class look at all of the boards to see if there was a pattern or some summary observations. This summarizing exercise concluded the class session.

While students seemed sleepy and many tables were quiet, it was interesting to observe how some students were more willing to volunteer ideas earlier in the class session, but even the quiet tables volunteered information from their individual tasks at the end of the class. The engaging activities, shorter focus intervals (no more than 15 minutes per activity), and opportunities to engage with the materials in different groupings and at different levels seemed to keep students active on the class, and not on their computers or phones.

My Takeaways

This was a great class to observe. Besides the usefulness of observing very organized group exercises, moments of engagement, and clear explanations, I also saw how it looks to be prepared, have control over time and activities, and add an improvised final group reflection to a class that ran out of time for original plans. I plan to use this kind of class structure – introducing a topic, then enabling engagement with the topic or information at many levels. I will also work on giving a very short definition of words or topics, then expanding to a more refined definition, then presenting an example. This explanatory structure was very clear to me.

My First Informal Early Feedback


In Fall 2016, I did my first Informal Early Feedback (IEF) evaluations after attending a workshop on IEF at the Center for Innovation in teaching and learning.

I was terrified when I gave them the link to my feedback form. I had had a peer review at a summer job one year, and the feedback I got was so scathing that I was deeply afraid of my insecurities as a new teacher being validated by student feedback. I was scared - so much so that I recorded this screenshot in my teaching journal:

After being reassured by my peers and my colleagues that students really aren't harsh, I finally looked at my feedback and was surprised and pleased to have gotten largely positive feedback. Thirteen students had submitted the survey, evenly distributed across my two lab sections. The big number (the one the university rates us on) was TA’s overall teaching effectiveness: 4.2. I knew I had room to improve.

What really helped me identify ways to improve was sitting down and talking through the summary of the student feedback below with Lucas, a CITL expert. We discussed the negative feedback and ways to make the classroom more engaging. The suggestions I implemented immediately were to validate student questions before responding, for example, "good question" or "It's really good that you asked that". To engage students, I shortened the mini-lecture I had been giving at the beginning of the class, and start walking around the classroom to ask students what they were doing, instead of just waiting for people to ask questions.

I presented these findings to students in class the following week.

Please explain (good things TA does, things you think would improve TA effectiveness, things that hinder TA’s effectiveness, etc)

Good things

explaining (3)

making us figure out problems on our own

getting to all questions (classroom management)

speaks loudly and clearly

double checks if you understand

explain thought process

pro tips


makes me feel like the question I asked was poor

answer questions more directly


remind of old terms/skills

About your TA (overall: 4.3)

On a scale of 1 (disagree strongly) to 5 (agree strongly)

4.7 The TA is enthusiastic
4.2 The TA’s explanations are clear
4.3 The TA effectively uses time during lab
4.5 The TA is available for questions
4.5 The TA provides adequate instructions for proceeding with the lab exercises
4.4 TA’s ability to answer questions
3.9 TA’s awareness of how well you understand the lab material (med 4)
4.2 TA’s office hours (med 4)

What is helping you learn in this lab section? How would you improve the lab sessions?

• Would like to watch someone do work
• Prefer more work time (2) More time in lab for lab assignments (independent work)
• Prefer less presentation/lecture (2)
• Helpful to do more tasks on the board
• Learn a lot; wouldn’t change (2) • Determination and patience
• Hard to work with background noise – quieter space (2)
• Would be great do review skills, not do each task once in the book
• Tutorials helpful


Student Self-Reflection

Level of effort (overall: 4.4)
4.3 Level of effort you put into the course (med 4)
4.5 Level of effort you put into in-class exercises

What can YOU do yourself to learn better? Engage self with more questions/ think more/master reasons behind tutorials (2)
Do readings (3)
Take better notes
Do tutorials before class / Work with software at home (2)
Practice more (2)
Ask questions (2)