Photo of empty lecture hall

Five lessons from designing and delivering lectures for the first time

Photo of empty lecture hall
Photo credit: unsplash, Po Hsuan Huang, CC0

In this extra post, Josh Fogg offers five lessons from designing and delivering their first set of lectures as an early career academic. Josh is a University Tutor in Mathematics, and an Optimization and OR PhD Student in the School of Mathematics.


In 2023/24, I was given the exciting opportunity to design and deliver lectures for first year Engineering and Natural Sciences students, introducing them to new concepts such as complex numbers, matrices, and parametric differentiation. I’d tutored in the School of Mathematics for four years, but this was to be my first-time teaching in a lecture context.

Now, at the other side, I’ve been reflecting on the experience. While it certainly wasn’t without error – and I fell into many a pitfall – I learnt so much. I hope these thoughts are helpful for any earlier career academics preparing to set out on their own lecturing journey!

1. Preparing takes so much time

The harshest and most abruptly apparent lesson was that it takes far more time to write and refine lecture content than I’d realised. Having worked in the School for several years at this point, I understood full well that prep isn’t a quick job. I had seen lecturers pouring over slides in the common room and heard my PhD supervisor talk about his experience too. Even with that, I still didn’t really appreciate that for every hour of lecture there would be several hours of prep to do beforehand.

This gap between expectation and reality came from not considering the many sub-tasks involved. It’s not just a case of creating the slides (for me with Overleaf, the best tool given the amount of mathematical content) but also ensuring that the narrative between slides was cohesive, that each lecture tied into what students have already seen, and that a reasonable balance was struck between key content and exposition.

It all became easier with practice for sure, and by the third lecture I was much better at predicting how long preparation would take. By far the lesson that surprised me the most though was this disparity between expectations and reality.

2. Just because you know, doesn’t mean you can explain

Another uncomfortable home truth was that I didn’t have an intuitive way to explain many basic key concepts that I’ve used without thought for years. I’d naively assumed that given how often I use them in my own work, in some cases having even tutored on them in workshops, that I’d be able to explain them from scratch in a lecture too.

While, thankfully, I realised this before the day in most cases, on one occasion I was humbled when several students left a lecture on implicit differentiation not understanding the fundamental “why’s” of the method. This had a knock-on effect of creating more work, as I needed to explain the idea again to confused students outside classes.

This wasn’t a lesson I had to learn twice! Particularly when delivering content for the first time, it ran far smoother when I practiced explanations of the core concepts during prep.

3. Prepare examples ahead of time

Speaking of added work that I brought upon myself: prepare all examples ahead of time! In a lecture on finding the inverse of matrices, I finished 15 minutes earlier than planned (more on that later). I thought it would be useful (and students agreed by show of hands) to go through an extra, larger example. This was a good idea.

However, it was not a good idea to ask students to shout out random numbers to populate the entries of the example. The result was a matrix which had a ludicrous determinant (286) and had me sweating buckets as I tried to work through “(4 × -16) – (6 × -20) + (5 × 46)” on a blackboard in front of several hundred students. In the end, the example took too long to finish in the extra time, so I wound up writing it up again in full afterwards anyway.

Making use of this extra time with an example was well received by students, but it could have been a much better experience for both them and me if I’d considered creating some extra examples beforehand. Even if they hadn’t been used, this wouldn’t even have been wasted work – they could just have gone on the tutorial question sheet for the next week.

4. Pacing will never suit everyone

Timing and pacing are not a problem unique to lecturing, and are notoriously difficult to get right when presenting in any context. We have all been at that seminar where someone busted out their 50-slide deck for a 30-minute talk, or where that nervous presenter raced through and finished hilariously early.

With lecturing, though, the variance in paces people are comfortable with will just be that much higher. That’s coupled with the fact that, if you go too slow, not all the content they must see will be covered, and, if you go too fast, you risk the majority not following it and creating more work recapping later.

It’s never going to be possible to meet everyone’s preference, but thankfully there’s a lot that can be done to mitigate that:

  • Provide lecture slides ahead of time (preferably with notes)
  • Ensure lecture recordings are set up to correctly capture all the content presented
  • Use tools like Wooclap, which let students access the presentations asynchronously on local devices.

These tips are all also good practice for accessibility, enabling as many of your students to engage with the content as possible.

5. Coming up with problems is spicy

As well as teaching delivery, I was given responsibility for one of the course’s workshop problem sheets. In workshops, students work in small groups on a small set of problems related to the last week’s content, and are encouraged to discuss them with each other, while being supported by tutors.

Like with lecture prep, I understood it was non-trivial to come up with good questions, but I’d still not appreciated the time it would take. It was tough ensuring that questions started easier (e.g., basic parametric differentiation) but ramped-up to edge cases students needed to see examples for (e.g., higher parametric derivatives).

The problem of setting problems only gets more difficult for exams, which was my final task. Striking the balance between having an accessible starting point while also having challenging components to differentiate the highest achieving students was so difficult.

Aside from that, and other expected challenges about error-free content, an unforeseen challenge was slight deviations in terminology between the course and its textbook, and the ordering of questions within the exam paper itself. Working with the course organiser, other lecturers, and previous staff on the course helped to minimize the risk here.

Conclusion

While some moments were hairy for sure, it’s important to stress that lecturing was such an enjoyable experience. Positive student feedback and the satisfaction of teaching a topic I’m passionate about was so rewarding. Having this experience was outwith expectations for the year, so I’m incredibly grateful to David Quinn for the opportunity, and hope that it’s the first of many!


photo of the authorJosh Fogg

Josh Fogg has been a tutor in the School of Mathematics since 2019/20. In 2023/24, they were a cover lecturer for Engineering Mathematics and Mathematics for the Natural Sciences. Josh is an Optimization and OR PhD Student in the School of Mathematics.

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