# Teaching by Slides, Yes or No?

Mathematicians use (Powerpoint/Beamer) slides for their lectures. My question is about using slides for teaching math. There are several positive and negative arguments about teaching by slide show. e.g.

Positive: One can show many mathematical processes by animations in Powerpoint. This will help students to find a better intuition about what is happening in the subject.

Negative: Students cannot follow slides as good as blackboard because the lecture speed in slide based lectures is higher than blackboard based teaching method.

Question. What are possible advantages and disadvantages of teaching math by slides? How should one use slides for teaching math such that its disadvantages become minimum.

• Results on slides: OK. Proofs on Slides: Not OK. – Gamma Function Mar 22 '14 at 3:19
• Do you mean to be asking about Poewerpoint (a piece of softawre from Microsoft) specifically or using computer presentations in general. – quid Mar 22 '14 at 10:58
• Also desirable: Answers detailing research on this. As opposed to anecdotes and opinions. – Gerald Edgar Mar 22 '14 at 18:49
• @quid: Somehow both! Beamer as the mathematical alternative of Powerpoint is more limited (or complicated to use) in features like designs, animations, movies, sound,... – user230 Mar 23 '14 at 1:48
• If you get a tablet laptop, you can do what my discrete math professor did and get the best of both worlds: slides you can write on during the presentation! – LinearZoetrope Apr 6 '14 at 12:22

First, a little background. I switched to slides a few years ago when teaching a 3rd year course at my university. Because of how teaching works at my university, this course is one of the first where as a lecturer I can assume that the students taking it are interested in mathematics as a subject in its own right. That is, they aren't students from another program taking it because it is required of them. This doesn't mean that they are all mathematically sophisticated -- in fact, they tend not to be -- but rather that they are expected to learn about how to do mathematics from the inside. So there are proofs, and proof techniques, and the like. It's also a fairly diverse course with topics from metric spaces to linear algebra to Hilbert spaces. (Finding a common theme through that lot was one of my difficulties in the early days!) Lastly, for background, I teach in English but the majority of my students have Norwegian as their primary language.

I taught the course using chalk the first time that I taught it, and then switched to slides the second time. I then taught it three times using slides before it passed on to another lecturer. The last time that I taught it, I was awarded the faculty prize for "Teacher of the Year", primarily for that course. I won't say that it was the slides that won it, I mention that to show that it was part of a general strategy that worked. On that, I can also mention that enrolment in this course also increased over the four years that I taught it, to almost double its initial numbers. Also worth knowing are that I experimented with slides before this course with a half-and-half method (on a different course) and it was the feedback from that which convinced me to try the full method, and that after teaching that course then I also taught a lower level course with slides and for that course then I have moved back to using chalk.

Here's what I was thinking when I switched, plus some commentary on whether it worked as I expected.

My primary consideration in switching was to consider the question "Where is a student's attention during the lecture?"

I completely agree with the theory that students learn by doing, and I love the idea of an inquiry-based course and of interactive lectures with communication in both directions. However, I'm not convinced that the lecture has to be where the students learn. In a course like this one, I saw the lecture primarily as the demonstration where the students would see what they should do and then they would go to their own labs and try it out. So the lecture is primarily to communicate mathematical thinking. Yes, a lot of knowledge as well, but never bare facts (definitions or theorems or even proofs) - every definition comes with a story[1] as to why it is that definition and not another, every proof is ladled with detail as to why each step is the natural one.

In this, then, the desired focus of the students is on me. I am trying to demonstrate what is going through a mathematician's head when (s)he contemplates a mathematical problem.

So what happens with a chalk talk? I say something, the students obediently listen, then I write something which the students obediently copy down. I then wait for them to finish writing, which some do quickly and some do slowly, before saying the next thing which half of them miss because they're still copying down the last thing I wrote. In addition, some of them are having difficulty copying stuff down because I wrote it in English and their mental error-checking codes are set up for Norwegian.

Using slides gives me the following advantages:

1. No time is wasted through writing. What I write appears on the screen so I don't waste time. I always make my slides available in advance (as both "presentation" and "handout" versions) so the students do not need to copy things down during the lecture: they can print them out and bring them along and make additional notes if they want but don't have to.

2. I know exactly what the students are looking at. Yes, when new stuff appears on the slide then the students look at the slide and read it, but I control when that appears and I know what it will be.

3. The students know what we will cover. They can see the slides beforehand and read them (if they want). I also provide references to the text book(s) or other resource pages for background material.

4. The students know that they will have the notes that I meant them to have. So they don't need to worry about missing a word in a definition or misreading a symbol.

I'm not quite sure where to put this next point so I'll put it here for lack of anywhere else. I only switched to slides when I knew that the technology could support it. I did not want to remove the flexibility of chalk so I needed to know that I could go "off piste" if necessary. To that end, I started out using a graphics tablet with (a slightly hacked version of) xournal. Once I had an iPad, I switched to that. My handwriting leaves a little to be desired, but nevertheless is workable. In addition, I supported the in-lecture material with a wiki and a forum to provide out-of-lecture support. This is how I got around the perceived inflexibility of slide lectures. The annotated slides were published after the lecture, so if I wrote something on the slide then the students didn't have to copy it down as they knew they'd get access to it later that day (this is one reason why I heartily dislike using slides and chalk, the other reason is to do with the lighting in the lecture hall).

Once I'd embarked on using slides, I encountered other advantages:

1. It forced me to prepare in advance and prepare well. Since my plan was to get the lecture notes up in time for the students to print off before the lecture, I had to have the lecture prepared the day before, not the hour before. In addition, as the notes were what the students would see and not just hints for what I wanted to write, I had to check them carefully. So I couldn't assume "Oh, I know how to do this" and not bother to prepare each example carefully.

2. It forced me to keep to time. I integrated my slide preparation with my lesson plan so I had planned how long to spend on each topic. If I changed the timings in my lecture then I had to have a very good reason for doing so. Note that I could change my timings, but wouldn't do so on a whim.

3. It forced me to think very carefully about what the students could see. It quickly became clear that the best slide was a blank slide, and that it stops being optimal when you start adding content. So the trick is to figure out just what you want the students to be able to see at any given point and put just that on the slide.

4. It forced me to think from the students' perspective. Since slides put me in full control of the lecture hall, I had to think a lot more about how the students would react and what they would need to know and when.

5. It gave me more flexibility in how to present material. Of course, once can always go too far (and some may argue that I did), but I think that it is much easier to be creative with slides than with chalk. An example that springs to mind is stepping through the proof of why the space of continuous functions is complete. I would have the same "slide" with small changes each time and a commentary on what was happening in each step.

6. In addition, once the computer (or iPad) is in the room and switched on, it becomes easy to use further functionality, such as animations or videos. It's all very well to talk about the SVD of a matrix, but there's a nice animation of why it works for 2x2 which makes it much clearer.

The main disadvantage that I encountered with using slides was the time taken to prepare the material. And even though I could re-use them the next time, I still wanted to tweak them and so it didn't cut down as much as I'd hoped.

All that said, as I mentioned above then I've stopped using them in the lower level course that I currently teach. I'd say that my main reason for doing so was that I felt that the students didn't know how to cope with maths being taught via slides. I don't think that they knew what to do with themselves in the lecture hall: they came to get a set of lecture notes and since that was being provided for them without them needing to do anything else, they didn't do anything else. So ultimately, whether they work or don't will depend on the students. The goal is to get the students learning and if they can't or won't learn from slides, there's no point in using them.

You can find slides from my lectures from links on my teaching page. The course that I'm talking about above is TMA4145; TMA4190 was my half-and-half experiment; TMA4115 is the lower level course. Some of the notes are located on the mathsnotes wiki, linked from the above teaching page.

[1] I don't mean anecdote here. I mean more in the flavour of an explanation.

• Very Very Nice. Thank you very much Andrew. – user230 Mar 24 '14 at 12:07
• I am still not sold on the idea of teaching with slides, but the answer is great: it makes a good case for them while being still very balanced. Perhaps I should give it a try once. – quid Mar 24 '14 at 13:45
• @quid Perhaps I should say this a bit more strongly in the above: teaching with slides works if and only if both the lecturer and the students think it will, and of those the most important - by a long chalk - is the lecturer. So if you are not "sold", don't do it. But if some of the above makes you think "Maybe" then give it a try. My half-and-half method might be something to experiment with, for example. – Loop Space Mar 24 '14 at 14:08
• I would like to highlight this part of the answer for those who want to reach a combination between slide and chalk based teaching methods: I heartily dislike using slides and chalk, the other reason is to do with the lighting in the lecture hall. It is a really important problem because when you are using slides, the classroom should be dark and when you write on the blackboard you need light. Switching frequently between these two situations (if it is possible for lecturer) could cause a very bad feeling in audiences. – user230 Mar 24 '14 at 14:50
• Fantastic answer! I really like the idea that preparing slides can force you to "polish" a lecture in a way that you can't when using the chalkboard, and I like the point of view that it's ok for a lecture to be non-interactive as long as you think of it as a "demonstration". I also hadn't considered the possibility that slides might work better for upper-level classes than for lower-level ones. – Jim Belk Mar 24 '14 at 15:24

I know a lot of people use slides to teach, but I cannot imagine doing so myself. Here's why:

1. Slides are boring. It's vital to good teaching to keep the students interested in what's happening, and one of the best ways to do this is to keep things spontaneous. Slides kill spontaneity.

2. Slides are one-way. They are entirely about the professor conveying information to the students. But this isn't how a classroom should work at all -- there should be a give and take between the students and the professor, with the professor responding to students' questions, and deciding what to do next based on how well the audience seems to understand things so far.

3. Slides are inflexible. What do you do during class if a student asks a question and you decide to talk about something unexpected for 20 minutes? What if your lesson plan isn't working and you decide that you need to talk about some prerequisite topic for most of class? Using slides forces you to stay on a certain track.

That being said, there is a huge advantage to having good pictures or animations for certain topics, and in some classes I routinely have my laptop attached to the projector for this purpose. But I see a huge difference between showing pictures and animations vs. having "bullet-list" style PowerPoint slides. Among other things, pictures and animations are interesting, and bulleted lists of talking points are not.

• "No", "No", and "No". Slides don't have to be boring, nor one-way, nor inflexible. You just need to think best how to use the medium. – Loop Space Mar 22 '14 at 18:53
• I'm bookmarking this question in order to write a proper answer! But it might not be until after the weekend. – Loop Space Mar 22 '14 at 18:58
• I've never considered teaching with slides myself, but what strikes me about your list of reasons is that I've heard all of them given as arguments against lecturing altogether. – Mark Meckes Mar 23 '14 at 11:13
• @MarkMeckes Interesting . . . so you're pointing out that slides can be made to work by a good teacher, in the same way that "lecture" can be made to work. I suppose that's true, but I'm still having trouble seeing the advantages of slides, at least for me. – Jim Belk Mar 24 '14 at 6:02
• Actually I'm only making a weaker point: the same criticisms you make of slides are applied by some people to any method of lecturing. And we both agree that they are not valid criticisms of well-done lectures. But I've never taught with slides myself, or thought about how I would do it, so I'm also not making claims about how using slides well could work. I'm hoping that @AndrewStacey will share his thoughts, though we already have a couple other good answers about that. – Mark Meckes Mar 24 '14 at 8:07

Slides are great... if you know how to use them correctly.

• It works without blackboard (e.g. at a conference, or unprepared lecture room, sometimes even a pale wall will do if at some unusual venue).
• You can present pretty pictures (and animations) that would take ages to draw (or would be plain impossible).
• It helps to organize the class (e.g. students will know where are we (to enhance this aspect, some of my friends use applications like prezi), how much material there is yet to cover, which parts they should write down, and so on).
• In some cases it is possible to print out copies and let the students make the notes there.
• Typed fonts are usually more readable than handwriting (and it's easier to use colors, esp. useful with source codes).
• You can do interactive-demonstrations, e.g. complex calculations with input from the students that would take too much time by hand, but it's possible with prepared programs (you can argue that it's not slides anymore, but it fits into general laptop+projector use).

• It doesn't work without electricity, projector, laptop, etc.
• It takes a lot to prepare good slides.
• Slides tempt you into many bad habits (e.g. too fast, no proofs, one-way communication).
• Slides tempt the students into many bad habits (e.g. don't take notes, fall asleep, ask no questions).
• Slides without commentary often do not constitute a good help by themselves, e.g. when publishing online (so it would take even more work to make the slides and then apply appropriate commentary).

I hope this helps $\ddot\smile$

• A very nice answer. Thank you very much. – user230 Mar 23 '14 at 11:38
• I believe slides should not be published, or at least not published without more detailed lecture notes. Slides should be bullet points of important landmarks, not the material in detail. – vonbrand Mar 23 '14 at 22:25
• @vonbrand True, nevertheless some seminars publish the slides of their speakers and it's good to have at least something after the talk (for those who attended slides are often enough). – dtldarek Mar 23 '14 at 22:37
• This answer is actually very helpful for understanding some of the advantages of using slides. – Jim Belk Mar 24 '14 at 6:04

One advantage of slides (I don't use PowerPoint, I use Beamer) is that it is a memory prompt that keeps me on track and in order. However, like many people I use a combination: I might have a definition on the slide and do examples at the board. That helps me keep to a pace they can follow and also helps me avoid being just a slide reader.

Unfortunately, nowadays there are more and more university lecture rooms where there is no proper blackboard, so we are facing this question even if we do not want to do anything with technology. I have been using slides (powerpoint) for over ten years now in large lectures. They have certainly advantages and disadvantages. Some were mentioned earlier, so there will be some repetition here.

## Pro:

I try to combine traditional blackboard lecture with slides. I do not use slides as static objects, but use them with a tablet device which allows me to use m handwriting. I usually comment, underline, write out details when necessary. I usually do not work out every detail in advance so that I can adapt my presentation to the needs of the audience. Slides are also great to include graphics and animations, even small movies into your presentation. This is something phenomenal if you teach multi-variable calculus.

You can do the same by combining presentation with traditional blackboard (if there is one), you do not need a tablet.

## Con:

It is much easier to give a boring lecture with powerpoint than with blackboard. Having the slides prepared, there is a great temptation not to prepare for the lecture. The missing mental tension makes the whole game tame. At least for me.

There is also a great temptation, as already mentioned, to be too quick. I usually build up my formulas in several steps to imitate the speed of handwriting. I have to admit that I do not always succeed.

• "It is much easier to give a boring lecture with powerpoint than with blackboard." I don't know about that. I've met people with a great talent for giving boring blackboard lectures. "Having the slides prepared, there is a great temptation not to prepare for the lecture." Some people have the same temptation with blackboard lectures, with worse consequences. – Mark Meckes Mar 23 '14 at 11:16
• @MarkMeckes: yes, you are right. These are my weaknesses, where I have to train myself not to commit these errors. Not being an educational expert, I can only speak about personal experiences. – András Bátkai Mar 23 '14 at 16:35
• I'm not an educational expert, either, and I'm also only speaking about personal experiences. (As a student and audience member, of course - my own lectures are always interesting and well-prepared.) – Mark Meckes Mar 23 '14 at 17:34

Creating slides is a lot of work. Using them exclusively makes handling random questions form the audience difficult (specially when they require a different derivation). And I like to adjust examples to data collected from the audience (or even have the audience conjure a problem, say build a graph or propose a regular expression), that becomes impossible with slides. Such interaction keeps them on their toes, and solving an arbitrary problem proposed by them with their help reinforces that whatever method is discussed works in general.

I use slides as an accompaniment to a lecture, like a music video to a pop song. This is something I can only do with slides- there is no way to do this using a blackboard.

Only a small percentage of what is on the slide is mathematical content- the rest is pictures (downloaded from google, drawn myself, or scanned in). The goal is to give a compelling visual background to words I'm speaking, and to provide visual intuition to content. I'll always provide pictures of relevant personages, graphs of relevant functions, pictures of places where things were discovered... examinable statements will be in red with a box around them, completely tangential assides will be in blue or green.

I don't only use slides of course. When I want to make a computation or to write a proof, I write directly onto a piece of paper on a document camera, which forces me to slow down and keeps the students on board. Important formulae and things I want people to remember are on handouts, and the assumption is that students have read the relevant parts of the textbook before coming to class.

I taught Complex Analysis using this approach, and I found it to be quite successful. Its drawback is that it's very time consuming.

So in conclusion, I would recommend slides for lots of pictures, animations, and visual accompaniments, and to colour-code and visually indicate relative importance of statements and their role in the "big picture" of the course. But for computations and for proofs, I never use slides- I instead write directly only a piece of paper placed on a document camera.

• Your approach in using document camera for showing proofs and detailed arguments simply solves the "light problem" in blackboard+slide approach. Also your efforts for designing a beauty "visual" general picture of the teaching material is quite nice and useful. Are the slides of your courses available online? If yes, Would you please provide a link? I am really interested in see some nice examples of a slide-based course. – user230 Mar 25 '14 at 15:40
• They're not available online, but they're on Google Drive (which makes it easy to add lots of pictures and graphical effects). If you message me, I can share them to you. Note they are made to accompany a spoken lecture. – Daniel Moskovich Mar 26 '14 at 0:28
• Would you please email me some of them at georg.f.cantor@gmail.com? – user230 Mar 26 '14 at 4:33

Maths that is already written down does not make any sense

You know yourself that when you read text, you have the tendency to read the words and skim over the maths. The same happens when reading slides. Also, maths is very dense in terms of meaning, so students will have trouble figuring out which bit you are referring to if they look away for even a second. Finally, students learning new notation need to know how it is pronounced so that they can talk about it, and so they know how their speech will translate into notation when they write. I see a lot of students who point to notation in the slides and ask "what does this symbol say?".

So if you choose to use slides you need to: * Read all the maths aloud in full.
* Preferably highlight any part of the screen/slide that you are talking about at any given moment. (If you are recording your lecture you need to do this in such a way that the recording device can capture your highlighting/pointing.)
* Consider seriously the option of pausing the slides momentarily to write some maths live, even if it will appear on the slide shortly.

Slides are not good for the students' personal study

Even though slides are effective at presenting a whole class, they are not the best thing for personal study. Well-designed slides tend to have only a small amount of information per slide, and to be arranged specifically for the format of accompanying a spoken component. Without the speech, they are often quite useless. Students visit my Maths Learning Centre with their slides dutifully printed out, but they cannot find information in them, and they often become frustrated when a maths example spreads across several slides.

If you want to give your students printed material as well (and you probably should if you have slides), you should probably prepare material specifically for the purpose. I suggest reorganising your content into a collection of one-or-two page summaries, or books of worked examples. Students seem to really appreciate this sort of thing.

If your content is not linear, consider using Prezi

If I do use slides, I use Prezi most of the time (though of course I make print resources specially and use handwriting on the document camera/blackboard too when necessary). In case you don't know, Prezi is like an infinite whiteboard, and instead of flipping through pages, you tell it to move along a path and zoom in on things in succession.

I find Prezi has several advantages.
* I don't have to put in multiple slides if I keep coming back to the same point -- I can just keep coming back to the same place in the Prezi.
* It's easier to skip to a previous part of the presentation if someone asks because you can simply zoom out and find it visually.
* I can put in a full worked example from a pdf and zoom in on different parts of it to analyse what is written there.
* I can also organise the content spatially to reinforce connections between things. This is particularly useful for maths because many things have multiple connections in multiple directions.

Prezi does have a disadvantage in that it is not well-suited to simply printing the "slides", but as I said, that's not necessarily the best plan anyway.

I use a tablet PC in class - it happens to be a Surface, which has been surprisingly robust and easy to use. I find if I use slides, I click WAY too quickly through them. So I write the notes on my tablet (I use Windows Journal) and then post the notes at the end of class. This way, students don't panic about getting everything I write and can focus more on understanding. The blackboards I use for specific examples or for equations, comments, etc. that I want available throughout the lecture so I am not scrolling back to review previous comments (I hate that as an audience member.)

I do think you need to find a medium that fits your teaching sytle - experiment but don't assume that if it works for someone else, it will work for you. And it could be different for each class -- what works for one might not work for another.