# Best form for slide / beamer presentation: display items in a slide as they are discussed or all at once?

I am preparing beamer slides for an online class, and I am unsure whether I should display different items in a single slide as they are discussed or all at once.

To be more precise: I am teaching Linear Algebra. Most topics discussed during class consist of 3 or so parts, displayed in 1 or 2 slides, such as "definition"+"example"+"warning" +/or "theorem", such as

• Definition: Linear span
• Example: $$(1,2)$$ belongs to the linear span of $$\{(0,1),(1,0)\}$$, because $$(1,2)=1\cdot (1,0)+2\cdot(0,1)$$.
• Warning: "The linear span of the empty set is $$\{0\}$$"

Similarly, a proof of a theorem could consist of several different steps.

I have the option to either display each slide fully right off the bat, or to display each part/step while I am explaining it. I am not sure if there is a better approach to how to prepare my class. Not preparing pauses would save me a little time.

• If I display the whole content right at the beggining, this might make students want to read it all and not pay attention to the explanation of the subject.
• If I display the content step-by-step, this might create several "mini-surprises" throughout a single slide, which could make them lose focus for a second or two, while they're reading more-or-less the same thing that I am saying.

Is there a "better practice" when it comes to introducing these pause between parts of the material? Is there a preferred approach? Experience and constructive opinions on the subject are more than welcome.

• This isn’t really related to your question, but I couldn’t help but notice. You said “0 is also defined as the linear combination of the empty set, with arbitrary coefficients”. I don’t think that quite makes sense. A linear combination of an empty set is a sum of zero elements, that is, an empty sum; so you can’t even have coefficients. Since an empty sum is zero, thats the reason why 0 is the only linear combination of the empty set. – Jolly Llama Aug 20 '20 at 17:06
• @JollyLlama I think of a "choice of coefficients" as a function from a set of vectors to the real numbers, and in this case "arbitrary" is vacuous, but I get your point. I changed it to how I would actually do it in class ;) – Luiz Cordeiro Aug 20 '20 at 20:12

A style which I really like is to have all the material on the slide, but have the material which you haven't reached yet in light grey. Then, as you move forward, advance your slides to turn light grey into black. That way, people who really want to see what is coming ahead can do that, but it is clear where their attention should be. Here are some slides by Kiran Kedlaya in this style.

• That's definitely a "middle-ground" approach which I hadn't given much consideration. Thank you. – Luiz Cordeiro Aug 20 '20 at 20:14
• Obviously (he says), this is a matter of taste. I personally find greyed out terms to be distracting. Either put all the information on the slide, or reveal it one step at a time. Of course, this really is just my opinion. I would be interested to know if there is any research on this... – Xander Henderson Aug 20 '20 at 22:25
• @XanderHenderson I'm sort of surprised that there haven't been any evidence-based answers that cite relevant research yet. It's not like there isn't a bunch of research on mathematics pedagogy. – nick012000 Aug 23 '20 at 6:28
• I think, @nick012000, that most of the folk on this forum are mathematics educators, and not math education researchers. We're all shooting from the hip here, and basing our answers on our personal experience. This experience shouldn't be discounted, but I, too, would like to see an evidenced-based answer. :\ – Xander Henderson Aug 23 '20 at 13:21

Ultimately, I think that this is a matter of taste and presentation style. You should create documents which allow you to present in a way that feels natural to you.

My preference (and this is a preference, I have no research to back me up) is to use \pause, \onslide, \only, etc quite liberally. I like to tell a story, which (for me) means having the space to spread things out a bit. By way of example, my PhD defense consists of 30 frames, only 23 of which contain any real content (the remainder are things like the title slide, ToC, references, section headers, etc). However, due to the liberal use of \pause and friends, the compiled .pdf file is about 140 pages long.

Of course, one should also keep in mind that what is on the slide should be disjoint from what you are saying. For example, if I give a definition on a slide, I will talk about the meaning of the definition—my students can read the thing; my goal in lecture is to give intuition.

That being said, beamer has a useful feature for (in some sense) doing both: the "handout" option in the document class. If you declare

\documentclass[handout]{beamer}


in your preamble, then your document will be compiled as if there were no pauses or other similar statements. This can monkey with the spacing a bit if you use \only at all, but otherwise works pretty well. Generally, when I make presentations, I create two files. The first is the "handout" version, a file called (for example) handout.tex which contains precisely the following

\PassOptionsToClass{handout}{beamer}
\def\ishandout{1}
\input{slides}


Then there is a second file called slides.tex (the file input by the third line of handout.tex) which is an ordinary beamer file. Either file can be compiled as usual (e.g. run

$pdflatex handout.tex  or $ pdflatex slides.tex


from the command line). Note that the flag ishandout can also be used through the TeX document. For example, maybe I want to write a proof out by hand while giving a presentation, but I want my students to have a typeset proof from the slides. Then in the slides.tex file, I can write

\ifdefined\ishandout
$$\begin{proof} ... \end{proof}$$
\fi


The proof will be included in the handout, but not the slides.

When teaching a class, I use the version with all of the pauses in it. I can then upload the pause-less version to wherever it is that my students can find it (e.g. to Blackboard or Canvas or Moodle or Dropbox or Google Drive or my personal website or whatever).

My preference is to use \pause or similar commands to review parts of slides little by little, but not to the extreme.

As you said, if you review too all content at once, students get distracted. Also, too much content on one slide creates a dreadful/boring impression.

On the other hand, beamer significantly slows down if you use too much pauses. That's because each pause generates a new PDF page. I had a slide show that took 2 minutes to compile. You can speed things up a little bit. But it is quite fiddly to do this.

I'd suggest that if you are familiar with jupyter, you can try RISE, which is much easier to create incremental slide shows.

• How can it get "much easier" than typing \pause? – Federico Poloni Aug 20 '20 at 22:30
• @FedericoPoloni In terms of compiling time. – ablmf Aug 21 '20 at 8:37

One technique I've seen used which I like is, for a given topic, to have just all of the parts up to the current one being discussed shown. This way there's no temptation to read ahead since it's not shown, the students can see the previous parts to remind them of what they were (and, if for any reason they didn't read some of it earlier, they can do that now) and you can more easily refer back to any previous part(s) if need be.

Using your example, the topic could be shown over $$3$$ slides as:

• Definition: Linear span

• Definition: Linear span
• Example: $$(1,2)$$ belongs to the linear span of $$\{(0,1),(1,0)\}$$, because $$(1,2)=1\cdot (1,0)+2\cdot(0,1)$$.

• Definition: Linear span
• Example: $$(1,2)$$ belongs to the linear span of $$\{(0,1),(1,0)\}$$, because $$(1,2)=1\cdot (1,0)+2\cdot(0,1)$$.
• Warning: "The linear span of the empty set is $$\{0\}$$"

A variant of this idea would be to have all of the parts after the one currently being discussed being greyed out instead of not being shown, similar to what David E Speyer's answer suggests. I haven't seen this variant used before, but I don't think I'd like it as much since I would find the greyed out text to be distracting. I'm mentioning it here anyway in case you might like it better.

• The added advantage of revealing things one at a time (as indicated by the example given) is that it gives the instructor a chance to pose the question "What is the linear span of the empty set?" before giving an answer. It is an opportunity for the instructor to build engagement. – Xander Henderson Aug 21 '20 at 14:35

I did a survey with my students, asking them what is their preferred presentation method. Here are the results:

1. 27% preferred the "invisible content", where the content is fully hidden and displays as the lesson goes on.
2. 42% preferred the "transparent content", where the content is transparent and displays as the lesson goes on.
3. 31% preferred the "visible content", where the whole content displays right at the beginning of each slide.

Based on that, I will use the "transparent content" style, as it is the preferred method among the students, and it seems to be a good middle-ground for the different possibilities.