14

When I feel my blackboard presentation is a little sloppy, and remembering to "just slow down" doesn't help, I try writing bigger. It has the benefit of actually slowing me down a bit, and students sitting far back can more clearly see what I've written.


6

Another idea: Use a document camera with lots of paper and markers. This gives you the advantage of drawing things before class without much planning and/or going back to previous "slides" by simply retrieving the relevant paper. I think you can route a document camera into an hdmi or vga connection. I like this as a solution since it is relatively low-...


5

When an inexperienced student sees $a=b=c$, I'd assume that both $a=b$ and $b=c$ are clear but the transitivity that yields $a=c$ might not be obvious. That's why I'd focus on this hidden equality when reading it out loud, by not just reading the equation (your first option), but rather saying "a, b, and c are all equal" or "a, b, and c are the same [number/...


5

I am teaching at the high school level, not university, but this has been my standard set up for a couple of years now: I connect my iPad to my notebook, and screen capture my iPad onto my notebook. I then display my notebook via a projector. I use the Notability app on iPad to write notes (using the Apple pencil), and this is projected for students to see. ...


4

My colleagues have been doing this using a Surface and Acrobat. If you just want to write onto a plain page, OneNote will probably serve the purpose, and has the best writing experience. The advantage of Acrobat is you can write onto pre-prepared slides. The disadvantage of it is price. I'm going to try using OpenBoard, which is free, but still somewhat ...


3

You might benefit from some deliberate practice. Take 15 or 20 minutes out of every day to give a "lecture" to an empty room (or a room with a colleague who can critique you). During that "lecture", pick some particular aspect of your board work to concentrate on (for example, writing larger, writing slower, keeping your lines straight, &c.—you ...


2

"Oh I just had my first tutorial today. First half I talked. The second half I told them they could stay to work on homework and I will answer questions. 3 students stayed. :D" I hope you learned a lesson from that! It's absolutely what I could have predicted. You should have also. Personally would mix it up some, but emphasize drill/work throughout. ...


2

You might consider to just use an overhead projector, with grease pencil and acetate. You won't have the multiple boards, but you can go back to earlier pages if needed. (Number as you go, to make this easier, on the fly.) If you want to keep the same feel as blackboard talk, I recommend to write them as you do the discussion. If you have a canned talk,...


2

I'll suggest that the best verbalization is the last one in the question: $a$ equals $b$, which is equal to $c$ Here's why I think so: It's the closest to a literal symbol-by-symbol reading of the chained equation, while still being a grammatically-correct English sentence. Note that this matches the top-voted (but not accepted) answer to the analogous ...


1

Personally, I often add a variety of different expressions. I think doing so not only makes the presentation marginally less dry, but also perhaps increases the fluency with which students will be able to deal with symbols by understanding their meaning. In particular, instead of just "equals" I would often use expressions like "the same as", "is nothing ...


1

I think how you read (and write) them depends on how they are being used. $$ x^4 - y^4 = (x^2- y^2)(x^2 + y^2) = (x - y )(x+y)(x^2 + y^2) $$ is fine but pedagogically $$ \begin{align} x^4 - y^4 &= (x^2- y^2)(x^2 + y^2)\\ &= (x - y )(x+y)(x^2 + y^2) \end{align} $$ is better. More important is dealing with this common misuse of chained equals ...


1

I would recommend a 2-in-1 laptop rather than a Surface Book due to the price, but of course, that comes with pros-and-cons. Office 365 or Office 2019 with Word, PowerPoint, etc. should be great for not only writing but also saving the notes you write, thereby allowing you to switch screens without the worry of losing the notes you wrote on screen upon ...


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