# How shall we teach math online?

Many universities, including mine, are now requiring we teach our courses online because corona. How shall we do this? Let’s brainstorm here.

Some challenges:

• My school provides limited online resources. I have access to Blackboard Collaborate. My only cameras at home are those on my MacBook, iPad and iPhone. I don’t have access to an online whiteboard (I think). How am I to write out all the math?

• I am a lowly paid adjunct. I do not want to spend inordinate time typing up technical documents. I do not have a scanner at home for written notes.

• How are we to give exams? I cannot trust these students with a take-home.

• I’m sure there’s more. I’ll contribute these later when I remember them.

Suggestions? Many of us are in this boat. Let’s get the ball rolling.

• One major problem seems to be students that do not have home internet. – Gerald Edgar Mar 12 at 15:05
• In the past three hours, I have gotten email from Wiley Plus, XYZ Homework and Top Hat publishing, all advertising that they are making their courseware (books, online homework tool) free for the rest of the year. That may handle the need for graded book-work during the term. – Nick C Mar 12 at 20:46
• As a side note, I strongly urge you to interact with some administrators, collective of other adjuncts or friendly full-timers, or something. On your own it's being at sea, but if you have a dozen people with you saying "Spend $100 on a document camera, you'll be saving money elsewhere with all this", you might have some luck on a unified approach by the department - which will look better than other departments if it has its ducks in a row. (And yes, I've been an adjunct, so I definitely feel the difficulties if you don't have anyone to turn to. I sure hope you do, though.) – kcrisman Mar 13 at 2:27 • Clarification question: Do you have access to your university classrooms? My university is switching online as well, but employees are still expected to work and generally be on campus, and they still have access to classrooms for using the equipment. – anjama Mar 13 at 11:33 • As a student, I wish I could upvote this 100 times. I’m glad to see some instructors are taking this seriously. – gen-ℤ ready to perish Mar 13 at 17:26 ## 17 Answers Instructor at University of Washington here - we were one of the early closures, so I feel like we're starting to get the hang of it. Here's what I'm using: Zoom: Zoom is similar to Skype, with better support for many-participant calling and additional features. It has a built-in whiteboard you can write or type on, mechanics for allowing students to "raise hands", and a "breakout room" option that allows you to split the class into small groups. The free version only allows 40-minute sessions, as I recall, which is a little too short for a class (though I would imagine you could do a 40 minute lecture followed by a 10-20 minute mini-assignment); the Pro version allows sessions of any length. Some schools are able to provide Pro accounts to faculty, but I can't imagine most are -- I also work at a local community college, and they don't have enough Zoom licenses for the faculty. Canvas and Panopto: Canvas was already an essential component of all my classes, but it's now extra useful. It links into Panopto easily, which is a platform for recording lectures -- if you have a way to write on a screen, it can record that, or you can use your own physical whiteboard. Or even just write on paper and hold it up, I guess. Canvas also has a functionality called "Conferences", which (based on my cursory inspection) seems to function a lot like Zoom. Exams: I plan to administer exams through Canvas, which handles timing for me. That does have the disadvantage that I have no way to ensure that they don't make use of the Internet or similar resources, or talk to each other during the exam. To ameliorate that, I'm adjusting my exam questions to lean more conceptual than technical -- utilities like Symbolab can calculate the roots of a polynomial, for example, but they can't write a few sentences explaining the interpretation of the roots in context. I'm also planning to have the exams open for only a fixed window -- for a two-hour exam, I plan to have the Canvas exam available for a total of two and a half hours, reducing the risk that students might complete the exam and then communicate the questions or their answers to other students. I also will be requiring students to submit their work (the process they used to get the answer) as image files or PDFs after the exam. Teamwork: The biggest advice I have here is stay in touch with other faculty at your institution. This is a confusing time for the students, and confusion does not help with learning. Anything you can do to maintain consistency will help -- if all of the faculty are using similar techniques for online teaching, that's likely to be more helpful to the students than if every instructor digs up their own alchemy of random online tools, no matter how effective those tools might be. • +1 for realism with the exams. – CGCampbell Mar 12 at 17:02 • Could you provide links to these resources? "Canvas" is such a generic term that I can't find what you are talking about. – Džuris Mar 13 at 12:46 • @Džuris: I assume canvas refers to https://www.instructure.com/canvas/?newhome=canvas . Not sure switching to Canvas quickly is practical. – Brian Mar 13 at 13:31 • You (or someone else) should edit the link into your answer so future readers don't have to dig through comments. – Peter Cordes Mar 14 at 18:38 • Zoom works on linux and the apple products. – Captain Giraffe Mar 15 at 4:48 Already put two comments but ideas keep coming to me so I'll just package them here. Keep in mind I'm not an educator, I'm just trying to think of practical solutions to the problem as a whole. Another answer recommends YouTube to upload source material but I feel this might be inadequate interaction. Other alternatives: Discord Recently in response to COVID, they've upped their free screenshare capacity to 50. The first approach could be assemble a small top-down view from of a portable whiteboard that you write on during the explanation. Something like here. You'd have to position a portable webcam to achieve this. Discord also has slack-like text and speech channels that you could maybe host discussions about dedicated topics. E.g. Algebra Channel or Calculus The issue with discord is that while you can stream/screenshare to those present, the stream media isn't archived which can be useful for future reference. However a service that does: Twitch.tv Although primarily used for entertainment purposes, I think you might be able to use it in your situation. If you still have access to your faculty building you could use an empty lecture theatre's whiteboard and effectively "stream" a lecture free to Twitch. Set up your laptop on a desk at the front, start streaming and conduct the lesson as normal. This has the added benefit that Twitch archives your past broadcasts so your students can use it as a reference repository in the future. Another potentially useful feature is that there is a chat sidebar so that your students can ask questions which you can answer in real time should that be necessary. It's not the most formal of arrangements but needs must. If you are concerned about privacy, I'm pretty certain you can restrict public access to private links you can distribute to your students. P.s. I find it most strange that your faculty isn't helping you financially nor advising you on the faculty process of teaching going forward. • We’re all thrown by this. I think no one knows what to do. And as far as financials are concerned, this is CUNY. The department could hardly afford chalk or copy paper. – Stephen Herschkorn Mar 12 at 15:50 • @StephenHerschkorn I sympathise with your situation. In the question you imply that you are a relatively junior in the hierarchy, do you have a way to contact those senior than you in the department? Sounds like someone should be making decisions and it could be that they are currently in the process thereof. Perhaps contacting the institution's administration for abstract guidance would be useful. – James Mar 12 at 15:54 • I did think of asking my chair, but I think all in the department wold ask, and I suspect he is as baffled by this as we. The main advice we have been given is to use Blackboard Collaborate. That’s why I thought opening up the question to a wider audience might help....[Can I put a line feed in comments here?] The university is sending out some general suggestions. I still am having real trouble envisioning an online lecture, since I write so much on the board that really needs to be seen. – Stephen Herschkorn Mar 12 at 18:35 • +1 for suggesting Twitch. – kcrisman Mar 13 at 2:08 • I should say that the administration is at least offering training sessions on Blackboard Collaborate. On Monday [16 May 2020], they will be offering two specifically for math professors. I will be going. – Stephen Herschkorn Mar 13 at 10:00 The case for WeBWorK tl;dr - use WebWork as an easy way of giving students as much practice solving problems as they can handle. Learn by doing lots of problems with a tight feedback loop. It engages the game-playing, obsessive nature in us. ### Main use case - Homework engine The two biggest features of a VLE/LMS are the presentation of materials and facilitating assessment. WebWork was specifically developed to provide formative and summative assessment for mathematics in a way that eases the burden on the instructor and allow the student to attempt problems as many times as they wish before the deadline. By immediately seeing which answers are incorrect while the problem is still fresh in their minds, students can try multiple approaches until they find the correct solution. • it has a library of ~30,000 math and over 1000 physics questions and includes such textbooks as Stewart's Calculus • it randomizes problem parameters (different numbers, drawing from question pools, MCQ ordering) so that each student gets an individual question which: • hinders copying • promotes student collaboration • immediate feedback and configurable number of attempts • allows the instructor to re-assign a problem set and students get new numbers • understands derivatives • hints and solutions available after cut-off dates • Student statistics shows you current state of progress. i.e. 19 attempts signals difficulty with a particular problem which could benefit from intervention • email student/instructor buttons (is this a good thing in your use case?) • LaTeX typesetting makes the Hardcopy version of problems look good on the page for those who cannot always work online. • 25 years of development with a good community • backing of MAA, wide adoption in the US ### Content delivery It has the basic delivery mechanism for presenting course content as webpages or PDF, but it would be better suited to pairing with your existing LMS/VLE environment, Blackboard and Moodle, either as a weblink or through the LTI bridge. ### Extensible Integrates with GeoGebra and other tools. ### Open source You can run this on your PC providing your IT networking team will allow it through the firewall. It has a Docker image which could be run from the cloud. There might be hosting options available ### Examinations To answer Stephen's comment below: If you consider an examination as a problem set completed under a time limit with only one submission, have a look at the documentation for Gateway Quizes . The access restrictions should let you set out a decently administered exam, given that the answers will be different for each student reducing the problem of copying, eg. you have 2 hours to complete the quiz which must be finished before the deadline. If you have more determined cheaters and need to verify their identity, the proctored quiz options permit you to require students to enter an examination center, suitably distanced in time and space, where a masked Proctor will enter the online key to allow the student to begin their exam. • Can't figure out the down votes here! Although WW is not appropriate for a collaboration tool directly, it is indeed a possible piece of the puzzle here. – kcrisman Mar 13 at 17:38 • @kcrisman There were two flags reporting it as spam, but that doesn't really make sense since it isn't a commercial product. Presumably this read like an advertisement from a company to some people. (It's not.) – Chris Cunningham Mar 13 at 19:24 • The online homework (WebAssign for one class, WeBWorK for another) is already set up, as we use that during any semester. The real problem to address here is how to lecture and give exams. Many helpful replies have been given – Stephen Herschkorn Mar 14 at 1:11 • A bit more clarity about what 'Webwork' is would improve the answer. – Tommi Mar 18 at 8:34 I gave a presentation to my department about this today. Like you, as I see in a comment, I am also at a CUNY math department. I haven't done all-online classes before, but I've used Blackboard heavily for ~20 years and have had a hybrid (partly online) class for the last two years. I have access to Blackboard Collaborate. My only cameras at home are those on my MacBook, iPad and iPhone. I don’t have access to an online whiteboard (I think). How am I to write out all the math? Blackboard Collaborate Ultra includes a built-in online whiteboard. Click on the bottom-right button to expand a menu; click on the 3rd box icon, and you get the "Share Content" menu. The topmost item here is the "Virtual Whiteboard". In this tool you can type text or draw with the manual pencil tool (in different colors). Math symbols are not supported by the typed text tool, so you'll have to draw them manually. Some people might try that with the mouse or a touch screen. Best practice would be to get yourself a "graphics/drawing tablet" -- low-end version on Amazon for about$30. (My department is working on a purchase order at this time.)

I am a lowly paid adjunct. I do not want to spend inordinate time typing up technical documents. I do not have a scanner at home for written notes.

For documents, worst-case scenario, I think, is that you could take any existing documents, or hand-write materials, take a photo with your phone, and upload that. Better would certainly to prepare materials digitally or scan them. I have an inexpensive "portable" scanner I bought for uses such as these which has worked fine for me.

How are we to give exams? I cannot trust these students with a take-home.

The truth is that you'll basically have to operate on the honor system at this time; there simply isn't any other reasonable choice (without in-person proctoring). There are systems in some places that require testing students to be watched by webcam, but (a) you probably can't procure that system through your college at this time, (b) you can't expect all students will have webcams, and (c) there are privacy concerns that would be wise for you to avoid.

Blackboard has an automatic testing facility (works best for multiple-choice questions; automatically graded, and students can't enter special symbols on essay-type questions). Or you could provide assignment sheets in PDF form to email back, or upload as an "Assignment" feature.

One thing that has worked well for me is to prepare tests using the Pearson TestGen application (includes testbanks for many major textbooks), and then there's a few-click process to (a) export from TestGen, (b) import as a Blackboard question Pool, and (c) create a Test from those questions in Blackboard.

Finally, I would personally recommend that you stick to whatever tools are provided, managed, and vetted by your college (in our case at CUNY: Blackboard). Using outside third-party tools have privacy, security, and possibly FERPA problems.

• +1 for your last comment – kcrisman Mar 13 at 12:15
• Yes, like-it-or-not, "honor-system" approaches to exams, and cessation of institutional distrust of students, is all that we really have here, at least for the foreseeable future. – paul garrett Mar 16 at 17:45
• For scanning with a phone, the CamScanner app works quite well, and much better than just taking photos. – Neil Strickland Mar 18 at 15:15

I like You Tube for posting videos. Once you get started it's pretty simple. There are various levels of privacy possible which you can read about. If your school has a convenient way to post videos and you have broadband (we're talking about 1-1.5 Gb files here, do NOT use HD resolution or worse yet the 4k resolution...). Given all that, basically the thing to do is to find a way you can comfortably write for a long time. I like writing on a desk or table in this context. You really don't want to fuss much with the camera or require any sort of post processing. I found making a wood frame to mount a small camcorder[$$\star$$] above my writing worked well. Key is the camcorder/camera needs to allow mounting on a tripod. I just use the tripod mount to fix the camera to my frame. The videos I posted here:

My Differential Geometry Online Course

[$$\star$$] (Canon, about \$250 because I needed the external mic jack for classroom applications, you can probably get a more basic model for around \$150 if you don't need to connect a wireless mic)

I can post a picture tomorrow of the set-up if you're interested. Added 3-20-2020,

The trouble with cell-phone cameras is they have the nasty habit of timing out because apparently battery life is an important design consideration in phones. I'm sure a sufficiently clever person could find a way to hang a cell-phone camera in the same fashion as I use the camcorder.

Now, if you like standing and writing. The easy fix is the white board at Home Depot or Lowes for about \$15 for a $$4' \times 8'$$ piece. It erases easy and you can hang it with removable velcro tabs which are pretty easy to mount. I can put one up with a friend in a class room which lacks proper writing space in about 15 minutes. It would take longer to do it level :) • my apologies for the locality of my answer. Feel free to replace Home Depot or Lowes with appropriate DYI store in your country. Also,$3.281 ft = 1 meter$. Unfortunately exchange rates are dynamic and as such I cannot include those here. – James S. Cook Mar 12 at 6:07 • At these wages, I am not inclined to spend my own money for this. Certainly not$100+. – Stephen Herschkorn Mar 12 at 6:30
• @StephenHerschkorn that is correct. Though there are cheaper options. – kcrisman Mar 13 at 2:12
• @StephenHerschkorn probably someone has made an application for taking longer videos with the cell-phone camera. I haven't looked into it, I just know the default camera software on my phone was not great. – James S. Cook Mar 13 at 3:02
• One issue about YouTube is that a bunch of our students have gone home to China and they cannot access YouTube there. There are various alternatives but I cannot give a reliable or up-to-date summary. – Neil Strickland Mar 18 at 15:18

Well, since I have also been obliged to teach from home due to CoVID-19 these days, I will describe here a possible solution to your problem.

As a fast and cheap solution - I have been granted no access to any platform, unfortunately - I use the following:

• Skype, as a platform to communicate with my students and conduct the major part of the lesson.
• Handwriting notes apps - like the open source Xournal++ for ubuntu/fedora/debian distributions. I simply share my screen (through skype) and then write my notes - you can use your mouse, keyboard and/or a stylus as an input device. You can also export the notes you are taking as a pdf - as well as in various formats - so as to share it with your class.
• Also, as for organizing students' work - e.g. handing out tasks etc - you can use some existing e-class platform - e.g. Google classroom - which can help you schedule students' tasks etc.

Of course, you can enhance these with the extra features provided by Blackboard collaborate - although I find some features of this specific platform quite uncomfortable and dysfunctional.

In some sense this question is waaaay too broad, but it is attracting a useful collection of hints, and it's super topical for thousands of college math instructors (likely to be followed by primary/secondary ones), so here are a few things which I don't see mentioned yet, collated from the far too much time spent on this subject today.

• Web/Doc cam. There are USB webcams that are very reasonably priced which you just plug into a computer, and which could easily be mounted (with popsicle sticks if you had to) to create a faux document camera. (Or you could ask a dept. to buy a small doc cam for about $100 for faculty to share, or use one on campus if that is an option though those don't necessarily plug into your computer - many will accept SD cards.) You could probably even use your phone to do this, if you could find a plug that let you direct the input directly to your computer (I do not know if that is possible). The advantage to this whole suggestion is that one doesn't need a whiteboard or good resolution or anything to film people doing math ... it's just on paper. (Mooculus uses just paper for a lot of its videos.) • Open Broadcaster Software (OBS) is available for all platforms - I was even able to download one for my ancient Mac. You can have it export mp4 files (see YouTube for many tutorials) and upload to your LMS, assuming that you have one provided. This means in particular that you don't have to try to use something fancier or pricier. • For many subjects, there are zillions of videos online for just solving problems, so you might be able to make a short video of yourself explaining what they don't say instead, just using your phone. (Or TikTok if you prefer that.) I like 3Blue1Brown for linear algebra, for instance. • If you are having trouble with student access to books, or if scanning is prohibitively annoying for various reasons, there is a growing number of open texts in mathematics which may cover the content you want - in which case, depending on what OS you have, you could even make a screencast. (There are many ways to do this, a number of which are free - you still have to have somewhere to host it, though I really hope your institution is providing that at least.) Good luck, and my apologies for any attempts at humor above that fell flat - you have to laugh or you cry sometimes, right? But we're in this together, keep asking and advocating. • +1 OBS is easier to figure out than it has any right to be. – Chris Cunningham Mar 13 at 14:25 • @ChrisCunningham - Right? Compared to the GIMP it's like a point-and-shoot camera. – kcrisman Mar 13 at 17:36 • There are truckloads of lecture notes available for free, there is the Open Textbooks Initiative, and several other such initiatives. – vonbrand Mar 28 at 21:55 • Yes, I actually linked to that in my answer :) though to be fair I have some links to that project in the non-electronic sense as well. The AMS is also posting a lot of open notes now, and the University of Minnesota one (open.umn.edu/opentextbooks/subjects/mathematics) etc. – kcrisman Mar 29 at 1:57 I am surprised that a school would effectively say "go figure it out". You ask for "brainstorming"... here are my thoughts.. You haven't quite defines your goal, although I did hear, loud and clear, you'd like 'free' or close to it. Still, there are a number of outcomes. Live video - I believe there are many options, but in general, a multiuser teleconference. You do this at the school, on a whiteboard, students dial in. You use your phone (battery concern? you keep it plugged in.) Recorded video - The iPad will let you screen record audio/video. A stylus can be had for cheap, since the Apple pencil is about the$100 you wish to avoid. For math, I am thinking this is a good video approach, as there's no need to see you up at a board. You can decide whether to edit or not. There are a number of apps to just let you write notes, the recorder feature is part of the OS.

Written notes - like a text book. Again, there are many 'scanner' apps for the iPhone/iPad and you can just use those. I taught the last couple months of a precalc (HS) class a couple years ago, and while I actually taught the class live, I made the prep notes I used available to the students that day, after the class, so they weren't looking ahead. This was well received, as they paid more attention during class, with less time furiously copying off the board.

2 comments - It seems to me, a school should have a common approach. My HS is currently meeting to discuss how we will remote teach. The goal is to be consistent, so students aren't needing to understand how to access, say 5 platforms, for multiple classes. If \$100 (only. of course, there's a limit) is the difference between doing your job well, and half-assing it, I'd highly recommend you think about this. If not for the students, then for your own career path. Projecting an attitude of "I'll do whatever it takes" will reward you far more than a single$100 investment in your own tech.

• I like your last comment some, because it's usually my attitude, but at the same time there is the issue of "the crisis becomes the new normal". The OP is an adjunct, and they are already poorly paid enough - it is delicate to say "and now you should help make sure the expectations for adjuncts are to work an additional 5 hours a week per class, or that spending even more money out of your own pocket is the new normal". Tough balance there, because (as a comment on the original post notes) the students are definitely feeling a bit at sea, which should be of concern to all educators. – kcrisman Mar 13 at 17:48
• One problem with the "common approach" thesis is that not all instructors are equally tech-savvy or equipped. Some are already teaching online and have video setups in their home office; others have never used the LMS before. Related, academic freedom means each instructor has the right to pick the best methodology for their class. That said I've recommended faculty stick with the set of tools in the LMS supported by their college and not run off to a bunch of 3rd party random tools. – Daniel R. Collins Mar 14 at 5:25

I'm a full-time faculty member at a community college in NJ. I've been teaching for 12 years but have never taught an online course. When our college left for spring break I was left scrambling for how to make use of the tools that I had at that moment: my course notes and textbooks, my laptop, and my iPhone.

With these tools I write, by hand, a short lecture with each slide representing a different point or step in solving a problem. I use my iPhone's scanning app to take a photo of each slide that I want. At the end I get a merged PDF. I then use Zoom to share my screen with the PDF pulled up (in full-screen mode) and record as if I were in class. The end result looks "good enough".

In total for a 30 minute recorded lecture I spent about an hour doing the write up by hand and then 30 minutes doing the recording. It's time consuming but it's the best that I can do with the tools that I have.

My university (I am in Spain) has Microsoft Teams integrated with student accounts, so I use this. My classes are two hours. I open a chat (there are 60-70 students). (Zoom for free only allows 40 minutes and I am not sure it can handle the 60-70 students; a colleague is using the free video mixing software OBS and broadcasting class via Youtube, but learning to us OBS is nontrivial.) I do not show my face. I speak over whatever I am showing. Class is a mix of microsoft's blackboard, which I use as a traditional blackboard via a drawing tablet, and graphics and code generated by or written in various applications (depends on the class I am teaching) such as matlab, C, geogebra, python, etc. (Before I realized I could use microsoft's blackboard I was using the freely available Mypaint and Autosketchpad as blackboards). I mimic what I would do in a classroom, with certain modifications to adapt to the format. Students can ask questions (controlling interruptions and excessive question askers is more difficult than in person, and engaging the passive and shy is a problem I have not solved). I use a headset (10 euros) and drawing tablet (the one I bought cost 70 euros and works fine); these I went out and bought the first day all this happened. The university does not provide us such resources.

I record class and put the video at the student's disposition. I also record (outside of class) myself solving exercises and make these videos available to students. Prepreparing quality videos requires a lot (a lot) of work. A virtue of using a drawing tablet is that it really mimics a traditional blackboard (even improves upon - more colors, neater writing, better drawings, no chalkdust, everything is saved for later consultation) and does not require the fine tuning that a preprepared video (MOOC style) does.

Time will tell how all this works but my initial experience is relatively good. I've had some technical problems - computer freezing up - because I'm working out of home. I run two computers at once, using one as a monitor the way stage performers do (both are old and slow, so one serves as a backup also, and I have had to use it). Also the internet connection is not what it is at the university. Uploading gigas of videos takes a lot of time.

Assessment is a difficult problem. The university has more or less suspended all assessment until it can be figured out what can be done. Exams with the students off site are considered useless because of the ease of obtaining assistance, collaborating, cheating, etc. As it seems possible that presencial examination will be not be possible in this semester (we are in Spain) other options are being explored. So called secure systems for online exams have been considered but they are not considered effective and they are very expensive. Indications are that we are headed towards a system of online oral exams. This will be very time consuming (in some cases four or five professors have to examine 600 students), and there are concerns about guaranteeing uniformity/homogeneity as well as concerns about the availability to students of resources to realize the exams. Something will have to be done, and some imperfections will have to be accepted.

To enhance my last comment, this is what I was talking about with Blackboard Collaborate Ultra. I did a trial session with some of the other faculty yesterday and it seemed to work alright. We come "back" from spring break next week, so I haven't had a chance to try it with students yet. It might be worthwhile to either do a training session with students before class, or resign yourself to the first 10 minutes of regular class being lost to getting-familiar-with-tech.

My home teaching setup. Still to be tested.

Here I broach only the case in which students have consistent internet access; the more general case is clearly much more difficult. Moreover, this answer is written for the present context, i.e., a sudden shift to remote learning (perhaps disaster distance learning is a more apt name) due to a pandemic. This is not an answer about teaching mathematics online using the full resources of, say, an Office of Distance Learning. Finally, I am writing essentially about teaching (at least) secondary school; the task at hand is, again, significantly complicated by a need to have students accompanied by an adult.

My advice for right now is to simplify drastically, and to make your goals fourfold:

1. Ensure that you are checking in with students, even if their work is not done;

2. To provide enough work for those who want to work on mathematics to have materials;

3. To ensure that if all students complete all work that it will not be too much for you, as the instructor, to handle;

4. To create a routine and structure in a time of great uncertainty.

Concretely, I am using a daily schedule of DO, WATCH, READ. For a senior level mathematics course, I have made my ongoing notes available online: the class is called Problem Solving & Posing.

Here is a separate suggestion for how this routine could be carried out in the context of, say, a course on Algebra 2 for which the goals centered are the four listed above:

Set up Google Classroom as a place where students can turn in problems; they can do the problems by typing them out, or by writing them out and uploading pictures. So, the DO here would be whatever list of problems you intended on covering before going remote; but, be sure that you are satisfying both number 2 and number 3 in the list of goals above.

For the WATCH component, assign consecutive videos related to the problems from Khan Academy. Is this ideal? No, it is not; but, we are operating out of a non-ideal world, and this is a simple structure that you can set up for students to operate within.

For the READ component, I recommend the set of MAA published anecdotes Living Proof (PDF). I have been asking students to read one anecdote in a day (about 2 pages) and then to google the person about whom they read the following day. You could alternate this across Mon/Tue and Wed/Thu, then assign something different to read on Fridays/weekends (perhaps nothing at all, depending on bandwidth). There are 41 anecdotes in the linked book; therefore, this structure would last for about 20 weeks. Is this ideal? Actually, I think these stories are powerfully humanizing for a discipline that is too often viewed in a dehumanized, decontextualized manner.

If you have a synchronous component too, then I suggest using that time to go over the problems. Asynchronously, I also suggest creating a shared document that all students in a given class can edit: in particular, they can ask questions and/or answer classmates' questions. If you can, download Screencastify for a nice way of going over how problems can be solved: you can solve them on the computer (I've used bitpaper) while recording yourself speaking. I imagine it will be better for many students to hear a familiar voice, and you can clarify the steps you are going through as you work out e.g. questions left unanswered in the shared document.

There are a number of routines (notice/wonder, number strings, which one doesn't belong, attribute-listing/what-if-not-ing, slow reveal graphs, etc) that you could begin to introduce at a later point for live/synchronous sessions; however, I think the DO, WATCH, READ structure is worth implementing and tinkering with before deciding to enact more demanding pedagogical approaches.

Start simple and be kind to yourself.

We're on Blackboard as well, here's some workflow's we've been experimenting with to do everything through that interface:

Lectures: Blackboard Collaborate Ultra works pretty well here. Just remember to turn your mike on, and to go into the settings once you've joined the session, click "Notification Settings" and turn on Browser Popup Notifications for things like hand raising and chat. That will allow you to use a different application to present the material.

If you're more comfortable with Latex, you can just use the computer, and use

https://www.twiddla.com/t0xq6n

Finally, you can hand write your notes out on the iPad, save them as a PDF, and them upload them to Collaborate Ultra and go through them with the students during class time, answering questions.

Homework: Use the assignments. Blackboard will allow students to upload PDF, Word Docs, etc. If students don't have scanners have them use their phone and take a nicely framed picture. You can add notes to PDFs on the file itself, or add a grade explanation under the score.

Quizzes: Blackboard has fairly good instructions for building quizzes:

https://help.blackboard.com/Learn/Instructor/Tests_Pools_Surveys/Create_Tests_and_Surveys

To administer them, announce the time they will become visible and give the students a finite amount of time to complete them.

If you don't want to create questions on a quiz through blackboard, hand write them with the iPad and save them as a Pdf. Then, only make the assignment file available at the beginning of class, and tell them that they have to upload it by the end of class.

If you're very worried about cheating, do it during class time and have them log into Blackboard Collaborate Ultra or Panopto with their video on (although smart cheaters will be able to get around this). Set the quiz time for 15 minutes and have it close 15 minutes after it becomes visible. And then, don't worry about the fact that there are ways to game this, most students won't cheat so don't try so hard to ferret out cheaters that you punish the students really trying.

Exams: I don't know if we have a good solution for this yet. Keep in touch with your administration and hope they come up with something. Plan for a take home exam, if possible, or to do a one-on-one Q&A's during finals week.

Good luck everyone, and keep the ideas flowing!

My approach:

Lectures

I use a tablet laptop at home, which I can write on with a bluetooth pen. I use to OneNote app to actually write thngs down, though there are many other options.

To do an online lecture, I use Google Meet.

Students (about 50 of them) gather online in the meeting room (a link I send them 15 minutes before the lecture starts).

I share my screen with them and ask them to turn off their cameras and microphones.

I have a couple of slides or multi-choice questions that I show while waiting for everone to "arrive".

When the lecture starts, I start recording the meeting, I switch to OneNote and deliver the lecture, writing down everything like I would on a whiteboard. I have another computer open by my side, which shows the screen as the students can see it. Importantly, I also have the chat window open on that screen and tell students that they can type in questions, which I can then address directly as I go along.

At the end of the lecture, I close the Google Meeting, send the students a link to the recording of the lecture and upload a pdf of the OneNote file (sometimes with added annotation that I type) to the Blackboard site.

I have to say, so far, so good. It actually works better than a regular lecture in terms of getting the students to ask questions. I think they prefer to type stuff in rather than raise their hand and ask something.

Homework

Just set the problems on blackboard and provide the solutions later. Students would normally have had access to a "problem class", so I will schedule an addiitonal class to go over some of the problems in the same way as described above for the lectures.

Exams

The exam for my module will be a timed test. Students will be sent the test at a particular time on a particular day 9they are told in advance !). The exam is also made available on Blackboard at the same time.

Students must answer the questions within a limited time. They must scan their solutions (they have been provided with instructions about how to do this using mobile phone apps like "camscanner") and then submit a single pdf file of their attempts through the "Turnitin" submission system by a certain time on the same day. We will have an "emergency" phone number for students to call if they are having problems scanning/submitting, in which case we may accept emailed solutions, jpegs, or as a last resort, students will be asked to post their solutions that day.

Clearly there is opportunity for collaboration and online use. Effectively the exam has to be open-book, so the questions cannot be too straightforward or easily googled. Students are remined that questions of authenticity will result in themselves having to defend their work in a viva.

This is probbly the least-worst system. We did think about different questions for each student, but this would be just too much work and potentially unfair on students.

We will be doing a dry run before any proper test/exam is done.

• If you are doing this for calculus then you should probably take some time to learn the common cheat sites. Wolfram alpha and others show steps, however, the steps are often inauthentic when compared to real human calculation. You'll know it when you see it. Running your problems though "symbolab" before you grade may be eye-opening. We found something like half of the students use a website for the online calculus test... even after being told to do no such thing. In the absence of proctoring it is a real problem. – James S. Cook Mar 25 at 14:48
• To second @JamesS.Cook's comment: we teach calculus out of Stewart, which has a quaint definition for the inverse secant function. (He did it so that its derivative would carry no absolute value sign.) If you tell any of the standard CAS to integrate what Stewart considers as the derivative of the inverse secant function, they will invariably come up with something else. To cut the story short: we have fairly strong evidence that statistically 20-35% of our students cheat on the online exam. – Willie Wong May 9 at 0:23
• I should add, I still think this is way way better than using something publisher produced for testing. That sort of test is even more likely to be ready to look up on Course Hero or that other "study" stie Chegg or Quizlet. Unless the test is newly written and the solution is handwritten and scanned it is hard to stop the gaming of the system. Even in the handwritten case, the absence of proctoring by humans opens wide the door for cheating. The solution is simple, it just involves some good old human interaction and a modicum of integrity on the part of all involved. – James S. Cook May 9 at 3:09
• I don't set tests which are of the form: "Integrate this function" @JamesSCook and I don't use questions I've found on the internet, since usually the solution is to be found too. Setting questions by reference to pictures/graphs is a good way of making it less easy to get internet assistance. – Rob Jeffries May 9 at 7:17

Though I taught electronic maintenance and simple math years ago, I am now a casual student. I actually clicked on the link to this discussion just out of curiosity. I may have some small insight into the problems you are now facing.

I recently found an online course that was free to take if I did not want a certificate. I thought it would help me bridge the gap between the last classes I took in early 80s and today's math. In my mind I see it as the difference between knowing that 1 + 1 = 2 and knowing why. That may not be a good description for you.

I started the very first lesson and dropped the course. I think I understood what was being presented. However, it was a video lecture. I do not have reliable internet. The course provided a transcript of the lecture, and I thought I would just read the transcript. However, the text did not include the content of what was, I assume, displayed as a slide or an electronic chalk board. Without that, I could not do the course work, take quizzes, etc.

Hope there is some value in this.

• Welcome to the site! Do you think you could edit your story in such a way that it directly answers the question? This is a question and answer site, as opposed to many other places on the internet. – Chris Cunningham Mar 14 at 0:47

This is best done via an email list. You write up lecture notes using LaTeX, produce a PDF file which you email to all your students. You can ask your students to submit homework to you via email. This way of teaching is far more efficient than teaching in the traditional way or the live online methods, as you can prepare the lecture notes whenever it suits you while the students can study when it suits them.

• I have 400 students in one of my classes. – Gordon Royle Mar 14 at 8:12
• @GordonRoyle All the more reason to not do things live. If you like to present lectures, then you can make a video and upload that for download to some suitable website or file sharing website (e.g. wetransfer.com ). Students can then watch whenever it suits them. – Count Iblis Mar 14 at 17:46
• It was the “email homework” part that I was concerned about. – Gordon Royle Mar 15 at 1:29
• Might be ok if ALL you have to do is sort through emails. Lecture notes should be available as a matter of course. – Rob Jeffries Mar 25 at 10:34
• I like this guidance a lot. Email is searchable and allows easy organization for the student. In contrast, LMSs are cluttered and all work is lost as soon as they change versions or the access code expires. With some attention to organization through creation of folders and a common subject line style, this has a lot of promise and very little start-up cost. – James S. Cook Mar 25 at 14:41