Making an online math course "interactive"

Question

I teach some fully online math courses (community college in the USA), and I'd like to hear how you have made your online classes successfully "interactive" along three axes: Student-to-Instructor (S2I), Student-to-Student (S2S) and Instructor-to-Student (I2S)

Based on student feedback to me (during and after the term), my classes operate alright on content -- they feel the coursework and lessons work well together. What I feel they (may) suffer from is a lack of person-to-person interaction.

Some things I already do:

• I provide written feedback to students on quizzes and exams (I2S)

• I hold open office hour "help sessions" (both online and in-person, regardless of which course section a student is in) which I remind students about and personally invite them to attend. (I2S and S2I, often becoming S2S)

• I make an introductory post at the start of the term in the “Discussion Forum” in our LMS and ask students to do the same with responses to another person's post. (S2S, I2S, S2I)

• I send semi-weekly (at least) emails briefly introducing the upcoming topics. (I2S)

Because our college has officially frowned on mandating any type of synchronous activities for online students, I have not found a way to encourage group-work (which would be a standard thing in my face-to-face classes). So, I don't know how to get S2S interactions happening in my class.

Do you have experiences that have helped on any of these axes? I would definitely appreciate hearing if using discussion boards have helped in math courses, other than the typical first "welcome to class" posts. Have you managed this in a system that discourages synchronous activities for students, all while keeping things "interactive"?

Edit: Note that this question is about a 100% remote, asynchronous format where students cannot be forced to do a certain thing at a particular time (per the college's rules). There is no "in class" time scheduled. [There are exam days, where a student must log in to take an exam sometime between 8:00am and 11:59pm.] I am seeking experience increasing interaction in this type of setting.

Answer 1

I do not have a silver bullet, just some experiences in a maybe similar enough direction to be helpful, or maybe that can be a warning.

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I have a different context, university level but mathematics education courses for teachers who want to get official competency to teach maths (but have often done it or are doing it at the same time). In-service teacher might be the English jargon.

We have weekly lectures after school teaching has usually stopped, on a fixed day, so the teachers have some change of adjusting their schedules to fit. About five to ten of the teachers attended those and got to enjoy the small group discussions and plenty of interaction. We recorded those and the records are available to all the students.

Also some written or video assignments etc.

This did lead to a core group of students forming. Those were the active and motivated ones, of course, and did very well and enjoyed their course. Others had much more variable outcomes.

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My general experience with discussion forums and such is that you need to heavily integrate them into the course if you want them to actually be used. It does not work to have something as a side offer. Also you as the teacher need to actively and aggressively model using the forum. Maybe there is a chance then.

Answer 2

For context, I majored in mathematics as an undergraduate, but minored in education. I held a secondary education certificate which allowed me to teach high school and middle school mathematics in the state of Nevada, and I taught at both levels for a couple of years.

I then spent most of my TAship in gradudate school working on a precalculus program which was designed to have three hours of "traditional" lecture per week (with 300+ students in attendance), combined with two hours of "recitation" (in groups of about 20). The long term goal of the program was to have the entire lecture occur online (synchronously), and for the recitation sections to be in-person. The primary instructor and most of the TAs held office hours virtually (office space was limited).

After completing my PhD, I took a position at a small, rural community college (where I am now). This institution has been "doing" distance education since the 1970s. Each of our nine locations has a radio broadcast tower (lectures in the 70s and 80s were delivered over the radio), and starting with the invention of VHS, lectures were often recorded at one campus and sent to other campuses via courier on VHS. About 15 or 20 years ago, the college contracted with Cisco to install "smart classrooms" at all of our locations, so that classes could be held synchronously with students in several different locations. We have also installed systems in many regional high schools, so that we can teach dual enrollment classes.

To make a long story short, I was pretty comfortable with online instruction before the pandemic, and I work at an institution where distance education has been a part of the mission for half a century.

Based on this experience (both personal and institutional), some thoughts:

• Written Feedback: Honestly, I have never really thought that written feedback was all that useful (despite being told, over and over again in my teacher education program that written feedback was super useful). The students who are struggling typically don't read the feedback (or don't understand it?), and the students who are doing well will generally break down your office door to understand what is going on. I don't think that written feedback fosters a lot of interaction.

  Instead, I tend to give fairly minimal written feedback on most work, and then require that students meet with me (generally over WebEx or Zoom, but in person is great) to go over any additional feedback. This works well for me, as I give a lot of assignments which have opportunities for revision and resubmission (the goal is to have a solid final product—how we get there is less important).

• Office Hours: Rather than holding regularly scheduled office hours and hoping that students show up, I have started requiring that students make appointments for office hours. I then (1) try to schedule students so that they meet with me in small groups, and (2) give them "points" in the class for attending office hours. I think that this is good for developing relationships with students, and it is a lot easier to know what they need when you can talk to them synchronously (generally not in person—again, we are almost always remote).

• Discussion Fora: I am not convinced that discussion fora are all that useful in mathematics classes (aside from, for example, our "Math in Society" class). It is a lot of work to develop good prompts for such fora, and it is a lot of work to get students to engage with those fora. Maybe other instructors have had success with such things, but I am not convinced that the juice is worth the squeeze.

  I will note, for general context, that I have tried a bunch of different things over time—I've used the discussion forum feature on a couple of different LMSs, I set up an IRC server ages ago, I've tried my own phpBB forum, and recently tried a Discord server (with a math typesetting bot!). None of these have ever generated a great deal of discussion, let alone productive discussion. I suspect that these kinds of tools might be useful in the social sciences or humanities, but I've not had much success in mathematics.

  In my opinion, they're not really worth the effort.

• "Flipped Classrooms": The model we used in our precalculus classes when I was in graduate school was a take on a "flipped classroom": students were expected to attend lecture (post-COVID, I am told that they can now watch the lectures asynchronously, too), then work in small groups during recitation to complete more difficult problems. A more "traditional flipped classroom" model would be to have students do all of the lecture on their own time, and then work on problems during class.

  This is a model which seems to create a lot of interaction between the students, and removes the spotlight from the instructor. Do keep in mind that this does require quite a bit of preparation on the part of the instructor: you need to come up with engaging problems, and you need to monitor the composition of groups (I try to mix them up every week or two). This is also something which, I think, doesn't work nearly so well remotely—students really need to be in person, face-to-face, for this to work.

  That being said, I have had limited success with an online model in which students watch pre-recorded lectures outside of class, and then online class time is meant for work. The "breakout room" feature of Zoom (or whatever software you are using) can allow small groups of students to fission off and work together, and the main room is often a bit more "teacher led". It's not ideal, but it kind of works.

• Email: Students just don't seem to use email anymore. That doesn't mean that you shouldn't use it—email is the official communication channel of my institution, and I do make it one of the requirements of taking the class (per the syllabus), but it seems to be a fading technology in educational settings.

  I typically send one or two emails per week, outlining what is due and inviting students to make appointments for office hours. I also award students points for discussing course material over email. I do think that email is a really good tool, but it is a lot of work to get buy-in from students.

  In addition, our LMS makes it possible for students to email each other. While I have no control over this and cannot offer a grade for it (because it is largely invisible to me), I very much encourage students to use this system to ask each other questions, and to set up study groups.

Answer 3

I'm a retired California community college professor. I taught in person until covid, then online, and then I retired because online teaching was so awful.

In normal times, with in-person instruction, I spent a lot of class time doing what you refer to as S2S and S2I, because that was what seemed to be supported by research. If I had my career to do over again, I probably would change that, the main reason being that students are used to I2S, it's easier for them, and they consider anything else to be abnormal. Therefore they generally didn't want to do any of the active stuff, and they complained a lot about it and dissuaded other students from taking my classes.

In my experience there are also some serious problems with S2S that are specific to a community college. A high percentage of students are unwilling to do the prep work, such as reading the textbook, that would be required in order to make it effective. In any kind of group work, there would tend to be a lot of groups in which all the members were either silent or using incorrect reasoning. In the shift to (synchronous) online teaching, I found that both these problems actually became worse. Students in an online class are generally less involved (so fewer are doing any prep), and are performing at a far lower level (so in group discussions on zoom, it's far more likely that they will simply get lost, give up, or head off in the wrong direction).

I had in-person strategies for dealing with these problems, such as walking around the room and listening in on groups, and, e.g., trying to unstick them if they were convinced of something wrong. These strategies worked less well in a zoom class because of all the added "friction" involved in trying to switch around to different breakout groups. In a completely asynchronous online class, I think this would get even tougher.

There are exam days, where a student must log in to take an exam sometime between 8:00am and 11:59pm.

Oh no. This is a total disaster. These are the days when your students will do all their S2S, but it won't be the kind of S2S that you want. With this type of testing setup, I can guarantee you that the majority of your students will be in a Discord session, discussing the answers. (Some will instead hire someone to do their exam for them.)

Any online class without in-person, proctored testing is a class in which the majority of students will get through the class by cheating and without making any effort to learn. In that type of class, interaction is of course very low, because interaction requires effort.

Answer 4

Non-commercial, non-official. For practice (plus to promote math/calculus,) have used free cross-platform simulators to produce math/calculus classes.

How this is interactive: have released all assets as FLOSS/Creative Commons + include instructions of howto use assets to produce more of this.

Examples of Bud Interactive used to produce virtual calculus classes:

https://www.youtube.com/watch?v=wSMTJ7NcyCA

https://www.youtube.com/watch?v=lKWeHFm-dZY

https://www.youtube.com/watch?v=ecU5wGG5eD0

The last two have a picture-in-picture (bottom right corner) from Sakura School Simulator of a class about how to have robots produce houses.

What have noticed others do to produce "interactive" math/calculus classes:

one community college had a math class (math 101?) all through the browser. The host ran formulas to produce random questions (plus check responses) for us.

(Not shown above) Bud Interactive has an option to add "Question AI" NPCs to virtual worlds; if you set the topic to "Calculus", it asks you random questions such as the ones at https://tutorial.math.lamar.edu/Problems/CalcI/ExpFunctions.aspx plus checks your responses.

Did not include this because Bud Interactive is too difficult to use with bluetooth keyboard/mouse, plus it kept messing up the phone's bluetooth settings, so am not sure if should suggest to use this.

But you can search for such simulators until you have one which suits you; the general practice above holds for most such simulators.

Advantage of such immersive/interactive classes is: lots of the new generation have addictions to games, to if you turn the games into classes, all of us have success.