Learning Math in a Digital Space

(long, but consumable post incoming!)

Learning math in a purely digital space is a pretty unique experience that comes with a lot of advantages, but A LOT of pitfalls. It is wonderful to see that online and distance learning has made education more accessible to so many people. This also means that it is also starting to change the shape of learning environments. Here are some do’s and don’ts I’ve picked up from learning math (along with a few other subjects) in a digital space.

Online Math Do’s:

  • Try making time for recorded live lectures. Choose a lecture time in your day that works for you. This will make each of these lectures feel unique and tailored to the needs of the students in each offering of the course. This, of course, can be a bit demanding, so perhaps choose a few lectures out of the course (preferably the most important or tricky ones) that you will present live to your students, so you may answer questions immediately and save yourself (and your inbox) a lot of trouble.
  • Record your lectures. Period. (This one applies to any subject!) Regardless of how you decide to present the information to your students, give it a little human touch. Nothing is worse than having to scroll through tons of wordy powerpoints in silence. The online/hybrid class should feel like a class, not like a required reading in a textbook. You want to make this experience feel as close to a traditional class as possible. This will also give your students the ability to change the pace of the lecture as needed. I can not tell you how many times I had to change a lecture’s playback speed to 1.5x because the pacing was too slow. Contrarily, students also get the advantage to pause and linger on pieces of a lecture that were particularly challenging to understand.
  • Use this technology to your advantage! One of the best things about teaching math in a digital space is that the technology affords you so many advantages that you can not always implement in a traditional classroom. Being able to spend time looking at animations and graphics in a lecture were always a mental treat. In traditional math classes, hand drawn graphs and concepts could be a little tricky for students to understand and copy (depending the instructor’s artistic abilities). Additionally, very few instructors use powerpoints and other digital means of presenting material in traditional setting, so pulling out a laptop and setting up a projector could often detract from the learning. These are no longer problems in the digital space, so generate some neat graphics and animations! They’ll flow seamlessly into your lectures and students will definitely appreciate the clarity in graphs!

Online Math Don’ts:

  • DON’T use online assessment tools (where possible). This tip boasts the same sentiment as last week’s post. Do your best to avoid tools that automatically assess your student’s assignments. Despite all the good they could do, they tend to do more harm than good while students struggle to get the computer to acknowledge simple human errors. Clearly students should receive no credit for incredibly small things like missing a negative or answering with two decimal places instead of three. Small clerical errors are not a sign of a lack of understanding, but a sign of simply being human. If it is both financially and physically feasible for you as an instructor (hopefully with access with teaching assistants), then you should NOT use online tools to assess work. The only exception to this should be for extremely large class sizes… which at that point you should already know there is not going to an easy way to complete grading without complications.
  • Don’t try to dictate your students’ schedules. Give suggestions and light warnings instead. We have all heard the warning “you can not do this in one night”. Yet, somehow, just about all of us have miraculously done it in one night. It is fair to try to warn your students of the effort an assignment may require, but understand that many students will try to test the bounds of required effort anyway to their own detriment. My biggest example is that of an online secondary education course I took in college. The instructor proudly stated that we should not attempt to finish each week’s assignments in one day because the course required about nine hours of study and work weekly. Of course, my stubborn response was “Nine hours? That is one day”. So, I started and completed each week’s assignments in one day. This drastically changed my expectations for the course and I did not take it seriously. I passed the course with good grades, but I retained very little detailed information from it because all of the learning was crammed into very boring nine hour blocks of my Sundays. Moral of the story: For your students’ benefit, give them suggestions on how they should prepare for your class, don’t give them a time frame they will obviously cram with little to no material retention.
  • Don’t make assignments closed book. This one is a tricky one, but let’s be entirely honest here: they are going to look at their notes anyway. We would like to think that our students will follow the honor code to a T, but the reality is that they won’t. Clearly we want our students to demonstrate their learning without the training wheels of their notes, but teaching in a digital space makes it a little difficult to enforce. Here are two solutions to this problem:
      1. Allow open book assignments, but change the available time frame for quizzes and tests. You will want the time frame to be suitable for students to glance at notes to get necessary formulas, theorems, and concepts, but not long enough to entirely familiarize themselves with those topics as if they haven’t studied. Bottom line, you want a ‘glance’-able time, not a ‘study’-able time. This should be somewhere around 5-10 minutes longer than a normal closed book time frame since quickly going back and forth through notes will take away some time.
      2. Do not allow open book assignments, but require summative assessments be taken in person. Since many students of an online course will be near your institution anyway, set a time and physical place to take tests and exams. This will force students to demonstrate their understanding while limiting open book cheating. This, of course, comes with many limitations. Not all of your students will will be able to meet at a single time. In this case, work with individual students to take tests/exams at a different time. You will, of course, want to limit this to prevent some students having an advantage over others. It may be wise, to gauge the general availability of your students before setting a time. For distance learners, the main institution’s campus may be feasibly inaccessible. In this case, you may want to coordinate with a test-taking facility (or instructors from a closer institution) to have your distance learners take proctored tests/exams and have their results scanned and emailed or faxed to you. (See? Fax machines can still be useful. They aren’t the relics we make them to be)

What are some other do’s and don’ts your instructors have (or you wish they had) implemented in your online/hybrid math classes?

Math Pun of the day: What do you call a young eigensheep? A lamb, duh!

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8 thoughts on “Learning Math in a Digital Space

  1. Jocelyn Hotter says:

    I really enjoyed reading your post, as I agreed with most of what you said. I first want to topic on open book- I agree this can be a very helpful tool as it allows students to learn the material, and not guess at what they think may be correct. I also like the idea of recording all lectures, though I think many professors may first be wary of this idea, as it makes lectures permanent and it gives students the option to not show up to class and still get the material.

    • gabrils says:

      Ah. I’ve seen this happen a lot where students decide to not show up because “it’ll just be recorded anyway”. The trouble is, there are students like myself who will say that, but most certainly don’t end up watching the recording or won’t consume the material in the same way because it is a recording with no feedback (which is why I prefer to be present for classes). Just about every helpful thing can be abused in some way, so I don’t like to think about how I can prevent the abuses. Instead, I try to find the right mix of things that helps the most people. If someone wants to take advantage of the structure of a class, they are going to find a way anyway.

  2. charyoutree says:

    I wanted to focus on one point you made in your post (even though you made so many great ones), “Record your lectures. Period.” Some online classes (and even in-person) I’ve taken have a million “lectures” that are just reading from power point slides. When I see a class like that I would just rather read a textbook and teach it to myself. However, that’s not what I want to do nor why I take a class (online or otherwise). It’s crazy to me that some professors do this and think that it is a good way to convey information. The one use I’ve gotten out of a class having a ton of power point slides is going through the slides quickly to find some equation or information I needed. But that’s what my notes are for and if they had recorded the lecture like a normal class, I would’ve taken notes. However, I don’t normally take notes when the power point lecture is all words! It seems to defeat the purpose of teaching the class when your class becomes a textbook in power point form.

    • gabrils says:

      Oh absolutely. The best part of a class is that there is a human touch in how information is shared. I love when powerpoints are shared ahead of time so that I can just add notes on the side that aren’t explicitly stated in the slides, but the instructor emphasizes. I feel that’s really how powerpoints should be used; they should simply be a discussion/lecture guideline for the instructor, not a script.

  3. Anmol Haque says:

    I really enjoyed your post- I have a similar notion on online assignments. I agree that is does get too harsh for giving no partial grades for a math and just using online tools for assessment. It definitely makes it easier for the instructor to grade a class of say more than 30 students- but I feel like it is not fair always. However, if you are just a student getting to teach a class with no TA on your behalf- how do we deal with the problem of online assessments? It does save us a lot of time if we do it online- but then I do not like this method myself- pondering for a while how to combat this.

    • gabrils says:

      This is a really good question with no definitive good answer. The struggle with teaching, I’ve found, is trying to choose the lesser of evils that defines who you are as an instructor. Ideally, we would love to have all the time in the world to thoroughly grade everything by hand and spend as much time as we truly need with our students to help their learning, but the truth is it NEVER pans out that way. At some point, you just have to decide what you are and aren’t willing to do for your sanity. Let’s face it, teaching likely isn’t the only thing on your plate. You can’t spend all the time and energy you want on these problems. Instead, you simply have to find the balance that works for you. That could be choosing which assignments are automatically assessed, reducing the grade impact of assignments that are automatically assessed, or simply reducing the number of assessed assignments given such that your grading haul is significantly reduced.

      Personally, at the university level, I prefer to assign homework where it is clear that the majority of it won’t be used towards your final grade and around 4 of those assignments will actually be graded. This way students have the freedom to practice without fear of failure and they are able to focus on the parts of the material that trouble them the most. There’s nothing worse than wasting a bunch of time on material you already understand. This way the 4 homework assignments that students are aware will be counted towards their final grade are an opportunity to prove their understanding without wasting a lot of your or their time. Additionally, I like to set up these graded assignments like a study guide for upcoming tests. They will have a better time on tests when the homework looks similar to it and they were given feedback ahead of time!

      Overall, it is entirely up to you to decide what feels right and wrong. Your choices may be uncomfortable for your students at times, but you still have to make choices that aid you as a functioning instructor. I feel if you remember to have empathy for your students, everything should be fine.

  4. mjessie1 says:

    This was great! Really enjoyed it, I was just commenting on another post about how there are different ways you can design a course that can allow for un-proctored exams or open book exams. I think this style of teaching naturally lends itself to better assessment techniques than are employed in the traditional classroom. One thing to me is that there is a lot of evidence in neuropsychology to suggest that our most talented mathematicians use visual coding systems to store and manipulate numbers, and I’ve long thought that virtual environments and animation might make for the best ways to teach math because we can get kids early and teach them this totally different way to conceive of, to visualize numbers and their manipulation. I thin it would be super cool to interview a bunch of great mathematicians and have them describe how they visualize a number line, and a number line in action and see if that couldn’t be animated or made virtual for the classroom.

    • gabrils says:

      Hm. That’s a really interesting thought. I never really thought of how I think of numbers and math. It’s mostly memorization, but my memory is extremely dependent on previous visual cues. That sounds like an interesting study to conduct. It sounds like collaboration material! 😉

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