Good Learners Make Good Teachers

It’s hard to say what exactly will help you find your teaching voice and your identity as an instructor, but I can certainly say, from my experience, being a good learner is imperative. I found that one of the most important things to finding my teaching voice was finding what was important to my own learning experiences. In order to do that, I had to be an active learner in any experience I could. What was it about a particular class that made assignments manageable to complete? What were the most important things instructors did that made lectures consumable?

Being able to reflect on all of these things and culminate the best experiences (and the lessons from the worst) into your personal style and firm teaching ideals is all that is needed to find your way to a teaching voice. Personally, I feel that as long as I am keeping a good sense of empathy for my students and fostering some sense of critical thinking or academic exploration, then I am successful as an instructor. This is not to say that I will find a set of ideals and stick to them forever; things change and so do we. It’s important to not just stick to a particular set of rules forever. Obviously, the important things like empathy, integrity, and critical thinking should be the foundation for all teaching philosophies, but that doesn’t mean how we express our teaching voice must remain the same.

Times change, students change, needs change, and so must our teaching voices. In order to do this, not only do we have to be good learners, but we have to be constantly learning. Being a good teacher isn’t an irrevocable status, the definition of a good teacher changes with the needs of students. So, as teachers, our methods and values must change and, consequently, so will our teaching voices.


Math Joke of the Day: What do you get if you divide a pumpkin’s circumference by its diameter? Pumpkin π

The Importance of Framing

Just about all of us have been there: that one dreaded math class that feels like a drag on your whole day. For some people, that’s been just about every math class. And for others, we’ve almost never been there (myself included). This typically stark contrast in outlook on math makes me wonder at what point does math education becomes less fun and surprising and more confusing and mind numbing?

Our recent discussions on critical pedagogy, made me realize that the biggest issue is framing. A lot of math classes take on the same form: topic introduction, repetitive practice, testing/assessment. Although most math classes take on this form, some are more bearable than others. So, what is the difference? It must be the framing. Here, by framing, I refer to how material is presented and the attitude used to approach it. For some people, the idea of learning a method and finding different ways to repetitively use it is mentally stimulating enough to stay interested. I find myself in this group of people; it’s like learning a new rule in a puzzle game and you get to play puzzles all day. However, for others, this is a nightmare. This kind of framing hearkens back to the need to educate students to repetitively carry out a task to be successful in assembly lines which were integral to the work force in the 1920’s.

With the rise of technology, this sort of student is no longer needed and repetition no longer provides students with the skills they need. Consequently, our framing of education, in general, needs to change as well. We no longer need that repetitive driving of knowledge into students’ minds. Instead, we should be constantly finding ways to incorporate different teamwork, critical thinking, and diverse problem solving skills. Our framing of education should be done in a way that can still excite students, whether it be game-style lectures, problem/project-based learning, or simply reworking/rewriting traditional lectures to include relevant topics to students. Of course, this is easier said than done, but I believe simply making an effort will make a world of difference. So drop that textbook you’ve been teaching from for the past however many years, and find a new way for students to discover information instead of trying to cram it in their heads.

At what point did the framing of your math classes become boring or unbearable for you (if it ever did)? If it didn’t, what kept the fun going for you?


Math Joke of the day: You might think my calculus jokes are derivative, but they are an integral part of me.

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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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