Education: Teaching Math Remotely
BY Jason H. Goodfriend
There can be no doubt the United States would have had a much more difficult road to travel coping with the pandemic were it not for the ability to connect remotely. I shudder to think how much more damage would have been done to the economy and to people’s lives if we had not had the capability to work and meet remotely.
Similarly, as schools and colleges/universities were physically closed, we probably had no choice in employing remote learning. However, as a math tutor and former adjunct mathematics professor, I have some observations to relay concerning the pitfalls of teaching math remotely. They have led me to believe that mathematics should not be taught remotely accept as a last resort (which occurred during the pandemic). I also have some observations about the use of computer software in having students work math assignments. Software and communication technology does not always offer a better solution.
I recently tutored a student who was taking Calculus II at a local community college. As all classes were online due to the pandemic, he would listen to the professor’s lectures remotely. There was little opportunity for the students to ask questions. (Admittedly, part of the issue here could have been with the professor.) Consequently, in addition to helping with the homework assignments, I basically had to teach the course. To add insult to injury, there was no textbook.
At the risk of sounding old-fashioned, I believe the only way to teach math is in front of the students with a blackboard or whiteboard. Students gain by watching the teacher deriving and struggling with the concepts and equations, and sometimes making mistakes. It also helps if the teacher stops and asks the students what they think comes next. Furthermore, students have to be able to ask questions when they do not understand a concept or derivation. Learning math is active, not passive.
Now, whenever I did not understand a particular lecture in my student days, I could refer to the reading assignment in an actual text. Go figure! I spent a good amount of time carefully reading the text and looking at the examples. For sure, the savvy student can almost find a good discussion of the topic at some website or video. Unfortunately, without being prodded by the teacher, many students do not know where to turn in the absence of a well-planned text.
I am currently tutoring a 14-year-old girl in Algebra, and the class is remote. She is so used to typing at the keyboard, she is often at a loss when I tell her to do a needed derivation on the side, using pencil and paper. Entering your answer on a computer when you are done working a problem is fine, but the computer is not particularly helpful when you are struggling with the derivation phase. Using paper and pencil, you can cross out your mistakes, make changes, and proceed with fits and starts.
Also, she is so used to always using the computer, she does not know how to quickly reduce a quantity such as 27/3, without typing it in and letting the computer solve it. (By the way, the answer is 9.)
I want to return the Calc II student that I was tutoring. His assignments were all online. To get credit, he had to answer the question online. Sometimes the computer software would mark his answer wrong because it was not expecting the answer in the form that he entered it, even though the answer was right.
The other problem with this method of giving assignments was that the student was not able to get partial credit for the homework. (I believe he was able to get partial credit for exams by taking a picture of his work and scanning it in.) While the computer provided an explanation for the answer after the student entered his answer, the teacher did not go over any of these problems in class.
Let’s contrast this with how I handled math homework when teaching in person. The first thing I usually did at the beginning of class was to ask the class if there were any questions about the homework that had previously assigned. If there were questions about a homework problem, I would then work through the problem on the board, giving tidbits of advice as I proceeded, and I often acted interactively with the class. Also, when I collected assignments for grading (which was not for every homework assignment), I provided partial credit if the student was on the right track.
Now, don’t get me wrong: I believe computer math software can be enhancement when used properly within a math course. The problem is when it replaces too much of the course. I think there is a lot teachers can do to make remote learning work to the students’ advantage. And please keep in mind that my knowledge base is for students in middle school through college.
Some of the below activities are already being employed by good teachers:
1. The teacher can still use a whiteboard/blackboard while on camera instead of giving prepared slides. This makes the experience more like a classroom interactive experience.
2. The teacher could still require a text (if allowed by the institution) or least email out handouts. When I was in school, the teacher would explain a topic, and then assign the reading of the chapter where the topic was addressed. There were times when I did not understand the lecture, but after reading the assigned portion of the text, I understood what was going on. It seems like reading is a lost art. The best way to learn (in my opinion) is to read the section, look at the examples listed in the section, and then try solving the assigned problems.
3. When the student does an assignment from the computer, the teacher could ask the student to work out the problem on paper and then take a picture of the work and scan it in. Then the teacher can give the student individual comments. (This can be done for at least some of the assignments.) I know that some teachers employ this technique more than others.
Jason H. Goodfriend, Ph.D. is a statistician/data scientist by trade, and a philosopher and commentator in his copious spare time. He is also a math tutor and has taught college mathematics as an adjunct professor. He is the author of the college textbook A Gateway to Higher Mathematics. He recommends it if you like math, or if you hate math and have insomnia. His other interests include centrism, reading, hiking, good restaurants, and karaoke (of course). You can find him on Twitter at @CentristJasonG
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The Modern Whig Institute is a 501(c)(3) civic research and education foundation dedicated to the fundamental American principles of representative government, ordered liberty, capitalism, due process and the rule of law.
Opinions expressed here are those of the author and do not necessarily reflect the views of the Institute or its members.
