Following up on Last night of summer, I wanted to take the time to talk about how my first day went. The major thing I was worried about last night was having my first meeting of my mathematics history class. Particularly because it is a three hour class period. How do you keep a class engaged, interested and involved for a full 3 hours?
As the day began, I was confident going into my calculus classes, since I’ve taught calculus so often. I began the semester going over the syllabus in the hopes that the students would listen when I told them what was expected of them and the grading system. Overall, the students seemed fresh and relaxed from their break. They payed attention, asked questions and were great. However, 10 minutes before the end of class, just about everyone was ready to fall asleep and had completely lost all ability to pay attention. This happened in both of my calculus sections and these were only 75 minute classes. What hope did I have for getting through a three hour class without losing everyone in the class?
I was honestly afraid that I’d have to let the students go half way through class because they would be so checked out. Now, if this wasn’t the first class of the semester, I would have felt more comfortable giving the students an assignment ahead of time so that they would hopefully be prepared to work together on questions during class and make use of the time they spent working together. In this case though, it was all on me.
What happened, well I started of going of the syllabus and expectations. Yes, this went just as well as earlier in the day and the students began tuning me out immediately. I know, this isn’t the greatest way to start off a class; however, I still feel it is important enough to give students a clear explanation of what is expected of them that it is worth boring them. In this class; however, I was thankfully able to get through the syllabus quickly. Because of this I was able to get into something a little more interesting.
Now, I felt like this was a gamble. I knew the students would be tired of listening to me talk after the syllabus, so I decided to go with group work. With no foreknowledge or instructions given I just threw them into it and hoped they’d do something. The questions I posed to the groups were the following; suppose you have one apple, explain to another group, without using numbers, the idea of 4,5,12,1543 and .5 apples, to the other group I asked them to explain how to put a set of objects in a specific order without using numbers as well. Luckily, this paid off. The students got into, thinking of ways to explain numbers without using the existing number system. They floated ideas about creating their own numbering system, comparing number to know grouping, and pairwise relationship instead of a complete ordering.
After the exercise I was feeling good and I looked at the clock. There was still 2 hours and 15 minutes left in class… What now? Well I had decided to lecture a bit and talk about Egyptian mathematics then let them go through examples using the technique presented for division and linear equation solving. It is a rather awkward process compared to using modern techniques and notation, and the novelty of it really paid off in retaining students attention. However, this still had a limited time of usefulness, so I had to move on again. Instead of detailing the entire lecture, I’ll just say that we moved from 15 minute to 15 minute activity again and again until we finally reached the end of the class day.
While this was the plan going into the day, I had never broken a class into so many parts. Thankfully, I believe it went well. The students seemed interested in each new problem, were willing to try things they hadn’t thought of before and switch between topics. I don’t honestly know if I could reproduce these results, and do have changes planned for next week’s meeting, but thankfully I made it through the first day with what felt like a success.
If you’ve taught or taken classes with extremely long meeting sessions, please comment and let us know how it went. What worked for you and what didn’t? I’d love to hear from you.
Furthermore, if you’re interested in Ancient Egyptian arithmetic or other mathematics history, I found the website by Jerry Johnson, Western Washington University a great source for interesting problems to think about and go over.