a guest post by Ellie Kennedy
Prior to the spring of 2013, I taught my discrete mathematics course via a traditional lecture style. I used to bore myself with those lectures. Counting principles seemed like a topic that students could develop on their own with maybe just a little problem-solving help. With induction I felt like I was lecturing and showing the students the same examples over and over and it wasn't sinking in. I needed to try something new and fresh, and inquiry-based learning (IBL) seemed like a method that might work for me. So, last spring when I taught discrete math, I used a modified Moore method. I'd like to share my experience as a first-timer and some of what I learned.
Ted Mahavier started me off with a set of notes, and Dana Ernst helped me sort out the logistics of the course. I was so thankful to have such great resources. Students would read definitions and theorems in the note packet and work on problems at home and then present the problems in class. In a traditional Moore method classroom, students are not allowed to collaborate, but I encouraged students to work together.
The counting and graph theory parts of Ted's notes were fantastic, but I did modify them a bit to fit the topics taught in our course. Ted's notes focused on strong induction and our course has a weak induction focus. This was not a difficult change to make to the notes. Ted's notes did not have anything on recursion, so I wrote an entire section myself. I was surprised how challenging it is to write IBL notes! I found it hard to build questions leading to the main idea when, to me, the main idea was an algorithm to solve recurrence relations. It made me realize how much I personally rely on knowing how and why an algorithm works but not the history of how it was developed in the first place. Very eye-opening for me.
I used the felt tip pen idea that Dana has written about, and it was a true success. While in class with other students presenting, the students would use only felt tip pens to mark up the work they had done at home. This allowed them to produce a solution set of sorts, and it made my grading super easy. I did not grade for correctness. I graded only on the math they produced at home (non-felt tip pen work). This method also allowed students to constantly self-assess, which can be an effective learning tool. The students felt it was easier to do homework when they didn't have to worry about getting it right at that very moment. They found they could just concentrate on the math that way.
I tried to make the class a comfortable place where students could make mistakes freely and without embarrassment. I made a list of "dos" and "don'ts" so the students were aware of some positive ways of pointing out that they thought someone was wrong. The first time a student did a problem wrong, I made a big deal out of it (in a positive way). I thanked the student for having the guts to put up something that was wrong. Then the class discussed what parts were correct and I had the students work on the problem for another night and we came back to it the next day. I always pointed out the learning experience that came from each mistake that was made. A student commented in my end-of-semester evaluations that I "showed respect for the students and encouraged [the students] to fail early and often (this is a good thing)." Mission accomplished!
In a traditional lecture-style course we start with a city and then tell the students what road to take to get the next town. We expect them to repeat the same route we just showed them. Yet in an IBL class we give the students the cities and states and then tell them to find their own roads and build their own map. Creating our own paths makes it much easier to remember how to get there the next time.
The number one thing that I learned from this new experience (other than that IBL is amazing and really does contribute to deeper student understanding) is that it is important to understand that being confused is not just okay but a really good feeling to embrace in mathematics.
When I first started going through Ted's notes, I found problems where I didn't understand the question. I realized that this was purposeful, intended to promote conversation. Confusion leads to questions, and it is in those questions that true understanding and learning occurs.
This current technological age pushes us to find the answer FAST. Even I am guilty of just "Googling it." It is challenging for students to work on a problem or question for an extended period of time. They don't understand that some questions go unanswered for centuries and that is normal for us mathematicians to keep trying. I feel that as educators we need to let our students know that as long as they get the important parts before the exam, it is okay (and fun) to be confused and search for an answer for decades or years. Let's encourage the struggle and show our students that struggling in math is really exciting! Hopefully students can realize the incredibly rewarding feeling of solving something after much thought and time!