When I was in my teaching Masters program, we talked a lot about intrinsic vs. extrinsic motivation. Intrinsic motivation is when you want to do something for yourself, e.g. you enjoy the satisfaction of solving a problem. Extrinsic motivation is when your reason for doing it comes from outside yourself, e.g. your parents tell you they'll give you $20 for every A you get on your report card. The district I worked in experimented with extrinsic motivators to get students to attend school and perform well on the test with rewards like food, gift cards, and electronics. That was enough to get some students to try to do better, but usually only the students who already had some intrinsic motivation. The students that they were really trying to motivate were the ones with no intrinsic motivation, and they largely ignored the rewards offered.

_Punished by Rewards_ is a great book on the topic. For your experiment, I curious how you controlled for suppressing counter motivations (e.g., peer pressure, pride, etc.)

The class was a required class for teachers to get their education degree. Back then, they had to have that degree in order to teach in the schools.

I doubt that many of them were thrilled for math, especially the more foundational topics we were going through so yes, their intrinsic motivation was mostly not high.

However their extrinsic motivation should have been off the charts. They literally couldn't get their degree without passing the course. Many were repeating the course having failed it before, so their chances were running out.

I do not recall any of the students being the normal 18 to 21 college students - - they were all older. They better understood why they were choosing their degree (looking back, based on demographics, I suspect many were divorcees prepping for a career or moms whose children had started school).

I gave the memorization question as a way to see how much of it was the work they were putting in and much was my inability to explain the difficult material in a way they could understand.

It may be that the manner in which you are teaching that topic is itself failing. Your students don’t understand, investigate how to improve your approach in explaining which results in them understanding. Decompose the steps to see where that understanding is not happening.

It was decades ago so the advice is too late. As I taught other students successfully at the time (in that most seemed to grasp the material), there may be some other problems.

I boiled it down to "just write the equation down" to see if it were my teaching or their desire.

The inability for many to successfully replicate the formula indicated to me that they weren't putting the time in to memorize.

Since these were more adult learners going for their teaching degree, and many repeating the class having failed to pass it the first time, my observations beyond "I wasn't capable" are: - the course material was difficult (a rapid survey of math foundation, including some group theory) - they couldn't make the time because of other life commitments, exacerbated by being a summer course where we met every day.

I had one student, who had never scored higher than 50 on a test, show up after the final to ask if there was anything she could do to pass the class as it was required and she had flunked now 3 times and couldn't repeat it. "All I want to do is teach 3rd grade, I don't need any of this" she explained. There was nothing i could do...