When I don't remember learning...

I remember when I struggled with many physics topics. I don't remember high school (AP) physics particularly well, but I can recall my experiences in Introductory physics as a freshman at MIT. I remember the feeling of looking at homework and having no idea what to do. I certainly remember my struggles in upper division courses - I was frankly surprised that I was even capable of teaching E&M at the advanced level, since I didn't think I had learned anything about it in the 5 years since I had taken it.

I try to recall these experiences as a way to empathize with the students and to structure my teaching. It isn't enough to teach students the physics concepts and calculations, I must also teach them how to determine what concepts are important for a given problem. I also try to assure them that it is normal for them to struggle with this material and find that it is never perfectly clear. This is especially true with something like quantum mechanics. When I cover QM in a few weeks, I'm sure some of the students will find it upsetting that they can't quite wrap their head around it. At this point in my life, I have taken 6 quantum mechanics classes. I understand it much better than the first time (or second or third) time I took it, but I also have learned to accept that sometimes it doesn't make sense.

I heavily rely on these memories of struggle, but it turns out that I don't have (useful) memories of struggling with math. I certainly struggled with some math at MIT, but they were upper division courses - not the sort of thing that is used in Introductory physics. I don't remember learning Calculus for the first time, or vectors. I certainly can't recall a time when algebra was challenging for me.

Some of my Intro physics students are struggling with vectors, which I did not fully anticipate. It is a much bigger challenge than I expected. I spoke with a math professor (who is teaching Calc II to many of them) who said that many of them haven't encountered vectors in college math. They may have seen them in high school, but they would only see them here in Calc III. So what I assumed would be a 'review' for the students might be the first time they are seeing it.

I want to make sure they understand vectors before I blow ahead into the next section of material, but I'm not sure that another 50 minute lecture on vectors will help much. Additionally, when we get to 2- and 3-dimensional motion they will get more practice with vectors. The 'physics' way of using vectors can be quite different than the 'math' way of dealing with vectors, so I'm not sure that spending lots of time on vectors as an abstraction will actually be useful scaffolding. The current compromise I decided on was:

• Post lots of tutorials (video/text) on vectors that the students can choose to utilize
• Have some 'hands on' practice with vectors (from a math point of view) in Workshop this week
• Not put vectors on the first homework
• Make sure I drill vectors when we get to physics applications of the vector
• Think hard about how this can be improved for next year

I wish I remember learning vectors, but I don't. This week we will start using calculus, which I know will be a challenge for some of them. The derivatives they need to do are relatively simple, but many of them are learning about integration for the first time in Calc II right now. We'll start applying it to physics on Friday! I also don't remember learning Calc for the first time...