When To Learn Vectors

I have been teaching physics a long time, and all that time I have been teaching physics at the college level, and at the freshman and sophomore level. During the entire time I have been teaching, vectors is something that is always surprises me.

For those of you that don’t know, or can’t remember, a vector is anything that has a magnitude (size) and a direction. For example, velocity is a vector but speed is not. Speed is simply what your speedometer tells you, and that is how fast you are going. Velocity would be that speed and the direction you are traveling. That direction is an important thing when trying to understand what an object is doing, or what will happen to an object when a force (which is a vector) acts on it.

Physics uses vectors from pretty much day one of class (ok, some teachers wait until a couple weeks in but still, pretty much from the beginning). Vectors requires the use of some algebra and some trigonometry, but that is all. There isn’t anything more complicated than being able to set up a right triangle (one that has a 90-degrees angle), and then finding the lengths of the sides and the other angles. Once you can do that you know the components of that vector, and once you know the components of all the vectors acting on an object then you can determine the net (total) result of all those vectors acting on that object.

NOTE – you have to be talking about the same type of vectors do combine them. You can’t combine velocity with forces. They are different things and so you have to work with them separately, but you do the same math for each.

In all my time teaching I am always amazed by when students learn about vectors. They are supposed to learn about it in an algebra 2 or trigonometry class. I taught a trig class a long time ago and I know that it is covered in detail in that class. But it never is, or rarely is. The number of students I have had over the years that have never heard of vectors when they enter my class is astounding. Just today I was told by my BSU students that none of them had heard of vectors until their calculus 3 class, and only a few of them are in that class right now. Most of them are only in calc 1 or 2 right now (that is what math class they should be in at this point in a regular learning sequence). So, when they come into a physics 1 class almost all the students have no idea or background in vectors at all. So, my job as a lab instructor is hard, the lecture teachers are also in the same boat. We all have to teach vectors to the students rather than assuming they know vectors and we just have to teach them how to apply that knowledge to the physics material. What makes this even worse is that in the algebra based physics classes students also need to know and understand vectors. But these students don’t need any calculus classes at all, and therefore none of these students will have taken calculus 3. So, the chances of these students having had vectors is all but 0.

When I was at the community colleges this was also an issue, but not as bad. I can remember having conversations with the math department about this and they agreed that is should be taught earlier and at SCC they started making sure it was being taught in earlier classes. They made those students better equipped for the physics classes. But at BSU I can’t see that happening.

Again, vectors aren’t hard with a little math. It is math that most junior high students learn to some degree (maybe 9th grade). So, to put it off until a third year of calculus seems very wasteful. Because it is something that is so daily, and somewhat useful when just thinking through things in life I don’t see why it isn’t taught at a younger age. Then it can be reinforced in later math classes for those that need to use it on a regular basis. Then students aren’t struggling to figure out in a college physics class when they haven’t been taught it at all, and it is a foundational part of the class.