# How should I teach linear algebra and vector geometry together at high school?

I'm teaching mathematics at my former high school and the next topic will be vector geometry. When I attended high school, I was only taught vector geometry and never learnt anything about matrices until university. I feel like my pupils would be missing out on something if I didn't teach them very basic linear algebra and I also have the permission to teach linear algebra.

There are two possibilites: Treat vector geometry and linear algebra as two "different" topics (i.e. with other topics in between, such as integration, probability, etc.) or merge the two.

I experienced the "merged" variant in university, but obviously following that course wouldn't make any sense for high schoolers. However, as I didn't learn linear algebra in high school, I don't really know how I should merge the material I already have from my time in school with new linear algebra. Whenever I try to come up with a plan, I end up putting all of vector geometry (scalar product, vector product, intersection problems) before and linear algebra (matrices, Gauss elimination, determinants, eigenvalues) after.

Do you have a suggestion, how I could teach the two topics in a comprehensive "linear algebra" course for high schoolers?

• What is the length of time you have to cover this material? If you are going to teach matrices, I'd spend a lot of time on the different ways to interpret matrix multiplication. Most students only learn that each entry is a dot product of a row and a column (worse, they often are only aware of the equivalent formula and have no understanding of where it comes from). Knowing that $A\vec{x}$ is both a linear combination of the columns of $A$ and the vector whose components are the dot products of rows of $A$ and $\vec{x}$ is really crucial to understanding everything else in linear algebra. Nov 21, 2014 at 14:55
• I have rougly 60 lessons, 45 minutes each. I can use a bit more but not too much.
– Huy
Nov 21, 2014 at 19:42
• It seems like you should tell us what experience level the kids are and also what ability they are. That will influence how the course is designed. Nov 29, 2018 at 19:35
• You say you have 60 lessons but then "next topic is vector calculus". So it's not clear really how much time is really available. FWIW, I think high school vector manipulation can be done in well under 60 classes. My advice would be to do separate special topics. I think merging will make too much of a new new entity and make it too hard. Also, there are uses of each concept without the merging. Nov 29, 2018 at 19:38