Q&A: How to Introduce Sigma Notation

Cross-posted from here.

Question

I attempted to introduce the summation notation $\sum$ to my students. The notation was unfamiliar to the students beforehand.

I worked through many examples with them, but for most of them, working with such an abstract notation remains challenging.

Do you have any suggestions on how to best teach someone who has very little prior knowledge of math? What is the most intuitive method to introduce this notation?

Answer

I’ve experienced positive results by first having students spend some time writing out sums in full (or using ellipsis notation if there are many terms).

That way, it gets annoying to spend so much time writing the sums, and I can present sigma notation as “a shorthand developed by mathematicians who, like you, were tired of spending so much time writing out sums.”

Once a student understands on a visceral level what problem an abstraction is solving, they are far more receptive to the abstraction as a solution to that problem. (Otherwise, if they don’t really “get” what problem the abstraction is solving, then it just feels like needless complexity, and their eyes glaze over.)

Of course, after the problem of writing out sums is experienced and sigma notation is introduced as a solution, it’s still necessary to scaffold the pedagogy well, starting with simple examples (the sum of even numbers from $2$ to $100,$ the sum of squares from $1^2$ to $10^2,$ etc).

And students would still need to have mastered the necessary prerequisites, such as writing a sequence given its formula and vice versa (and a prerequisite for that would be evaluating functions).

But properly motivating the notation should at least get you over the initial hump.