I am sick and tired of people complaining that nobody likes math when they refuse to admit that mathematical notation sucks, and is a major roadblock for many students.
I agree, and I think it’s a problem that plagues “students” in all phases of life—from elementary school to the very intelligent actuaries that I help pass their actuarial exams post-college.
The learning challenge presented by overly formal mathematical notation is fundamentally a data visualization problem. The “data” encoded in mathematical notation are the generalizations represented by the letters, numbers, and symbols.
This creates two major barriers:
Cognitively, it is difficult to parse complicated notation while simultaneously simulating the outcomes described by the notation. In other words, it’s not plain English, and the human mind is not the numerical simulator we’d like to believe it is. It feels like reading computer code to learn a generality.
Teaching generalizations is more like giving a fish than teaching how to fish. It encourages memorization, not individual discovery.
The approach I’ve adopted after years of processing overly formal notation is to rewrite it for my students in plain English—or in practical examples whenever possible. Much like a well-designed graph, a formulaic concept is well represented when its audience knows what it means after rereading it as little as possible.