Did Mesopotamian scribes have algebra?

Upon reading this article regarding Babylonian algebra, I find it very intriguing how at a time before algebra was invented, the Babylonians somehow found a way to develop sophisticated numerical methods for solving various forms of equations. People could express math relationships through repeated trial and error of equations and imaginative use of various tables at the time. To add on, by using a sexagesimal, or base-60 system, the Babylonians were able to solve various types of functions and equations through substitution and Diophantine method.

By looking at how the Babylonians created their own system of equations, it makes me wonder if math is all about generalization and abstraction. I think we have to consider both aspects depending on the context in which they are used. In such a way, we can use generalization for finding a pattern of addition and write out an equation for it. We can also use abstraction to explain hundreds of different scenarios under the same structure in math. However, since modern math is involved with other things such as proofs and measurements, it is safe to say that math is about a lot of things, not just generalization and abstraction.

When we're discussing general and abstract relationships, algebra is often involved. However, I believe that using words and statements is one way to express general and abstract relationships. It is also possible to use verbal and visual presentations to prove the relationships, such as using a diagram to represent the area of a triangle. Although these relationships can be proved without algebra, I think doing so becomes more complicated when solving problems.

As we watch our students struggle and learn at the same time, sometimes we teachers question ourselves whether students are learning in the way we want them to. I suppose students may go through similar stages of rhetorical and syncopated algebra as they move toward learning and doing symbolic algebra. Through the use of concrete numerical examples, students can gradually connect their understanding of the symbolic algebra, which plays an important role in modern math involving symbol expressions.