A person can be a very logical and reasonable, solution oriented person but if they don't know that 1 represents one which represents a single item as opposed to 2 which represents two and is equal to twice as much as one - what are they supposed to be reasoning and understanding?
The focus should be on understanding and problem solving, not on memorizing mathematical "facts" or methods. Obviously students are going to learn the facts they need, but the focus should be on the problem solving and grasping mathematics as a way to express ideas.
What does equals mean?
In order to understand the simplest algebra - as in 3n+8 =29- Do they not have to know that + means add and = means equivalent to?
You are bringing up an interesting problem for teaching algebra (and one that current math teachers do a horrible job with). Most students are taught to deal with an expression like the one you give with a preset set of operations without thinking about what is going on.
Let's start with 5th or 6th grade. Kids are taught that the equals sign is an operation, they are given problems like 3 + 2 = ______ where they are supposed to fill in the blank.
We gave kids a true/false test such as the following
1 + 2 = 3
2 + 4 = 7
5 = 5
Kids get the first two correct (saying the first is true and the second is false). Most kids will say (incorrectly) that the third expression is false. This shows that they are unable to understand the equals sign "equivalency". They only think it makes sense as the answer for some operation they have seen.
Later on we really confuse kids. We show kids equals as "assignment", with x=3. This is an assignment, we are actively defining what x is (this statement is neither true nor false).
Finally we add functions as in f(x) = x + 3. Of course, functions are the real key to Algebra, when mathematicians or engineers use Algebra, they almost always are using functions. Of course, by the time we introduce functions we have changed what the equals sign means so many times that most kids have trouble ever grasping it.
But the real frustrating part was, as a teacher, seeing a kid mechanically start subtracting terms from both sides of an equation without even thinking about whether this made sense or not.
Math is about understanding and expressing ideas. It is not about mechanically following memorized instructions.