The problem stems from the proliferation of worksheets, so entrenched into the American school culture. Get rid of the worksheets and teach students how to record a problem and a solution on a clean sheet of paper, preferably in a notebook, so that the record stays for at least the duration of a school year.
In short, use GFSA (Given-Find-Solution-Answer) or GFAS (Given-Find-Assumptions-Solution) process, which is used in technical colleges, but is completely absent from schools.
Given: write down what is given without repeating the problem verbatim; instead introduce constants and variables that later will be used in the solution; draw a picture if needed, use introduced symbols in the picture. The problem must be completely recognizable by reading the Given section without referring to the original problem in a textbook.
Find: clearly state what should be found.
Assumptions: this may be part of a Given part, for example, when solving geometrical problems involving vehicles or walking we may assume that the Earth's surface is flat, or when solving an equation we may assume that the roots are real numbers.
Solution: a step-by-step process, which usually involve some textual explanations, but not too much. There should be enough text to understand what numbers mean. Solve symbolically first, then plug in the numbers.
Answer: clearly state the answer, some professors require to underline it for clarity.
The above problem can be solved as follows:
Given: rectangle (draw a picture) with sides (mark sides with letters, say "a" for the longer side, and "b"). On the picture mark segments of the longer side as a1 and a2, for example. Then write a1 = 4m; a2 = 3m; b = 2m
Find: Area of the rectangle (introduce a letter, say "s"), write s - ?
1) Generic formula: s = a * b = (a1 + a2) * b;
2) Plug in numbers:
s = (3 + 4) * 2 = 7 * 2 = 14;
s = (3 + 4) * 2 = 3 * 2 + 4 * 2 = 6 + 8 = 14;
Each separate calculation is terminated with semicolon. It must be beaten into the subconcious that equal sign means that stuff on the left equals to the stuff on the right, so 3+4=7×2=14 is incorrect solution, and the problem is marked as not done, plain and simple.
Students must be taught to split task into clearly marked steps, like:
s = s1 + s2, where s1 = a1 * b, s2 = a2 * b;
Then students would write:
Area of the left part: s1 = 3 * 2 = 6 (m2)
Area of the right part: s2 = 4 * 2 = 8 (m2)
Notice (m2) in parentheses. There are two approaches to dimensions: one is to write dimensions everywhere throughout the expression, like: s = 4m * 2m = 8m2 (no parentheses), this is useful for dimensional analysis, like meters times meters equals meters squared, but can be clunky for school math. Another option is to specify dimension of the resulting value only, in this case put it in parentheses.
s = 6 + 8 = 14 (m2)
Answer: the area of the rectangle is 14 m2. (underline "14 m2").
Obviously, this particular problem does not require such an elaborate solution, but the students must be taught the principle, the scaffolding of the generic solution. The above problem can be solved simply as:
1) s = a * b;
2) s = (3 + 4) * 2 = 7 * 2 = 14;
Answer: 14 (m2)
Introduce symbolic solution as early as possible, this improves conceptual understanding, and will pay back when they start algebra.