The successful specification of the appropriate arithmetic operation for solving a math word problem depends on several factors, such as the accurate decoding of the words included in the text through which the problem may be presented. All evidence – based problem – solving models denote the importance of the most significant factors.
However, it should be stressed that one of the prerequisite factors stands out for its significance and profound effect on choosing the correct arithmetic operation. In specific, after the clarification of the problem’s details and their dynamic interaction, students must be able to mobilize the appropriate cognitive schema of arithmetic operation, in order to ultimately solve the problem. This means that problem solvers, based on their knowledge and experience from managing quantities of objects, have to identify which type of real – world actions resembles the situation described in the problem, and to which of the four arithmetic operations correspond these actions. For example, actions of combining, putting together, merging, uniting, prolonging, and accumulating correspond to (or are expressed in Mathematics through) addition. Similarly, actions of throwing away, destroying, loosing, diminishing, and reducing correspond to (or are expressed in Mathematics through) subtraction.
All evidence – based models of problem solving include a stage or phase in which the solver designs activities and selects arithmetic operations for finding the solution to the problem. At the heart of this stage or phase stands the mobilization of the cognitive schema of arithmetic operations. Maybe in certain problem -solving models the importance of this activity is not strongly enough accentuated, but all models include at least some kind of actions leading to this end.
