Instruction Methods for Solving Word Problems in Mathematics Education

The purpose of this paper is to report on three methodologies that I practise in business mathematics lectures. In business mathematics, a problem to find is more important than a problem to prove. Thus, my target is a problem to find. The first methodology is to solve a problem visually to the extent possible, not only using existing algebraic methods but also a visual method that includes mathematical software, such as Maple and Mathematica. In business mathematics today, problem solving using the visual approach is more important than that using the algebraic approach because business requires the speedy modeling of the target and prompt analysis of the model. Thus we can say that the visual solution skill is also required as digital literacy in the business mathematics field. Therefore, lecturers are recommended to take greater advantage of this new visual approach. The second methodology is to practise Polya's famous heuristics, described in his book, “How to Solve It”. It is particularly important for students to first write down the given data and the unknown to understand a word problem. The third methodology is to have students construct rule databases in their heads to make a deduction. Using deduction, they can easily find the connection between the given data and the unknown to devise a solution plan. Based on my experience with deductive database system construction, I think that the procedures used in a deductive system can be applied to students’ solution procedures. In my lectures, I repeatedly teach students deductive patterns. Thinking patterns using these three methodologies are helpful in cultivating students' ability to solve future problems by themselves.