Rethinking Word Problems (For Sept 28th)

The word problems at the beginning of the reading immediately caught my attention. They looked interesting, so I started trying to solve them, although I got stuck on the second one. At first, I thought I could approach some of the questions without advanced mathematical knowledge. However, knowing the operations involved did not mean I immediately knew how to find an answer. This made me wonder how much of the difficulty came from the mathematics itself and how much came from understanding the situation and organizing the information.

I was also drawn to the connection between Babylonian word problems and the society around them. The problems included situations involving agriculture, trade, law, and military administration, which seemed closely related to the work that scribes were preparing to do. At first, I liked that their learning connected to the world around them. As I continued reading, however, Dr. Gerofsky’s discussion challenged that first impression. Some problems involved unrealistic measurements or questions that people would probably never need to answer in their daily work. A familiar setting did not necessarily make a problem practical. These situations could also provide a way to explore mathematical ideas beyond their everyday uses.

Ainley’s point that problems can have only a superficial connection to the real world especially resonated with me. Growing up, I often felt that our textbooks were outdated. Many of the situations seemed to belong to the 1980s and had little connection to my own life. When I encountered a word problem, I thought about what we had recently learned in class and tried to apply the method that seemed to fit. My attention was mainly on recognizing the expected approach. I felt that I was just solving math word problems, with little sense that I was solving a problem connected to real life outside the classroom.

This experience connects closely to the questions at the end of the reading: do we use word problems to help students understand mathematics, or mainly to practice methods they have already been taught? It also made me reconsider my first thought that I could improve problems simply by updating their settings. Replacing an old situation with something familiar to students might make a question more appealing, but would it change how they approach it? If students are still trying to guess which formula the teacher wants them to use, a more modern story may not make much difference.

In my own teaching experience, some students have struggled to find a starting point when a word problem looks different from the examples they have done before. I wonder whether this is partially related to how we teach them to approach these questions. If most of their practice involves recognizing a type of problem and repeating a procedure, developing their own approach may feel unfamiliar. A familiar context could help them picture the situation and suggest strategies, but that connection alone is not enough. I would also want to give students space to discuss their ideas, try different approaches, and explain why a method makes sense.

Problem wording matters as well. Unclear language can make it difficult for students to understand what is happening or what they are being asked to find. This reminds me of the AP Calculus free-response questions I have worked with, where I appreciate the care taken to describe the information and the task precisely. Still, clear wording does not automatically make a question meaningful. In my future teaching, I want to think more carefully about the purpose of each word problem. Whether I am asking students to try a method, explore a mathematical relationship, or investigate a practical situation, I want the problem to support that purpose and help them understand what they are doing.

(I used ChatGPT to help translate my ideas from Chinese into English. The personal experiences and reflections are my own. )