The POW’s are a central part of a strong math program for middle schoolers. It requires them to tackle problem solving with an investigative or non-routine type of problem.
People too often approach math from a procedural approach. Schools too often teach a procedure, with or without justification, and then have the students practice these procedures on very similar problems. While this has a place, it reminds be of learning how to read words and phrases, but never delve into the meaning of a book.
My essays are designed with specific ideas in mind. First, read and understand the problem, and show this understanding by stating the key info, discarding the irrelevant, and identifying what type of problem it is.
The second paragraph explains approach to the problem. What worked and what led astray. It is not always about getting it “right” the first time, but rather, the investigation of methods and the recognition that we often don’t do things in isolation, but search for help.
The third paragraph describes the answer and lays out alternative answers or multiple answers, as many problems are not single answer events.
The last paragraph is a reflection of the learning process with a small eye on the future (behavioral adjustment to improve learning).
The maximum size of the essay is one page, perhaps 500 words or so. Most paragraphs can be 5-7 sentences.
I value process much more than procedure in math. By that, I mean seeing the importance in the why we do something and understanding it vs. the sole focus how of doing something and perhaps not understanding as well.
I have heard much feedback over the years that families and students come to appreciate the impact of writing structured essays explaining logical thinking on their everyday approach to other subject areas. I do understand, though, that the approach is unusual for many of us who had a different educational experience (such as I did).