In the last post, I attempted to define what I believe learning through problem solving is. This brief post will explain what it is not.
Word problems assigned at the end of a lesson are not learning through problem solving.
I was going to stop there, but I’ll elaborate. The word problems given at the end of the exercise section in textbooks are just further practice. I am not criticizing textbook publishers. They spend a great deal of time and money writing decent contextual problems (and the occasional blatant and painful Pseudocontext). What they do wrong, however, is place them at the end of a lesson and after a bunch of rote practice questions. Many of the well thought out problems they create would be much better used if they were placed first in the lesson. By giving them first in a lesson, we can let the students struggle with them for a while, and see what they learn. At best, it’s a compelling hook for the lesson. At worst, it shows the students that they need you to teach them something. Either way, it’s better than having them assigned at the end of the lesson.
The learning through problem solving process can include word problems if used properly. But word problems are not the only way we should be presenting problems to our students. We must also let them come up with their own problems after hearing stories, reading articles, watching a video, looking at a picture, listening to a song, and wherever else we see math around us. Sometimes it can be as simple as asking a straight forward math question, but doing it before you teach them how to do it.