I think we often forget how much influence forgetting has on learning. Learning isn’t binary between knowing and not knowing. Learning is part levels of understanding and how well we retain it. I’m not a neurobiologist, but it seems to me learning likely has something to do with strengthening the connection between neurons. Its a biological process, and biological processes take time. Because of this it takes time to learn information and it can be forgotten if it goes unused.
A recent article in Journal of Chemical Education, “Decay of Student Knowledge in Chemistry“, tried to quantify how quickly the information is lost in general chemistry after the assessment. They suggest that a spiral approach to teaching helps slow knowledge decay. This is interesting because I think many times courses are taught in a linear format. You learn one skill/concept, which lets you move to the next/skill concept, etc. You do reuse some ideas over and over, which keeps them fresh in your mind, but many skills are seen only once or twice.
Is it truly that surprising students don’t remember basic math skills, when they haven’t had to use them for years? I think we underestimate sometimes how quickly we lose knowledge when it goes unused. With this in mind, educators need to be sensitive to the fact students might not retain every bit of information in those prerequisite classes and not even all the ideas you taught them last week. That is unless you consistently connect the topics and force students to reuse skills throughout a course.
I suppose to summarize, students need to realize that learning is not instantaneous and faculty need to keep in mind that unused knowledge is often forgotten.