Lecturing and the absence of Learning

It seems to me that the argument propounded in the last posting, about learning from lecture, really is worth considering further. We need to know how to motivate students to learn, and whether or not the modality of information delivery is significant. Since these postings are solely concerned with mathematical based science, we eschew topics of interest to the larger community.

The punctuated model of learning that we have is historically embedded in our agrarian heritage. We know, for instance, that total immersion learning for languages works; works to such a degree that learning German in Germany is virtually trivial compared to learning German in 1 hour per every other day sections as usually done in American Universities. Clearly, immersion learning in calculus, which would be incredibly strenuous, would work better than what we do now, but no one is espousing it.

We start with the book, the text, the font of all knowledge. Any casual inspection of current textbooks, comparing them to past efforts, will show that they are significantly improved. Although the reading level has decreased, that decrease does not necessarily lead to intellectual pollution. The idea that students learn to solve canned problems leads critics to shake their heads, but the fact is that performing at such a minimal level is certainly a first step which is necessary before progress can be made. We all really learn by re-visiting the material at a spiraling level of sophistication, placing it into its niche within the intellectual space we are building. The re-visiting is important.

When I teach, I tease my students about what they've forgotten (and I've been criticized for it, and in fact punished for it) but the teasing has a purpose. They are studying a subject whose predecessor materials have been learned (and forgotten). They need to re-learn the material, now from the point of view that they need it for the current material they are muddling through. My teasing seems a better method than assigning them to re-learn the material. They're adults; assigning freshman materials is demeaning (IMHO). But teasing them, puts them in the position, after re-learning the material, of being able to feel superior (certainly to the freshmen who are struggling with the material) since not only have they easily re-learned it, but they did so for a reason which was absent the first time around.

We have all forgotten material that we've learned in the past, partly because this material was never used again, never needed again, and therefore buried under newly learned material which was more important (temporally).
The trick is to change the examining system so that precursor materials need to be known during examinations. This would make the re-learning of material worth while, and would motivate students to retain relevant material as they progressed. Like a muscle being exercised, what we know is what we've used recently. The longer the material has lain dormant, the less we remember about it. If our examinations did not excuse precursor ignorance, we would change the culture of learning, so that as we progressed, as we learned more and more (about less and less?) we would retain more of the precursor material we see now disappearing.