I learned a lot from W. E. Deming, one of the main gurus in the quality movement. One of his principles was to be suspicious of numbers in goals or directions, such as "Load with no more than six persons." He had often found that the number specified was arrived at somewhat arbitrarily and without much or any data. So, whenever I spot a number, I wonder about it. Similarly, with speedy checkout counters. Some specify no more than 10 items while others have signs with a limit of 15 items. Since different sorts of items and different clerks are often at the same counter, one wonders if the parameter (the number) is set at its most useful value.
Similarly, I am suspicious of ordered categories, hierarchies, such as grades or steps. Frequently in instruction, one is told to learn A and then B, being careful to learn A completely since it is the basis for B. Yet, when I come upon a learner who is having trouble with A but performs B satisfactorily, I can see that the supposed step-dependency doesn't hold. School, education, instruction and training might be improved if we were a little more restrained in announcing what we think are step-dependencies.
Learners who are very cautious or highly motivated to be "perfect" can fail to move forward when they are told it would be wrong, immoral, dangerous or silly to try further steps without mastering the early levels. So, they can self-restrain, as well as be held back of course, simply because all involved think the logical steps are the only route possible.
My experience is that it is best to present material in as logical and helpful order as possible but not to make too much of the supposed order underlying the material. Whenever, one teaches over time, there will necessarily be something taught or presented first and then later, something else. Whenever we find learners scattered among the items to be learned, with mastery of this but not that, we have evidence of a lack of genuine dependency. Actual information as to WHAT was mastered and WHAT was not is often omitted. Learners are accustomed to being told the number or percentage of items that were wrong but not WHICH ones.
In a related way, I have seen many people stay mute in discussions on the grounds that they didn't read the assignment or the book. Of course, when a participant is completely in dark, it is only polite to stay quiet or skip the gathering. However, once I learn that Rosemary was betrayed by her landlady, I may have a completely legitimate comment or question, whether I read the story or not. The spottiness with which we all remember read or heard material is testament to the lack of dependency between exposure to the material and complete grasp of every word, idea and possible question related to it. Often, discussion reveals angles to the material that we would not grasp without interaction with others.
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Bill
Main blog: Fear, Fun and Filoz
Main web site: Kirbyvariety
