But I've been thinking lately that the expectation and need for these most fundamental skills is often not communicated to our students; in the era that frowns on structure and drills for automatic knowledge, many of our students have never seen such a requirement assessed directly anywhere. Of course, I'm thinking of the times-tables drills that people my age did in the 2nd or 3rd grade, and nowadays may possibly be done in the 8th grade or high school by the more exceptional and dedicated teachers (so I hear).
Might it be the case that in any class, there's at least one specific skill that is expected to become automatic, even if many of us overlook communicating and drilling on that? For example, it's occurred to me that we might expect the following regular speed drills to take place:
- In early grammar school -- Times tables.
- In late grammar school/college remedial arithmetic -- Negative number operations.
- In junior high school/college remedial algebra -- Matching a slope-intercept equation to the graph of its line.
- In statistics -- Estimating the area under part of a normal curve, or interpreting confidence intervals and P-values. (?)
What do you think? Have you used timed drills to communicate the expectation of automatic skills? And for anything other than times tables?