My son-in-law teaches math at the senior high school level, and at family gatherings math and the teaching of math is often a topic of conversation. We are both dismayed by the number of students who are not proficient in basic addition, subtraction, multiplication and division. There is something disturbing about helping students solve an algebraic equation, only to find that they must draw a lattice to multiply 2 times 11, or use fingers to subtract 5 from 7 (and often still get the wrong answer). Most of the students that I work with are unlikely to ever use algebra after graduation, but would always benefit from knowing the basic math tables. So, are we missing something here?
My son-in-law and I agree that the decline in basic math table proficiency is largely due to the widespread use of the calculator (which teaches you virtually no math), and the increased number of advanced topics now being taught at the grade school level, which reduces the amount of time available to master more basic topics. The dilemma is that those students who do know the basic math tables and who can absorb advanced subjects, benefit from an accelerated program. Separating students according to ability at an early age would allow each student to reach their fullest potential, but there seems to be a lot of opposition to this. As it is, all students try to reach a fixed level of achievement regardless of their ability to do so. Another possible improvement might be to eliminate material of trivial and questionable value from the math program, and use this time to bolster more basic topics. This is equally unlikely to happen. In any event, the present system allows the better students to learn more, but results in the poorer students learning less, thereby widening the gap between the two extremes. I personally learned "advanced" grade school math in a small rural school in Kentucky. The teacher assigned different problems and gave additional instructions to various groups of students in the class according to their ability. This was 65 years ago.
This widening of the gap between the two extremes is not limited to math proficiency, it is a phenomena that seems to be prevalent in many areas of our society. We now have proportionally more millionaires and billionaires than ever, while at the same time having more people below the poverty level. We have an increasing percentage of people who are obese, while at the same time having more under-nourished children. And in physical activity, our athletes break world records while at the same time we have more couch potatoes than ever. Perhaps we are witnessing a modern-day version of Darwin's survival of the fittest.
It is said that our society is on the cutting edge. That seems to be good or bad depending on which end of the limb you're sitting on.
John Schwarz