Ambition, Distraction, Uglification and Derision

In my math ed class this week I talked about ambition and distraction and uglification and derision but no-one knew what they were so I asked who had read Alice in Wonderland and could remember the Mock Turtle. Perhaps three students out of the eighteen raised their hands. I was initially somewhat alarmed by this but then I started thinking that what is termed a classic piece of literature  probably changes over time. But I'm not an expert in this area so I'll just wonder about it.

Something else we did pursue in class through a really interesting discussion is  whether the incredible amount of time we spend teaching algorithmic procedures  such as 54   is still
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worth it given the culture in which we live. Is the use of endless tedious practice exercises really worth it given the extent of the work we now do on numeracy skills as well as the technology-based tools available for computing. Shouldn't we be spending our valuable time teaching children to compute simple problems mentally and more complex problems using some sort of calculator? Shouldn't we be spending our time teaching children the meanings of the operations such as recognizing joining, separating, comparing, part-part-whole, groupings, Cartesian products and multiplicative comparisons?  The essence of solving a math problem is deciding which operation to use. Once this has been done the problem becomes simple arithmetic which can be solved either mentally of through the use of a calculator. In the discussion with the students I was playing devil's advocate; well maybe!

There are very few places in more advanced mathematics where the use of paper and pencil algorithms is required over mental or technology based computations.