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> One of the earliest example of such interesting or useful results is rules for manipulating symbols so that the results correspond to the behavior of physical
by _448 5y ago
> One of the earliest example of such interesting or useful results is rules for manipulating symbols so that the results correspond to the behavior of physical objects (like sheep, or baskets of grain, or plots of land)...
Or was it the other way round? First came the objects and then people saw patterns in the transactions and then abstracted it away with symbols?
One of the reasons children find maths difficult is because we tend to describe maths in this reverse order i.e. from symbols to physical objects(the way you described above). But explaining it in the actual order i.e. from physical objects to symbols will make maths accessible to many more kids.
- lisper 5y agoThe evolution of math came by way of things like tally marks on sticks and pebbles in pots. The line between symbol and physical system is fuzzy. I think one of the reasons that people find math difficult is that the emphasis is on the symbol-manipulation rules and not on the reasons that certain sets of symbol-manipulation rules are useful. Kids are taught to count "1 2 3 4..." as if these symbols were handed down by God rather than being totally arbitrary. They should be taught to count "*, **, ***, ****, ..." and then, when they get to "***********" or so, they should be encouraged to invent shorter ways of writing these unwieldly strings. (Note, BTW, that when you use the "*, **, ***, ****, ..." numeral system, addition and multiplication become a whole lot easier!)