Domain-specific background knowledge is incredibly important.
You see that when you hand word problems with more than one step to the poor kids. They use "solution strategies", that is they circle numbers and what they think are keywords, and they full well don't know what those words mean.
They circle "concentration", and they even can calculate a concentration given a mass of solute and volume of solvent, but they never thought about solutions and what solutions of different concentrations might do for you.
There is a paper somewhere in the Journal of Chemical Education where they handed numerical and conceptual questions to kids from Yale and FAMU. Quite contrary to expectations, the Yale kids did much better on the number questions, but on the questions what it all means both cohorts did equally lousy - 1/3 of kids at either school had an idea what those numbers they just calculated meant.
You see that when you hand word problems with more than one step to the poor kids. They use "solution strategies", that is they circle numbers and what they think are keywords, and they full well don't know what those words mean.
They circle "concentration", and they even can calculate a concentration given a mass of solute and volume of solvent, but they never thought about solutions and what solutions of different concentrations might do for you.
There is a paper somewhere in the Journal of Chemical Education where they handed numerical and conceptual questions to kids from Yale and FAMU. Quite contrary to expectations, the Yale kids did much better on the number questions, but on the questions what it all means both cohorts did equally lousy - 1/3 of kids at either school had an idea what those numbers they just calculated meant.