Designing mathematics standards in agreement with science [pdf]

>>> To learn mathematics, historically students had no choice but to memorize fundamental facts and apply memorized algorithms. Since 1995 in the US, all states have adopted standards to govern K-12 mathematics instruction, and in most, standards have de-emphasized memorization and emphasized reasoning based on concepts.

My kids are both past high school. My view is that while states may have adopted standards, the curriculum was to a large extent governed by standardized testing. "The test is the curriculum." This suggests that memorization and algorithms remained central to school math. I saw it in the homework assignments that my kids brought home, or worked on through online courseware. If I'm not mistaken, the tests and the courseware are in some cases made by the same company. Moreover, the prevailing culture was reinforced by demand from parents.

My message to my kids was similar to the thought expressed in the abstract: "Trust me, math gets interesting but the low level stuff has to be practiced until it ceases to detract from thinking about the interesting stuff."

To be effective at anything academic (not just math), you have to strike a balance between memorization and reasoning. I'm glad to see someone finally produce data to verify that common sense observation.