Students learn math when they can fluently recall concepts, confidently solve routine problems, be able to approach non-routine problems and understand enough to explain to one’s self and to others.
Students understand concepts and skills only when these are properly integrated into the context of their background knowledge.
Once learned students can explain concepts and skills in terms of simpler ones, easily connect them to others, convince themselves that they are true . They can also recognize the similarities & differences in applying skills in new situations.
So how do we know what students are supposed to know – and when? The California Math Content Standards tell us that. The California Stae Test (CST) questions are derived from them as are the textbook topic treatments and teacher lessons.
That is why our daily deep math practice adheres strfictlyto the standards.