• Understanding Mathematics
    The new Common Core Standards define what students should understand and be able to do in their study of mathematics.  Asking a student to understand something means asking a teacher to assess whether the student has understood it.  But what does mathematical understanding look like?  One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student's mathematical maturity why a particular mathematical statement is true or where a mathematical rule comes from.  There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b + c) (x + y).  and a student who can explain where the mnemonic comes from.  The student who can explain the rule understands mathematics, and may have a better chance to succeed at a less familiar task such as expanding (a + b + c) (x + y).  Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness.