For math, as for most topics, there are those students who love it and can't get enough, and there are those who find math as mysterious as a foreign language written in an entirely new alphabet, who are constantly frustrated and annoyed at having to learn something they find so perplexing.
In an ideal world, we could present students with math concepts and ideas from an early age, in a fun and engaging way that gives them the gift of numerical competency and a more comprehensive understanding not just of the how-to's of math, but of the more conceptual whys of math.
Like artists who learn to see colors and shapes in artistic ways, children and young adults can be taught to notice math in everyday activities--apportioning a pizza or pie, building a birdhouse, mixing up a recipe, balancing a checkbook, understanding compound interest on a savings account--exposing it not as a foreign language, but as a vital subject that permeates our daily activities in ways too numerous to, well, count.
It is the conceptual understanding of the whys of math that helps students to see problems in a larger context and, in later academic work, to be able to solve multi-step problems using many strategies that work in concert. Rote memorization of formulae or "to-do" steps may help a student get some answers correct on a specific quiz, but do less for their larger problem-solving abilities. It is also this ability to strategize and logically solve math problems that can spill over into solving problems that crop up in engineering, chemistry, biology, computer science, and other topics that American students seem to find too difficult to bother with.
Gifted math teachers understand that it's the relevance to a student's everyday life experiences that can trigger the sometimes elusive "ah-ha!" moment, which indicates they finally understand how to solve a problem.
In an interview I did on my radio show last week with Nigel Nisbet, a math expert with the Los Angeles Unified School District who is currently working on a math project for HippoCampus, there is a discussion of how students are not necessarily mastering the basic math skills (addition, subtraction, multiplication, division, etc.) taught in the early grades. This lack of mastery tends to first be revealed when students start struggling with algebra. Nigel argues that those standardized tests given in the elementary grades really can help parents, teachers, and schools see how well students are mastering those basic topics. Catching this early leaves enough time left to remediate if a deficit is found. (Listen to the interview here.)
My take from the interview is that if a student manages to bump along with a half-baked understanding of math until they hit algebra, it's going to be much more difficult to go back and fill in the missing information, and by then it's much more likely that the student will be developing an aversion to math that could haunt them throughout high school (and possibly into college).
For the math-loving student who either isn't challenged at school, or is challenged and is looking for like minds with whom to collaborate to learn new strategies, I have a recommendation. Richard Rusczyk, whose own gifts with math are surpassed only by his gift for teaching math to others, has a whole online following that includes many of the brightest young math minds in the country. Richard and a core of other dedicated yet unconventional teachers have taken matters into their own hands, creating an extracurricular community of math-lovers who relish digging into a juicy problem and finding creative and clever ways to break it down and solve it. His company and online community are aptly named, "The Art of Problem Solving." I've done several interviews with Richard on the Countdown to College Radio Show, three of which can be found here. Note: Guest blogger Beth Pickett is the producer and host of Countdown to College Radio Show, and as such as interviewed numerous teachers and math experts on the current state of math in the U.S. today, and the opinions she has expressed here are those she has formed after listening to those who are on the front lines of teaching math. She is also the primary blogger for the HippoCampus Countdown to College blog.