I've been catching up on back issues of The Mathematics Teacher. Great quote from October 2008, opening an opinion piece by Gregory Freeman and Lisa Lucius:
"I learned to ride a bike at age six. The experiences leading to my first solo bike ride are still vivid memories. First, my father gave a wonderful explanation of bike riding. The mechanics of leg motion required to pedal were explained. Hand placement on the handlebars, and the nuances of steering were described with clarity. Braking, maintaining balance, and every other conceivable aspect of bike riding were laid before me. Next, my brother modeled bike riding. Down the block he rode: pedaling, steering, maintaining balance. He managed a 180-degree turn, returned, braked, and came to a perfect stop. Having gained a conceptual understanding of bike riding and having observed successful bike riding, I was able to ride the bike by myself at first attempt. I attribute my riding independence to my father's excellent explanation and my brother's superb modeling."
Of course, this is pure fiction, and few people would believe this story. And yet so many are ready to believe similar nonsense about learning math. Not long ago, an expert in computer learning explained to me that after six months of research on math education, and from observing his two daughters, he concluded that there are two ways to learn math: listening to explanations, and looking at "worked examples". Sigh...
One learns to ride a bike best by riding a bike, with guidance from an adult. Likewise, one learns to do math best by doing math, with guidance from an adult.