I learned my multiplication tables in fourth grade, and they've been mine ever since. I've had my worries over the years, but figuring out 8 x7 isn't one of them. It's 56, every time.
In Traditional Math, retired teachers Barry Garelick and J.R. Wilson argue teaching math explicitly is efficient and effective, minimizes confusion and helps "students develop mathematical reasoning, understanding, and confidence." They learn math.
The book "breaks through the myth and straw man that explicit instruction is just boring chalk-and-talk rote learning of facts that cannot be applied when needed," writes Paul A. Kirschner, emeritus professor of educational psychology, in the foreword. "It also breaks with the misrepresentation that traditional math teaches kids to work as automatons without understanding what they do."
I learned math a few years before "new math" came in, and well before pocket calculators. Even then, in the Jurassic era, teachers didn't stand up and lecture. They tried to explain concepts. We tried to solve problems, showing our "work" for full credit. Admittedly, our story problems were more focused on allocating fruit than analyzing arrest statistics, but the idea that kids ought to understand why they're searching for the lowest common denominator is not new.
To learn well, students need both fast, automatic, rote learning and slow, deliberate, flexible thinking, write Barbara Oakley and Terrence Sejnowski, co-authors of the book and online course Uncommon Sense Teaching, on Law & Liberty. They want educators to follow the neuroscience.
"For close to fifty years, fluency, especially in math, has been de-emphasized and even ridiculed by educational leaders," they write. Stuck on what's 8 x 7, students' brains are too busy to think about complex ideas. Where's the calculator? Did I punch in the right numbers?
Math reformers blame "ever-declining math scores" on "drill and kill" teaching, write Oakley and Sejnowski. But "there is little evidence" of what they prefer to call "drill to skill." Instead, reformers have taken over the entire education system.
Oakley and Sejnowski criticize other teaching fads, such as telling teachers not to tell a student that her answer is wrong, lest it hurt her feelings. It wastes time and confuses the class, they argue.
The “praise wrap” approach makes matters even worse — this is the idea that three or even four layers of praise must be provided for every criticism. The never-ending, increasingly saccharine and artificial-sounding praise means that praise becomes expected. This expectation of reward, even when a student doesn’t deserve it, can in turn kill feelings of pleasure about successful learning. . . . these approaches are a significant waste of time and can turn frustrated students away from school. Worse yet, students can become cynical about their teachers, never certain about whether they are receiving praise or pablum.
Teachers also are told that students must be able to explain a concept to show they understand it. However, "explanations can be memorized and regurgitated with no real understanding," they write. By contrast, students who know the answer intuitively may be unable to put their understanding into words.