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.

I don't care what anyone says, I knew perfectly well why 8 x 7 = 56, even back in fourth grade. The idea that drilling the tables into me somehow prevented me from knowing the "why" of it is silly. after that I *was* an automaton when I was multiplying single digit numbers, though, and that's how it should be.

Having spent yesterday afternoon at my volunteer gig, watching students skip-count repeatedly to do each step of long division and equivalent fraction problems...yes, tremendous amounts of thinking could occur if students actually knew their math facts so that they could focus on something other than than counting. The skip counting usually works when the problems are with 2s, 3s, and 5s. Most people aren't very adept at counting by 7s, and the kids usually had to switch to repeat addition. Problems that should take 10 minutes take 45 to do...that extra 35 minutes could be better spent playing than counting. They could actually learn the times tables easily in the time that is wasted counting, but I'm just a home…

I learned math the drill and kill method as we were doing math drills until 7th grade and

you were expected to know your multiplication tables, order of operations, place value, exponents, and other required math skills to be able to move on to algebra (if you chose to do so) or other math in high school (general, business, etc)...

Though in my day, you were required to pass two units of math, two of science, 3 of English, half a credit of health, 1/4 credit in drivers ed and 1/4 credit in careers, US and State History, US Government, 2 years of phys ed, etc...

We were required to show our work on multple step problems, etc...

Students who…

I'm a math teacher, not an English teacher. I don't want or need to read essays to determine if a student understands how to solve a problem. Step by step calculations and manipulations show me what I need to know, not a bunch of blah blah blah.

--mrmillermathteacher

Students who know the answer intuitively don't always have the vocab to express the idea solely with words....and that's because the adults around them haven't informed them of the agreed upon vocab and/or haven't bothered to teach penmanship. The academic dumbdown has also resulted in whole class teaching that is inappropriate for many, which is why unclassified fourth graders are 'showing' their multiplication work by laboriously drawing 8 rows of 7 while they are on grade level or higher at the afterschool math center/tutor.