The ninth-grader needed to multiple 3 x 9 to answer an algebra problem. She didn't have a calculator, and I wouldn't let her go look for one. After five minutes of guessing, she came up with 27. She failed algebra.
Teaching students to be fluent in addition and multiplication is controversial, writes Stephen Sawchuk in Education Week. Some teachers think learning multiplication tables is boring, and "timed tests and 'mad minutes' of worksheet problem-solving" are stressful.
But cognitive scientists say "having these facts at their fingertips frees up working memory for students to attend to problem-solving, applying procedures to more difficult problems, and other tasks," he writes.
Students won't learn "deeper, conceptual math" if they're hung up on 3 x 9.
“Multiplication facts seem boring to us because we know them,” noted Dylan Kane, a 7th grade math teacher in the Lake County district in Leadville, Colo. “But successfully learning new things is motivating for students. Because it’s old and boring for us doesn’t mean it’s old and boring for them.”
In a survey for Education Week's excellent Math Foundations for All report, most math educators agreed that fluency in math facts is "essential" for students to be able to tackle higher-order, conceptual math problems, Sawchuk writes. "But more than a quarter said that it was 'helpful, but not essential'.”
For a long time now, educators have tried to skip past the fundamentals in both math and reading to get to the higher levels of learning. They don't want to "drill and kill" math facts or phonics. But trying to do math without automatic recall of math facts is a hard slog. You might call it the "flail and fail" method. For that matter, will kids who can't decode develop a love of reading?