A leprechaun has two pots of gold, each with 10 coins in it, plus three extra coins. How many coins does he have in all?

Some kindergarteners solve it quickly. Others are baffled. The teacher doesn't explain. The five- and six-year-olds are supposed to figure it out for themselves.

Los Angeles Unified is piloting "cognitively guided instruction" (CGI) in partnership with the UCLA Mathematics Project, reports Will Callan on The 74. Teachers are told to "let student instincts guide math class, often resulting in hands-off instruction." One goal is for students to see themselves as good at math.

It's "extremely popular" with teachers and administrators, writes Callan. But, so far, there's __no evidence it works____ __to improve math achievement. Scores remain very low. At schools that have used CGI for five years or more, about 30 percent of students are proficient in math. That's roughly similar to the non-pilot schools.

Advocates want all the district's elementary schools to use CGI math, but board members don't want to expand the program without data on effectiveness.

An early study of teaching math with minimal guidance "showed a small positive effect on student achievement," Callan writes. More recent research found mixed results.

There is evidence that explicit, step-by-step instruction is more effective for struggling learners, he writes. "A 2008 research review published by the U.S. Department of Education found that explicit instruction involving 'clear examples' and 'extensive practice' had consistently positive effects for students who struggle with math." That jibes with other studies and research reviews.

"The debate echoes the recent reckoning over balanced literacy, an approach to reading instruction that often deemphasized basic skills like phonics," writes Callan. “CGI is a movement. You feel the passion right in people,” said Carlen Powell, the district's administrator of elementary instruction, at a Jan. 26 board meeting. “It’s not a religion, but it’s something.”

"__A little less passion and a little more instruction____,__" suggests Greg Ashman on Filling the Pail. Give that poor confused kindergartener a hand.

Daniel Mollenkamp provides an example: on EdSurge. A __student comes up with a novel way of telling which fraction is larger__: Add to the numerator to get a whole number. The teacher considers it "brilliant." But it is "unreliable." That's because it's based on a misunderstanding of fractions. In my day, the word for that was "wrong."

"It can be tempting to fall back on procedural rules, particularly since students’ strange alternative rules can be time-consuming to explore," writes Mollenkamp.

Things might go faster if the teacher explained fractions first before discussing misconceptions. Even faster: Stop pretending every student is a young mathematician with brilliant ideas. Kids aren't that stupid.

It's hard to say how important kindergarten arithmetic is -- the debate about burnout effects from early childhood education continues, last time I checked -- but 30 per cent proficiency in achieving California's state mathematical standards suggests that no one should be following LAUSD's lead in math teaching until some more definite evidence supports it; instead, the relevant syllabus should recommend achieving better standards via direct teaching that leaves no one behind, as is seen in East Asian cities.

Cynical and/or snarky. I suspect that one reason that teachers like this method is that they themselves never learned the math well enough to teach it.

I agree with Richard. If the teachers aren't going to teach, then we should just shoo them out of the classroom and let the parents take over at home. If this is indeed a problem where kids are supposed to use imaginary "counters" or fingers to total things up, then the numbers should be small, say "two pots of gold, each with four coins."

A SMART kid would ask, "what coins? Quarters or nickels?"

"There is evidence that explicit, step-by-step instruction is more effective for struggling learners, he writes."

In fact, it is more effective for non-struggling learners as well. The Kirschner et al study referenced in the article states: "In so far as there is any evidence from controlled studies, it almost uniformly supports direct, strong instructional guidance rather than constructivist-based minimal guidance during the instruction of novice to intermediate learners. Even for students with considerable prior knowledge, strong guidance while learning is most often found to be equally effective as unguided approaches. Not only is unguided instruction normally less effective; there is also evidence that it may have negative results when students acquire misconceptions or incomplete or disorganized knowledge." See: https://barrygarelick.substack.com/p/effective-math-instruction-hiding

I'll favor this "learn it yourself" policy -- as long as the teacher unions agree to allow the classes to be taught by the janitors. Shucks, employ the drug-addled homeless to run the program. With this "innovation," we won't need no stinkin' teachers.