Students should learn "foundational concepts" in math "__deeply and conceptually__" through engaging, "rich" tasks, write Jo Boaer and Cole Sampson on EdSource. "Every important idea in mathematics can be learned visually, physically and conceptually," they argue. Students should draw, build and learn through real-world examples.

Boaler, a Stanford education professor who helped write *California’s **new mathematics framework**, *is the author of* **“Math-ish: Finding Creativity, Diversity & Meaning in Mathematics**.” *Sampson is the administrator of professional learning for the Kern County Superintendent of Schools Office.

A Kern County elementary school, which is trying this approach, saw proficiency levels rise, they write. Students were more engaged and confident.

Teachers used “number talks,” posing a problem, collecting students' approaches and representing them visually, write Boaler and Sampson. "They also started using richer, deeper tasks, encouraging students to discuss ideas and learn with visuals and manipulatives."

That's more effective than "working through sets of procedural questions," they argue.

Boaler and the California math framework are very controversial, and comments were scathing.

San Francisco schools tried a __curriculum based on Boaler's work __for 10 years, with "disastrous results," comments Maya K. It also promised that groups of students would would "work through a series of ambitious math tasks" to build conceptual understanding.

Relying solely on inquiry-based learning is like feeding students chocolate cake for every meal, writes Doug D'Ault.

Barry Garelick, a retired teacher and author of __Traditional Math____, __ argues that learning "__procedures and understanding occur in tandem.____" __

It is not "necessary for students to show their understanding by using convoluted and inefficient methods that rely on first principles every time they wish to solve a problem," he writes. Robert Craigen, a University of Manitoba math professor, called that "the arithmetic equivalent of forcing a reader to keep a finger on the page, sounding out every word, every time, with no progression of reading skill.”

I was in elementary school when the Soviets beat us to space with Sputnik. There was a lot of talk about "Ivan" being superior to "Johnny." As a patriotic American, I resented Ivan.

So we got new math, which was supposed to teach conceptual understanding instead of mere procedures. I just missed it, but I remember my younger brother's homework. They learned about Venn diagrams, and used a much more laborious method of long division. When my brother struggled, my parents got him __Cuisenaire rods__ to use as manipulatives. Finally, they sent him to a very traditional summer program that taught him math.

And we beat the Soviet Union! But I don't think we out-mathed them.

Cake! What a great idea! Have the students form a corporation that bakes and sells nutritional chocolate cakes. With the students doing all the logistics, sales, and accounting necessary to make this a going concern. I suspect there'd be a lot of useful math--everything from double-entry bookkeeping to ops research--in there.