Japan is also a world leader in after-school math practice using traditional approaches–see Juku: The Stealth Force of Education and the Deterioration of Schools in Japan by Manabu Watanabe. Watanabe makes the case that it is not Japan’s approach to teaching within schools that is behind Japanese children’s success in math–it is Juku.

In fact Japan teaches through problem solving as an Ontario math leader I have attended wksps by Japanese teacher/leaders. I can put you in contact with s brilliant woman who is in Toronto who speaks Japanese and wrote her doctorate on Bansho or the Japanese lesson structure including trips to Japan. Singapore brought in Japanese teachers to transform their instruction. Read Liping Ma’s work that shows Chinese educators have always taught more conceptually than N. American teacher. Read the Teacing Gap. PISA is just a pointer, you have to read the follow up ethnographic research to find out why these countries do well. Anyone who switches to a problem solving approach never goes back because the kids learn both the conceptual understanding which cannot be taught by direct instruction and the old goals of math of doing long division are pre-digital world just ask Siri literally. I have been teaching thru problem solving since 1988. Over many EQAOs in 3 and 6 my students laugh at EQAO. Data means nothing if the research uses just computation to judge the strategies used is at best highly incomplete because it is arithmetic not mathematics and at worst is preparing students to be successful in the 20th century.

But my understanding of mastery is that it isn’t drill based instruction – it’s concept-based wide instruction that is slow enough to allow everyone to achieve the minimum level (using differentiation to ensure everyone is learning at their level)

The top seven places in the world, for math scores, according to Pisa test results (2015) are Singapore, Hong Kong, Macao, Taiwan, Japan, China and South Korea. And every single one of these places uses the mastery approach to teaching math.

I live near Toronto, Ontario and Marian Small and Dan Meyer have a big impact on the resources and PD that is put out by our Board. So my comment is simple. Show me the data. Is there a state, city, or school district that is using the ideas/strategies/resources related to Marian Small or Dan Meyer that have seen significant positive changes in students understanding and ability in math??? Research and evidence based instructional strategies are components but they are not the final result.

Don’t get me wrong, I truly respect Mrs. Small and Mr. Meyer. They are scholars and experts in mathematics. But show me the data!!!! As an educator and a parent, when I look at the data. If I had to choose between mastery and Mrs. Small or Mr. Meyer’s approach to teaching math I would be picking mastery hands down!!!

(P.S. Canada ranks 10th and the U.S is 40th in the PISA 2015 Math results)

I agree with much of what you contend. I teach 7th and 8th grade math and Algebra and I try to avoid equating math with the real world examples. We can use the examples to show one of the ways math can be used but to infer that it is just a tool for “normal life” seriously detracts from the power of math and give students opportunities for artificially simplistic thought processes rather than driving harder toward the understanding the abstract nature of math, particularly algebra.

Is is pretentious, but I want to suggest the problem is in the content now taught. I have no illusions about changing the system of school math education. I would like to move discussion toward content. though. Pedagogy discussion grinds inexorably to another battle in the culture wars.

I assert school math circumvents abstraction to race toward ” fluency” at he expense of building a foundation for learning the math to come, the math that will be critical to success in the world today’s students will see.
Mathematics is the result of extracting its essence form the real world where it may have first emerged. This abstraction is what it is, and why it is powerful. Mathematics is self-contained.

On the other hand school math takes mathematical meaning from connections made in the real world: “subtraction is removal” confuses a mathematical operation with the physical subtractive process leaving students at a loss when asked for meaning of subtraction of a negative. The meaning of negative is taken from real world as “down”, or “the other side of” which are asserted to be intrinsically negative. They are not. The mathematical meaning of signed numbers follows from the construction of the integer number system. They are constructed from . oriented pairs of natural numbers.
A parallel argument holds for fractions and rational numbers. Fractions as parts of things is not a mathematical concept.

All I know is that I posted my rebuttal and waited and waited for days, and you didn’t approve it to appear, even while your posting was obviously getting much traffic.

Can we ever get past this cherry-picked strawman? You know that’s not the position that many of your critics take. All traditional math textbooks and teaching methods introduce concepts first in a carefully-built scaffold. Then comes the homework to get individuals to better understand the subtle variations that are far more mathematically meaningful than basic concepts. Even basic skills require subtle understandings. Very few things are ever rote. This deeper level of understanding has to be carefully constructed on a unit-by-unit basis over years using individual problem sets. That’s what all STEM-prepared students get with AP and IB math sequences.

I’m open to seeing other opt-in sequences for those who might have other beliefs, but drill-and-kill, if it ever existed, has been gone from K-6 for decades without any opt-out options. Where are the results? I had to help my son at home with math when his schools foisted MathLand, and then Everyday Math on him, but once he got to high school, I didn’t help one bit. He just got a degree in math. All of his STEM-prepared friends had to get help at home or with tutors in the early grades. When I grew up, I got to calculus in high school with absolutely no help from my parents. That’s no longer the case with full inclusion and curricula like “trust the spiral” Everyday Math.

All properly-taught math sequences start with concepts, and engagement and curiosity are no magic wands for ensuring mastery. What works is what we see for AP and IB math. I don’t see STEM-prep success cases any other way. The problem now is that students in lower grades are stuck with a CCSS slope to no remediation in College Algebra and that the only ones who make the nonlinear transition to proper high school math have to get help at home and with tutors in the lower grades. If that doesn’t happen, it’s all over and no amount of engagement and concepts or “Pre-AP” math will fix it.

This has never been a question about basic concepts. it’s a question about eliminating low expectations and ensuring proper mastery and mathematical understanding on grade-by-grade basis that keeps all math doors open for each individual student for as long as possible. With curricula like Everyday Math, schools trust the spiral and have abdicated all responsibility of mastery beyond the low CCSS slope. Just ask us parents of your best students what we had to do at home. Engagement and curiosity was not my main focus, but that didn’t stop him from playing with GeoGebra for hours at a time – something that was neither necessary or sufficient. Mastery increased his curiosity, not the other way around.