Elizabeth Green compiles the history of math education in the United States from New Math to the Common Core:

Americans might have invented the worldâ€™s best methods for teaching math to children, but it was difficult to find anyone actually using them.

She also tours through some of the best ethnographic research you’ll read in math education but doesn’t cite two of them explicitly (that I counted) so I will.

- A Revolution in One Classroom: The Case of Mrs. Oublier (Cohen, 1990) describes how one teacher’s transformed
*beliefs*failed to transform her*practice*. - Candy Selling and Math Learning (Saxe, 1988) describes the informal math Brazilian children used to sell candy and how it failed to translate into formal classroom math.

**Featured Comment**:

It might be worth noting that the paragraph about â€˜answer gettingâ€™ seems to be referring to Phil Daro and his whole take on answer-getting.

Simon Terrell writes about his trip to Japan with Akihiko Takahashi.

Dan Goldner on his resolutions:

Of all the great things to focus on in this article, this is the one that spoke to me where I am now. Student-initiated in 40%, not 100%. 41% of time practicing, not 5%. Half the time on invent/think, not all the time on invent/think. Iâ€™ve been working so hard on making â€œinvent/thinkâ€ the dominant activity in my room, that practicing, which is

alsoa cognitive requirement for learning, has been de-emphasized. The next paragraph in the article acknowledges that Japan isnâ€™t perfect, either, and these percentages certainly arenâ€™t a perfect recipe. But as my personal pendulum finds its equilibrium itâ€™s great to read this and take from it the encouragement that thatallthe modes of learning have to have a place during the week.

## 19 Comments

## Howard Phillips

July 23, 2014 - 12:59 pm -I have just read the whole NYTimes article. It should be compulsory reading (twice, at least) for all those in charge of education, especially math, at all levels, and also for all Republicans. I will post the link on my blog, and credit yours with finding it.

## Clara Maxcy

July 23, 2014 - 1:16 pm -The NYT article is one of the clearest explanations of difficulties in the classroom and some good points on why Common Core is being vilified. I am forwarding the article to my math curriculum group. I think it important to have this conversation. Thanks for sharing!

## Mathy McMatherson

July 23, 2014 - 8:40 pm -Dan,

If the extra links in your post are meant to guide readers to some of the references that are made in the article, then it might be worth noting that the paragraph about ‘answer getting’ seems to be referring to Phil Daro and his whole take on answer-getting:

Thanks for posting the article.

## Dan Meyer

July 24, 2014 - 1:54 am -@

Mathy, good one. I’ve added it to the post.## Allison Krasnow

July 24, 2014 - 4:48 am -The sheer number of hours Finnish and Japanese teachers spend tearing versus US teachers ( 600 in Japan vs. 1100 in US) is so telling. When will the big decision-makers in education realize that the investment in ongoing PD such as lesson study is a far more powerful expenditure than yet another after school program using Khan Academy? And though “I do, You do, We do” was the loud mantra of our district math coach 2 coaches ago, it’s still posted prominently on fluorescent paper in the district’s PD office. Sigh…

## Chris Klerkx

July 24, 2014 - 12:17 pm -“He participated in a classroom equivalent of ‘Iron Chef,’ the popular Japanese television show.” Does anyone know what show this refers to?

## timfc

July 25, 2014 - 6:55 am -Chris,

I think they’re trying to say that “lesson study” is like “Iron Chef” for teachers.

## Kyle Pearce

July 25, 2014 - 6:46 pm -Dan & Crew,

What a great (but sad) article.

I found it really interesting regarding those with very little education being able to calculate complex problems in their head:

“A 12-year-old boy who accurately computed the price of four coconuts at 35 cruzeiros each was later given the problem on paper. Incorrectly using the multiplication method he was taught in school, he came up with the wrong answer. ”

Lately, I have really been challenging my own beliefs of how students should learn math facts. While I memorized much of the math I learned from K through grade 12, I’m somewhat embarrassed to admit that it wasn’t until I began teaching that I learned strategies to do more complex calculations in my head. I was the opposite of the 12-year-old boy in the article. I could do anything on paper via procedure, but would have sweat to do the calculations on the fly in the market.

Even though I believe there is no single way to teach mathematics effectively, at least Dan and others like him are helping the masses realize that “traditional” isn’t one of those effective ways.

## Simon terrell

July 26, 2014 - 12:57 pm -I just returned from Japan on a trip with Dr. Takahashi, and Professor Fuji. Although the article gets the details of lesson study mostly right, there is a lot of effort by teachers to take the mathematics, (I.e. Which numbers to use for a lesson so that solutions will flow more naturally) and make them interesting and meaningful. In the teacher’s lesson plans, they always mentioned that they wanted the students to be eager to solve the problems. Student interest is a major part of the thinking when planning lessons. I saw classrooms that were noisy but the students were always talking about the problem they were solving.

In one case, a teacher was teaching a lesson about division with remainders and the example was packaging meatballs in pack of 4. When faced with the problem of having 13 meatballs and needing 4 per pack, one student’s solution was “I would eat the extra meatball and then they would all fit”. It was so funny and joyful to see that all thinking was welcomed and the teacher artfully led them to the general thinking that she wanted by the end of the lesson.

However, teaching in this way requires a deeper understanding of how children learn mathematics, the deeper elements of mathematics, and an ability to recognize how to take students thinking and make it useful to the whole class. It requires a lot of strategy and thinking in the moment in order to craft a coherent narrative. With standardized testing and a demand for results at the end of each year, most teachers wouldn’t be willing to risk their jobs in order to go through the pains and failures of learning to teach this way.

It was a delight to be in classroom like this, and all except the high school classroom, at several different schools, operated in this way.

## Dan Meyer

July 28, 2014 - 7:18 am -@

Simon, thanks for the recap of your trip. Super helpful.My assumption about Japan was that their teachers attended less to issues of motivation and engagement because their students enter school with enormous social pressure to succeed academically. Where did my logic break down there?

## Dan Goldner

July 28, 2014 - 7:22 am -“Japanese students initiated the method for solving a problem in 40 percent of the lessons; Americans initiated 9 percent of the time. Similarly, 96 percent of American studentsâ€™ work fell into the category of â€œpractice,â€ while Japanese students spent only 41 percent of their time practicing. Almost half of Japanese studentsâ€™ time was spent doing work that the researchers termed ‘invent/think.’ (American students spent less than 1 percent of their time on it.)”

Off all the great things to focus on in this article, this is the one that spoke to me where I am now. Student-initiated in 40%, not 100%. 41% of time practicing, not 5%. Half the time on invent/think, not all the time on invent/think. I’ve been working so hard on making “invent/think” the dominant activity in my room, that practicing, which is ALSO a cognitive requirement for learning, has been de-emphasized. The next paragraph in the article acknowledges that Japan isn’t perfect, either, and these percentages certainly aren’t a perfect recipe. But as my personal pendulum finds its equilibrium it’s great to read this and take from it the encouragement that that ALL the modes of learning have to have a place during the week.

## Joel Patterson

July 28, 2014 - 1:18 pm -With standardized testing and a demand for results at the end of each year, most teachers wouldnâ€™t be willing to risk their jobs in order to go through the pains and failures of learning to teach this way.

That method of too much practice, too much drill on only the kinds of questions on the test–that gets some better results on the upcoming test but it doesn’t make for lifelong learners or perpetually curious thinkers. It’s what David Perkins calls an “oasis of false promise” for the teacher who is looking for the students to understand the math.

## Simon Terrell

July 28, 2014 - 7:37 pm -Dan,

I was definitely looking for the cultural differences in those Japanese students, and I suppose that the cultural importance of working hard does come through, but I also saw kids who were disengaged at different times during the lessons, on kids who were being somewhat naughty, so I can’t attribute the total difference in classroom behavior to culture alone.

There is a large amount of time spent on classroom management in the US – in the elementary school with behavior charts and rewards and consequences etc. I saw no evidence of this in the Japanese classroom, the classes were relatively noisy, especially compared to the value placed on quiet and orderly classrooms in many US schools, the kids were engaged.

From teacher debriefs, I really got the feeling that they consider student interest very highly and do not blame the kids if they aren’t engaged, they look at the lesson itself as the culprit.

All in all, it was a wonderful opportunity.