Math Education?

yesterday, Scientific American published an article - really a book excerpt - challenging math instruction both "around Charlottesville (Virginia)" and across the United States. The article is here (on the Scientific American site) though it also appears here (in a Yahoo! mirror) which supposedly accepts comments, except mine. I think the article requires a response, so I've reprinted the whole (very long) piece here, with my response at the bottom. I have also commented directly on the Scientific American article. Your thoughts are welcome - of course - either place.

Math Teachers Feel They're Poorly Prepared

By Anna Kuchment | Scientific American – 20 hrs ago

When William Schmidt, an expert on math education at Michigan State University, moved his family from East Lansing to Charlottesville, Virginia for a year's research leave, his work took a personal turn. He noticed that the public school his daughters would be attending outside Charlottesville was academically behind the one they had attended in Michigan. Back home, his second grade daughter would be learning multiplication tables up through the number 5, yet in Charlottesville, multiplication was not even part of his local school's second grade curriculum. 

His daughter's experience, he explains in a new book excerpted below, is not unique. The [American] system of schooling represents a game of chance that few are even aware is being played, he writes in Inequality for All: The Challenge of Unequal Opportunity in American Schools, co- written with Curtis C. McKnight. The inequalities pose a risk to every child, they write, regardless of socioeconomic background or race. They stem from differences in state education standards, in school funding, in curricula that districts choose to adopt and in the content that individual classroom teachers choose to teach. In this excerpt, Schmidt and McKnight focus on variations in how math teachers are trained and how that, in turn, affects student achievement. 

The following is excerpted from Inequality for All: The Challenge of Unequal Opportunity in American Schools, by William H. Schmidt and Curtis C. McKnight. (Teachers College Press, 2012). 

One thing that most of us remember best about school is our teachers. Thus, when solutions are proposed for reforming American schools in response to critical reports or disappointing test results, teachers are always among the first to be singled out. Proposals often turn first to improving the teaching force by focusing on higher quality. For example, in the NCLB [No Child Left Behind] era, considerable emphasis has been placed on a highly qualified teaching force.

Districts must certify what percentage of their teachers is highly qualified. However, the states and school districts define what they consider highly qualified, resulting in a great deal of ambiguity.

What does it mean to be a highly qualified teacher? The definition of a high-quality mathematics teacher has never been standardized. Therefore, although improving the quality of teachers and teaching is a common cry when we seek to improve schools, there is little agreement and scant empirical evidence that indicates what characteristics define a high-quality mathematics teacher. Even an obvious definition, such as a knowledge of mathematics, is problematic, since there is generally no agreement as to what specific mathematics knowledge is needed.

The literature identifies two types of knowledge that are clearly related to providing opportunities to learn: mathematics content knowledge and pedagogical content knowledge. For mathematics, recent empirical work has advanced our understanding of what mathematics knowledge is necessary for teaching mathematics. The rest of this chapter lays out how this knowledge in particular, mathematics content knowledge is related to inequalities in content coverage, and provides data related to teacher content knowledge for a sample of teachers.

What Teachers Tell Us About Their Knowledge of Mathematics

We approached the question of teacher knowledge of specific mathematics content indirectly, by asking a sample of more than 4,000 teachers from the PROM/SE project [Promoting Rigorous Outcomes in Math and Science Education] to respond to the question, How well prepared academically do you feel you are that is, you feel you have the necessary disciplinary coursework and understanding to teach each of the following? We asked this question for multiple mathematics topics. The list of topics varied for teachers in primary and teachers in middle and secondary school combined.

By relying on teachers reports of their own feelings of adequate preparation, we only get at their knowledge indirectly. Fortunately, this approach is sufficient to demonstrate how much variation there is in teachers content-specific knowledge, or at least in their feelings of adequate preparation. Furthermore, the candor of the results suggests a degree of face validity and, hence, integrity in the responses. The overall tenor of the responses is very consistent with other data on the issue, some of which suggest that the pattern reported here might be a best-case scenario. All results reported in this chapter are based on the PROM/SE data.

Primary Teachers (1st Through 3rd Grades)

Primary teachers felt academically prepared to teach only the topics they taught to their students. Even for those topics, about one-fourth to one-half of the teachers surveyed reported that they did not feel well prepared. The teachers we surveyed were from 60 PROM/SE districts located in Michigan and Ohio.

Is it reasonable for teachers to focus only on the topics that they will teach? However reasonable such a position may appear, many of the more advanced topics for which teachers did not feel well prepared provide the mathematics background necessary to be truly well prepared to teach the more elementary topics at their grade level. To define a qualified teaching force, we adopted a criterion of 75% of teachers feeling well prepared to teach a given topic. We found that, over all sampled teachers, only two mathematics topics met this criterion: the meaning of whole numbers, including place value and operations with whole numbers.

Virtually all of the geometry topics (aside from the basics) are excluded by the 75% criterion. So are all of the proportionality topics and all of the algebra topics. These results imply that the quality of learning opportunities surrounding many of the mathematics topics taught in 1st through 3rd grades was not likely to be high. They also suggest that there is large variability in self-reported content-specific knowledge. For many of these topics, only a bare majority of 50% to 60% of teachers felt well prepared.

The other striking feature of the results was the large variability across districts. For example, for fractions, in some districts all of the primary teachers felt very well prepared, while in other districts only about half of the teachers felt very well prepared. For geometry basics (lines, angles, and so on), the results ranged from one district with only about one-fourth of its teachers feeling well prepared to another district in which about 90% of the teachers felt well prepared.

Upper Elementary Teachers (4th Through 5th Grades)

The results for districts for 4th- and 5th-grade teachers were quite different. For example, for eight different topics, all of the teachers in at least one district felt very well prepared academically for each of those topics.

At the district level, the results for whole number meaning and operations were similar to those for 1st- through 3rd-grade teachers. Further, fractions also had a median value around 75%.

However, the variability across districts remains a striking feature for 4th- and 5th-grade teachers, particularly for decimals, percentages, and geometry basics. These are all topics that were supposed to be introduced in these grades in Michigan and Ohio. For example, for decimals, in one district only one-fourth of the teachers felt well prepared, while in another district virtually all teachers indicated that they felt well prepared to teach decimals.

Middle School Teachers (6th Through 8th Grades)

We examined the pool of teachers from all of the districts taken together. From this perspective, there were no topics that at least 75% of the teachers felt very well prepared to teach. Only two topics came close. Among the whole pool of teachers, 73% indicated that they felt well prepared to teach the topic of coordinates and lines. Sixty-nine percent of the teachers indicated that they felt well prepared to teach the topic of data.

Eleven topics qualify if we relax the criterion to topics in which at least 50% of the teachers felt well prepared. This included the two topics just mentioned as well as nine others negative, rational, and real numbers; exponents, roots, and radicals; number theory; polygons and circles; congruence and similarity; proportionality problems; patterns and relations; expressions and simple equations; and linear equalities and inequalities. The Michigan and Ohio standards call for including many of these topics at the middle grades. The fact that only about 50% to 60% of the teachers felt very well prepared to teach these topics suggested something of the magnitude of the problem that school districts face.

For example, there has been a strong national movement to include elementary algebra topics in the middle school, particularly in 8th grade. The Michigan and Ohio standards reflect this, as do the Common Core State Standards, which are in the process of becoming the new Michigan and Ohio state standards. Adoption of the Common Core State Standards brings states more into alignment with international benchmarks of what is expected in the equivalent of middle school.

The severity of the problems faced by these districts and, by inference, by the United States as a whole, was indicated by the fact that only about half of the teachers felt academically very well prepared to teach expressions and simple equations, as well as linear equalities and inequalities. Even fewer teachers (only around 25% to 40%) felt they had adequate content knowledge to teach other important algebraic concepts, including proportionality (41% of teachers), slope (38%), and functions (39%).

High School Teachers

The story for high school teachers is rather different, which is not unexpected given their typically greater preparation in mathematics. Almost 60% of the topics met the criterion of having at least 75% of the pool of PROM/SE teachers from the 60 districts indicating that they were well prepared academically. The areas in which high school teachers indicated that they felt less well prepared were number bases, three-dimensional geometry, geometric transformations, logarithmic and trigonometric functions, probability, and calculus. These findings are, however, still cause for concern. For example, there is an increasingly strong push for the inclusion of probability and statistics in high school, as is found in the Common Core State Standards, yet less than half of the surveyed mathematics teachers felt well prepared to teach it. Teachers self-perceptions of their preparedness seem likely, if anything, to overestimate what they know and how well prepared they are rather than to underestimate it.

Moving from the pool of all 60 districts to the district-by-district results for a large number of topics (16), at least 25% of the districts had all of their high school teachers indicating that they felt well prepared to teach those topics. However, there was still great variation across the districts, especially for geometry topics including transformations, three-dimensional geometry, polygons, and circles. There was similarly great variability in the percentage of teachers who felt that they had the coursework to make them well prepared to deal with calculus, probability, number theory, and logarithmic and trigonometric functions.

Why Teachers Feel So Poorly Prepared

We have surveyed how well prepared in terms of disciplinary course work teachers at various levels felt for teaching various mathematics topics in what is a fairly representative sample of 60 districts. In general, we would summarize the findings by stating that many teachers felt ill prepared to teach mathematics topics that are in state standards and in the new Common Core State Standards for mathematics. Why did these teachers feel so ill prepared?

There is perhaps a simple answer for the elementary and middle school teachers: They felt ill prepared because if we examine the coursework they studied during their teacher preparation, they were ill prepared. The new TEDS study results suggested this to be the case more generally, which clearly does not bode well for equality of learning experiences for students in these districts.

College-Level Preparation

In this section, we summarize what teachers have told us about their preparation in mathematics at the college level and as graduate students.

In 1st through 4th grades, less than 10% have either a major or a minor in mathematics. Teachers at this level are typically generalists they must be prepared to teach many different subject-matter areas. They do not have adequate time in their preparation to get a major or a minor in each of those subject matters.

At 4th grade, the international data paint a different picture. Unfortunately, the definitions are not precisely the same, but the data do provide us with a benchmark of sorts. Including those primary teachers with either a mathematics major or a minor in mathematics or science, around one-third of 4th-grade students on average had such a teacher in the countries that took part in TIMSS, [the Trends in International Mathematics and Science Study].

Taking this estimate from the TIMSS data as an indicator of the percentage of teachers who had majored or minored in mathematics or science, this proportion was considerably higher than for the PROM/SE 4th-grade teachers, where the comparable percentage was 5%. The percentage was over 50% in Singapore and Russia. This suggests that, from an international perspective, other countries typically have around six times as many primary teachers who have a specialization in mathematics or in a related field of science.

The result is even more disturbing when we turn to the middle school mathematics curriculum and the higher level of mathematics offered there.

Three out of four middle school teachers in the PROM/SE sample did not have a specialization in mathematics. At 6th grade, the percentage was much like that for primary teachers only around 10% had a major or minor in mathematics. In 7th and 8th grade, this percentage increased to around 35% to 40%.

These numbers indicate that a very large percentage of middle school students were being taught increasingly more complex mathematics, as called for in the Michigan and Ohio state standards, by teachers who lacked a strong background in mathematics. These results offer one explanation for why so many middle school teachers did not feel very well prepared to teach many of the middle school topics discussed in the previous section. This also foreshadows problems of implementation, at least as the newly adopted Common Core State Standards are put in place, in Michigan and Ohio.

What about high school mathematics teachers? We would expect that all high school mathematics teachers would have at least a minor in mathematics, if not a major. But the actual results for high school are quite surprising. Less than half of all high school mathematics teachers surveyed had a major in mathematics. Almost one-third did not have either a major or a minor in mathematics.

These numbers varied across the four grades of high school taught by the surveyed teachers. Almost one-half of the teachers whose major teaching responsibilities were at 9th or 10th grade did not have any specialization in mathematics. In 11th and 12th grades, over 71% of the teachers who taught primarily at those grades had some kind of specialization in mathematics.

Lest it seem too heartening that those teaching the most advanced courses (usually taken in the 11th and 12th grades) are better prepared in mathematics, we need to consider several caveats. It may be even more important to have well prepared teachers in entry-level courses usually taught in 9th and 10th grades. These courses serve as the foundation for more-advanced courses, may be even more difficult to teach, and are just as important in terms of preparing students for further study. But for these foundational courses, teacher content knowledge was not nearly as strong. It is worth noting that on some of the more advanced mathematics topics (number theory, geometric transformations, logarithmic and trigonometric functions, and calculus) up to half of the teachers did not feel very well prepared to teach them. Perhaps these same 50% were those who did not have a major in
mathematics.

Mathematics Knowledge

One key part of the PROM/SE project was planning and carrying out content-based capacity building for teachers. As a part of this component, we administered a test of mathematics knowledge to a sample of teachers. [The results] strongly suggest that elementary and middle school teachers perceived their weaknesses accurately and reported them honestly. They appeared to be reporting that they were not well prepared academically to teach the mathematics content that they were being asked to teach.

Across grades, the percentage of teachers who did not have a major or minor in mathematics ranged from nearly all of the teachers at 1st grade to around one-half of them at 8th grade. These same teachers were able to answer correctly only about half of the items, as compared with teachers with mathematics majors who were teaching at the corresponding grades. The teachers with mathematics majors were able to correctly answer about 70% of the same items. This gap of almost 20% is sizable and very important. It confirms what the teachers told us when they said that they were not well prepared.

The problem at high school is more a problem of variability. The data indicated that most of the teachers had mathematics majors and that their mathematics knowledge was reasonably good. However, about one-third still did not have strong academic preparation.

The Effects of Teachers Mathematics Knowledge on Opportunities to Learn

Given these results about teachers mathematics knowledge, it is tempting to blame elementary and middle school teachers for not being prepared, but we believe blaming teachers is a mistake. Why? Because teachers prepare themselves according to the standards and guidelines established by the states that certify them and the teacher preparation programs that train them. Our point here is that such variation in academic content knowledge is likely to affect the quality of content coverage. Since the content coverage described previously varied appreciably, these data indicate one possible reason for such variation as it is very likely that this lack of knowledge influences not only the quality of the coverage of particular topics but also the bigger picture as to how the teacher makes choices about which topics to cover, for how long (to what depth), and in what sequence. Such lack of knowledge further exacerbates the variation in content coverage in mathematics across classrooms, schools, and districts, resulting in further inequalities in opportunities to learn.

Used with permission from the Publisher. From Schmidt & McKnight, Inequality for All: The Challenge of Unequal Opportunity in American Schools, New York: Teachers College Press, 2012 by Teachers College, Columbia University. All rights reserved.

Ask Scientific American on Twitter @SciAm and @SciamBlogs. why I can't comment... © 2012 ScientificAmerican.com. All rights reserved

My Response: Maths are Creative, Pacing Guides are Absurd

I hate to challenge a Michigan State colleague, but I work with schools both in Michigan and "around Charlottesville, Virginia," and I disagree with a number of the assumptions suggested here.

The first, of course, is that I'm with Conrad Wolfram on the concept that "order" is really not important in maths education (you can find Wolfram’s TED talk on YouTube or via my blog post “Changing Gears: Maths are creative, Maths are not arithmetic”) and thus I strongly disagree with those who might measure either students or schools according to some pre-determined pacing guide.

The other assumption which I find flawed is the comparative measurement structure suggested here. I see low quality maths instruction in many places, I see high quality maths instruction many places, but mostly I see that high quality maths instruction is suggested when students have a deep grasp of mathematics concepts no matter what their arithmetical skills are... and this I am quite certain we have been building in the schools around Charlottesville (see my blog post “Among Schoolchildren”).

We are doing that by embracing a different concept of professional development, one based in "teacher entrepreneurship," social engagement, and grounded theory action research combined with a view that we look at the whole student "result" not any single measure. We do this because we believe that students are humans who develop different skills at different rates.

As for TIMSS and other “international comparatives,” I wish to draw everyone’s attention to the work of Yong Zhao who demonstrates the inverse relationship between international standardized test score results and national economic creativity (see slide 8/8). The nations which score lowest on these exams lead the world in patents per capita, and new product and service introductions per capita. It is the choice between being a nation which invents iPads and a nation which builds iPads at slave labor prices.

“Around Charlottesville” our goal is to raise a generation ready to lead, to invent, to solve problems. It is not our goal to raise test takers. And it is our goal to help teachers develop into educators who can support that mission.

- Ira Socol

Changing Gears 2012: social networking beyond Zuckerbergism

(1) ending required sameness     (2) rejecting the flipped classroom     (3) re-thinking rigor     (4) its not about 1:1      (5) start to dream again     (6) learning to be a society (again)     (7) reconsidering what literature means     (8) maths are creative, maths are not arithmetic     (9) changing rooms     (10) undoing academic time     (12) knowing less about students, seeing more     (13) why we fight

Facebook began in the toxic social environment of the Ivy League...
The Social Network as a ranking system, if I win, you lose

Mark Zuckerberg isn't really an evil guy, as I think the film The Social Network made quite clear. He is simply a guy without the social skills which would allow him to understand the impact of his work. I don't just say that because I watched the film, I know people who know Mark, surely who knew Mark growing up. He is a great success in many things, but has always been a total failure with humanity, which makes it unfortunate that he created a tool with so much impact on humanity. Ah well, that is simply not a rare thing. Mitt Romney, who seems about to be chosen by the Republican Party to run for president of the United States seems completely unaware of what a human is, despite growing up with a remarkably humane father. Our leaders, whether from the privileged economic background of David Cameron or the privileged intellectual background of Barack Obama, all seem to struggle with this. We know this, the exceptions who can actually communicate in two directions with other humans, whether Robert Kennedy, Bill Clinton, Ronald Reagan, or Tony Blair, stand out in shocking contrast against their "peers."

One of the things which comes with this lack of humanity in our leadership is a belief in human competition which is wholly at odds with actual human experience - when that competition has not been aggressively trained in to people. Most humans do not really compete in their family groups, their "tribes," their "clans," or even their workplaces. Most people try to cooperate, to build things together, to move forward together. "[T]here are theoretical reasons to suppose that mentalizing demands of cooperation and competition differ in some aspects," says an fMRI study from 2004, "In case of competition, the opponent’s upcoming behavior is less predictable than in the case of cooperation in which there is a clear expectation for the behavior of the other agent. Research ... demonstrated that one’s own actions are facilitated when actions of the other are at the disposal of the self. This is the case in the cooperation trials, but exactly the opposite during the competition trials."

In other words, though both competition and cooperation are "natural," cooperation is not just more efficient for humans - "In accordance with evidence from evolutionary psychology as well as from developmental psychology, we argue that cooperation is a socially rewarding process ... these arguments are consistent with the hypothesis that executive functions evolved to serve social planning in primates and, in humans, are applied to both physical world and the social realm" - but that we see with less prediction - we see more clearly and innovatively - in cooperative mode than in competitive mode.

Cooperation is not something foreign to the human race.

I'm certain that Mitt Romney once knew
why Mormons chose the beehive
as Utah's symbol, but life in the
culture of Harvard and Bain Capital
stripped that knowledge away.

Richerson, Boyd and Henrich (2002) call this the "tribal social instincts hypothesis," "Humans are prone to cooperate," they say, "even with strangers," yet, the enculturalization is key to these behaviors, "The elegant studies by Richard Nisbett’s group show how people’s affective and cognitive styles become intimately entwined with their social institutions. Because such complex traditions are so deeply ingrained, they are slow both to emerge and to decay. ... The slow rate of institutional change means that different populations experiencing the same environment and using the same technology often have quite different institutions."

Mark Zuckerberg, like most of our leadership, grew up in the rather anti-human confines of the wealthy, Wall Street obsessed, suburb. In these places where the institutions of the culture have embraced selfishness and competition in all things as a "good." Though, yes, "Human societies represent a spectacular outlier with respect to all other animal species because they are based on large-scale cooperation among genetically unrelated individuals" (Fehr and Fischbacher 2004), the social norming those authors describe seem to overwhelm the natural, creating places in which competition, in every single thing, is trained in from birth. My kid's Apgar score is higher than your kids, and onward and upward to 5,000 square foot homes for four people and Mercedes-Benz station wagons in the driveway, and $5,000 commercial ranges in kitchens that are turned on twice a year, and SAT test tutors and paid preparers for those Harvard applications.

In that world, as the Zuckerberg character in Aaron Sorkin's film makes clear in the first scene, being in one of the most prestigious fraternities of the most prestigious university in the nation is simply not enough, because it is not the "most of the most." Now Zuckerberg has neurological issues (I'm pretty sure) which make this especially difficult for him, but no matter the brain wiring, the world of Harvard and Harvard-like places is built on this essential set of what might be called personality disorders. A "zero-sum" world in which your success is only possible through the (relative) failure of those around you.

Able to not just speak to those different
from himself, but to hear them as well,
Robert Kennedy was a remarkably
rare type of political leader.

"It is a revolutionary world we live in. Governments repress their people; and millions are trapped in poverty while the nation grows rich; and wealth is lavished on armaments.  For the fortunate among us, there is the temptation to follow the easy and familiar paths of personal ambition and financial success so grandly spread before those who enjoy the privilege of education. But that is not the road history has marked for us.  The future does not belong to those who are content with today, apathetic toward common problems and their fellow man alike. Rather it will belong to those who can blend vision, reason and courage in a personal commitment to the ideals and great enterprises of American society." - Robert Francis Kennedy, 1968

We need a different kind of leadership in education. "The future does not belong to those who are content with today, apathetic toward common problems and their fellow man alike." We need a believe in our shared capabilities as people. And it has to begin with a radically different conception of our educational social networks. We need a concept of social networking where we are not comparing schools, teachers, and students in ways little different than Mark Zuckerberg's FaceMash.

Because I simply do not want schools to compete (the goal of the profiteers of "ed reform"), teachers to compete (the goal of Barack Obama, Bill Gates, Michael Gove, and many of America's Governors), or students to compete (the goal of way, way too many adults in schools and around children), I want them to succeed in their own ways, in their own time, and mostly, cooperatively. I want them all working together, helping each other...
• Might this student do better in your school? This student with that teacher? These three students if working together?
• What can this school learn from that school? How can this teacher help that teacher? What can this student learn from that student?

FaceMash: Which school is hotter?

Not competing, not ranking, not rating, but doing something much more directly human... helping each other.

We don't really want schools fighting over the "easy to educate" students, or teachers refusing to help other teachers escape that "bottom 5%," or students refusing to help each other do better, do we? And if we do, what are we suggesting? About ourselves, about society, even about our businesses?

Now comes the hard part, rethinking our own positions. Because if step eleven of Changing Gears 2012 is going to be "un-competing" in our social networking, we need to begin with our own behaviors. We do a lot of things which, often unintentionally, send the wrong messages, and those messages not only impact our students, they impact ourselves.

I've had my fights with online colleagues/friends I respect over stuff like the EduBlog Awards, and I know they "recognize" many people, but determining quality by letting people organize "vote for me" campaigns is the essence of building competition into something in which competition serves no positive purpose. And I'm troubled when people beg for more followers on Twitter (or friends on Facebook, or...). That's competition based in the most meaningless count, quantity where you don't even know what you are counting (bots, multiple accounts from one person). (I tend the other direction, I remember blocking new followers when I approached 500 followers, for whatever reason "500" seemed like a lot, and I wondered if "a lot" of followers would change the way I was communicating.) I'm troubled when people quote stats about number of readers of blogs too often. And I know I don't want to be that person people ask for help most often.

Obviously, our "official" rankings are problems - those "Honor Rolls" (I mumble, being one of the perpetually unhonored), class rankings, the whole idea - I'm always stunned by this - that the instructor is doing something wrong if everyone does well in the course, concern about "grade inflation," or the dreaded "awards ceremony."

Perhaps I'm strange, but I always think that being at the top - in this (especially American) work - encourages you to worry about staying at the top instead of encouraging you to do what you need to do. One issue. The second - and far more important issue is this - when you rank you are turning to artificial and external motivators to replace your own heart and soul. You are no longer trying to be the best you can be, you have given away your own internal measures for some flimsy badge which represents someone else's ideas.

A top retailer, 1972. Fighting to be on top
doesn't always work.

But perhaps I'm not alone. Toyota is still trying to recover from the disastrous quality control lapses they accepted because their goal was to sell more cars than General Motors. I've seen many businesses over-expand themselves out of business. The jury is still out on what Volkwagen's desire to be number one in sales will do to their long term reputation. Sometimes, a decent slice of the pie is better than either none of it or even all of it, because "number one" can be a tough thing: If I go back forty years to 1972, the top American retailers were: Sears, A&P, Safeway, J.C. Penney, and Kroger. The top airlines were United (yes, still up there), TWA, Pan Am, American, and Eastern - with only two of those five still even existing. I couldn't find my way back to 1972, but in 1976 the top selling cars in the United States were: the Oldsmobile Cutlass, Chevrolet Caprice, Chevrolet Monte Carlo, Ford LTD, and Chevrolet Malibu. No real need to point out that the basic design of our schools, the functional engineering of our schools, is a lot older than 40 years, as is our systems management, as are our grading systems, subject structures, and most of our course materials designs.

The change, among smart businesspeople, was apparent in late 2008-early 2009 when Ford joined the rush to Washington to get help for, yes, General Motors and Chrysler. Ford put considerable muscle, and took a lot of absurd abuse from Republicans, behind efforts to not just keep their competitors in business, but to reduce their debts far below those of Ford's. Why? Ford knew that their supplier chain needed healthy customers beyond themselves. Ford also knew that a health industry would be good for the country, and Ford knew that a full-scale depression spinning out from the nation's center wouldn't do much for its sales. Plus Ford knows that a healthy multiplayer industry is good for everyone. The Big Three in the US, Volkwagen, BMW, Daimler in Germany, Toyota, Nissan, Honda, Mitsubishi in Japan.

It was also apparent in Google's recent conversations about Mozilla: "So it's very easy to see why Google would be willing to fund Mozilla: Like Google, Mozilla is clearly committed to the betterment of the web, and they're spending their resources to make a great, open-source web browser. Chrome is not all things to all people; Firefox is an important product because it can be a different product with different design decisions and serve different users well. Mozilla's commitment to advancing the web is why I was hired at Google explicitly to work on Firefox before we built Chrome: Google was interested enough in seeing Firefox succeed to commit engineering resources to it, and we only shifted to building Chrome when we thought we might be able to cause even greater increases in the rate at which the web advanced. It's not hard to understand the roots of this strategy. Google succeeds (and makes money) when the web succeeds and people use it more to do everything they need to do. Because of this Chrome doesn't need to be a Microsoft Office, a direct money-maker, nor does it even need to directly feed users to Google. Just making the web more capable is enough."

So, the world's biggest companies know something educational reformers, and our political leaders, can't quite figure out. I know Ford would like to sell more cars in the US than General Motors, but that kind of win is not their goal. And Google, which could dominate many things, chooses not to.

The Nash Equilibrium: It is not all about competition
"Adam Smith, is wrong"

Mark Zuckerberg doesn't understand that, which is why Facebook will always be about rankings and superiorities. More friends, more messages, more writings on the wall. Even Barack Obama, doesn't fully understand this, he wants America to be triumphant - whatever that may mean - in education. But we look around our schools and we see so many differing talents, so many differing personalities, so many differing skillsets, and we know that we'll always be better together.

I don't want FaceMash or SchoolMash or Students-in-MathMash. I sure do not want algorithms which will artificially rate people. I don't want counts of followers or popularity contest awards, and I don't want kids accorded an "honor" because they got one more answer right on some multiple choice test than another. I don't want teachers rated on test scores or graduation rates, and I don't want schools rated those ways either. We've tried that for generations. It sucks for just about everybody.

So let's try something different. Let's join together, in all of our learning spaces, with as little hierarchy as we overtrained animals can muster. Maybe we'll discover something.

- Ira Socol
next: knowing less about students, seeing more