I read the thoughts about Common Core Bill Gates offered at AEI couple of days back, and I thought Mr. Gates can benefit from some education. Here are his comments, interspersed with my commentary.
Bill Gates: OK. So what is the Common Core? It’s a very simple thing. It’s a written explanation of what knowledge kids should achieve at very various milestones in their educational career. So it’s writing down in sixth grade which math things should you know, in ninth grade which math things should you know, in twelfth grade which math things should you know.
Ze’ev Wurman: That, indeed, is what content standards are supposed to be.
BG: And you might be surprised to learn how poor those I’ll call those standards, but to be clear, it’s not curriculum. It’s not a textbook. It’s not a way of teaching. It’s just writing down should you know this part of algebra? Should you know trigonometric functions? Should you know be able to recognize a graph of this type?
ZW: Wrong. I wish Mr. Gates would actually read the standards rather than rely on what others tell him. Common Core standards are more than just content standards, they also dictate pedagogy and hence curriculum. Here are a couple of obvious examples.
“Grade 1 standard 1.OA.6: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).”
This standard does not require only knowing addition and subtraction within 20, as a content standard should. It insists on knowing four specific ways to add and subtract. In other words, it dictates pedagogy and curriculum.
“HS Geometry G-CO: Understand congruence in terms of rigid motions.
6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
7. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.”
These standards do not require students to understand and prove triangle congruence, which is what content standards would. These, instead, require the study of triangle congruence using a very particular pedagogical approach (which, incidentally, is experimental and has a track record of failure).
In ELA, Common Core requires to split teaching time between informational and literary texts to about 50-50 in K-8 and 70-30 in 9-12. This is a pedagogical/curricular directive par excellence.
BG: And doing that very well is hard because there are certain dependencies: if you teach it in the wrong order; if you try and teach too much at once, too much too early, which the US was doing a lot of that, it can be very, very poor. And if you compare we have 50 of these things and there was quite a bit of divergence.
ZW: Mr. Gates is correct that doing it very well is hard. Mr. Gates is incorrect in implying that there is only one way to do it “right.” The curricula of the top-performing countries are not a copy of one another. Rather, they vary a lot in pacing and in ordering of topics. They are similar in that all of them are coherent, hierarchically building on previous knowledge, and have rigorous expectations of students. But to believe that there is only one way to success is unsupported by international evidence.
BG: Some states had trigonometry, some didn’t. Some had pie charts, some didn’t. So, ironically, what had happened was the textbook companies had gone in and told the committees that make these things up that they should add things over time. And so we had math textbooks over double the size of any of the Asian countries. And we had the ordering in almost every one of our 50 which is strange.
ZW: While I am sure that many, or even all, state standards could have been improved, the variability of content is not an indication of quality or lack thereof. It is reasonable to have some trigonometry in a Geometry or Algebra 2 class. It is also reasonable to have trigonometry as a separate course. This is true across top performing countries too.
Mr. Gates is correct about the size and the lack of depth of US textbooks. Yet Common Core is not going to address this issue as—despite its claim—Common Core is not significantly more focused than many state standards. We see clear evidence of this from the fact that all the “Common Core Aligned” textbooks are not thinner than before. If at all, they are bulkier.
BG: You think if you had 50, one of them would randomly be really, really well ordered. (Laughter.)
ZW: Mr. Gates has no idea whether some of the textbooks were well ordered. Nor does anyone else, really. Clearly, their publishers thought they were. Many, but not necessarily all, were wrong. Nor does the Common Core impose any strict “order” on teaching, certainly not within a grade level. And even across grade levels, some content needs to be taught ahead of the grade in which the relevant standard appears. A trivial example is the case of the standard algorithms for arithmetic (grade four for addition/subtraction, five for multiplication, six for division): Does Mr. Gates think that teaching the standard algorithms starts only at the grade they appear in the standards?
BG: Some were more ambitious than others. So, for example, being high; that is, having the twelfth grade expectation be high, there were a few like Massachusetts that were quite good in that respect. And so when kids from Massachusetts take international tests or the SAT, anything, they do better, better than the rest of the country. And so often, when you see those country rankings, they’ll take Massachusetts and show you where it would be if it was a separate country. And it’s way past the US, that now is virtually at the bottom of any of the well-off countries, with the Asian countries totally dominating the top six slots now. Finland had a brief time where they were up high, and now they’re not even the European leader anymore.
ZW: Mr. Gates refers to the Programme for International Student Assessment when he mentions the U.S. ranking, where most of the “well-off” countries are above us. Still, we have there the not so awful company of Norway, Italy, Russia, Slovakia, Sweden, Lithuania, and Hungary. More interesting is our position on the Trends in International Mathematics in Science Study that Mr. Gates didn’t mention, where we (8th grade) are above average in the good company of Finland, England, Hungary, and Australia, and above New Zealand, Sweden, Norway, and Romania. It is true we don’t do as well as we should, but we are not nearly as terrible as Mr. Gates wants us to believe.
BG: So a bunch of governors said, hey, you know, why are we buying these expensive textbooks? Why are they getting so thick? You know, are standards high enough or quality enough? And I think it was the National Governors Association that said we ought to get together on this. A bunch of teachers met with a bunch of experts, and so in reading and writing and math, these knowledge levels were written down.
ZW: Well, not exactly. Not “teachers met experts.” Rather, a bunch of poorly qualified ed policy “experts” (chosen by Mr. Gates and Marc Tucker) met with testing experts from College Board and ACT and made the decisions. Then they brought in teachers as window dressing to create the image of broad support.
BG: And at some point 46 states had adopted that curriculum, a variety of competitive curriculum, now that small companies can get into it because it’s not just doing a book for Florida, and so the sort of barrier to entry that was created by the large firms there goes away. The idea that those committees write so you can’t use the old textbooks, you know, that idea will go away because in math, this can have real durability.
ZW: Interesting Freudian slip. So even Mr. Gates realizes that what the states adopted is effectively a curriculum. Further, Mr. Gates pretense that now, with a national market, small companies have a better shot is disingenuous. To the contrary, fragmented state markets were much more friendly to small companies and upstarts. It is much harder for a small company to penetrate a national market.
BG: Changing your math standards is not like some new form of math that’s being invented. And there has been in a sense a national expectation. When you take the SAT test, it has trigonometry on it, so if you’re in a state that doesn’t have that, you’re going to get a low score. And they use a certain notation in the way they do math and certain states were different than that, so you’re screwed.
ZW: Already addressed above. Mr. Gates is confused and confusing. All states offered trigonometry. The difference was whether they offered it as a standalone course or as part of another course (Geometry, Analysis, Algebra 2).
BG: If you move from state to state you experience discontinuity because of this.
ZW: Less than 2 percent of students move across state lines every year.
BG: And it’s made it very hard to compare things. And this is an era where we have things like Khan Academy that are trying to be a national resource and yet they you sit down, it will tell you, are you up to the sixth grade level? Are you up to the ninth grade level? Are you ready to graduate from high school? And so this Common Core was put together.
ZW: This sounds like incoherent rambling. We have the National Assessment of Educational Progress to compare states. We’ve had it in place for many years. Contrary to Mr. Gates, Khan Academy can easily support a diversity of state standards and curricula because it has a large selection of fine-grain topics, making customization to any given state or school a cinch.
BG: Somebody in states will decide this thing. Nobody is suggesting that the federal government will, even in this area, which is not curriculum, dictate these things. States can opt in. They can opt out.
ZW: Not so fast. They can opt in. But if they won Race to the Top money (12 states), or if they got No Child Left Behind flexibility waivers (43 states and counting), they cannot easily opt out.
BG: As they do that, they should look at this status quo, which is poor. They should look and find something that’s high achievement, that’s got quality. And if they can find something that’s that, if they have two they’re comparing, they ought to probably pick something in common, because to some degree, this is an area where if you do have commonality, it’s like an electrical plug you get more free market competition.
ZW: I am not as certain as Mr. Gates that “commonality, it’s like electric plug.” Had Massachusetts chosen commonality 15 years back, it would have mediocre educational achievement like everyone else. Because it did not, it could create its own excellent program to make itself shine. Except that now it was coerced to abandon that shining success for the Race to the Top money and join the “common” mediocrity …
BG: Scale is good for free market competition. Individual state regulatory capture is not good for competition.
ZW: It is unclear that scale is good for educational competition. The best programs around were not done in large markets. Singapore, Hong Kong, Finland, … or Massachusetts come to mind. But why would a federal regulatory capture necessarily be better than state regulatory capture is beyond me.
BG: And so this thing, in terms of driving innovation, you’d think that sort of pro-capitalistic market-driven people would be in favor of it, but, you know, somehow, it’s gotten to be controversial. And, you know, states will decide. Whatever they want to decide is fine. But, at the end of the day, it does affect the quality of your teaching, does affect when your kids go to take what are national-level tests, whether they are going to do well or not do well.
Image by Mohammad Jangda.