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How Elementary Teachers Master Their Subjects in Top-Performing Countries

NCEE's Center on International Education Benchmarking released an important new report this week by noted Australian researcher Ben Jensen and his colleagues at Learning First. Not So Elementary: Primary School Teacher Quality in Top-Performing Systems looks at what may be described as one of the biggest sleeper issues in American education. 

In the United States, elementary school teachers are expected to teach all the subjects in the curriculum. It is not until secondary school that teachers specialize by subject. Perhaps this is because the subjects taught are...well...elementary. After all, aren't all high school graduates supposed to have mastered arithmetic, fractions and the other topics in elementary mathematics years before they graduate?   Ditto the basics of reading? It might not be so easy to teach a child to decode the letters on the page, but the mechanics of decoding should not be mysterious to a college graduate. Right? Surely a teacher's college graduate mastered the mechanics of simple writing years before she threw her cap in the air at graduation. 

Years ago, Lee Shulman told me I had to read Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States, by Liping Ma.  He was right. It instantly joined the ranks of the ten most important books I've ever read on education. In it, Liping Ma presents detailed observations of the teaching of elementary school mathematics in both China and the United States. On page after page, it becomes indelibly clear that the Chinese teachers cannot only perform the standard algorithms for solving the typical problems in all the topics in elementary school mathematics, but, unlike many American elementary school teachers, they know why these algorithms work.

This is very important, for at least two reasons. First, students do not come to school without some basic exposure to mathematics. They all know something about numbers and how they work. But a good deal of what they think they know is actually wrong. It is not just that they don't understand. It is that they misunderstand, and that misunderstanding gets in the way of understanding what the teacher is trying to teach them. To fix this, the teacher can tell the students what she wants them to know over and over again, but that often does not help. What does help is understanding the students' misunderstanding, getting inside the students' heads, so the teacher can grasp the flawed logic and then correct it.  But that is impossible if the teacher herself does not understand how the mathematics works.

The second reason this is important is because, though a student who is good at executing the standard procedures may get the right answers on standard math quizzes and do well in elementary school, when that same student gets to middle school and is faced with algebra, it will be very difficult to "get" algebra if the student does not understand why the arithmetic works.

When the TIMSS scores first came out, the press noted that American elementary school students did well compared to students from other countries at the elementary school level, much less well at the middle school level and even worse at the high school level.  They concluded that we do a good job of teaching mathematics at the elementary school level; the problem, clearly, was with the way we teach mathematics at the secondary school level. But that is not true. The failure to teach for understanding at the elementary school level set the stage for failure at the secondary school level.

When you think about what we know about the way our system works, this is exactly the result we should have expected. We source our teachers mainly from the bottom half of high school graduates going to college. The data on these graduates tells us that their command of high school mathematics is typically very poor, their command of middle school mathematics is shaky at best, they are poor writers and they typically read at a 7th or 8th grade level. A large fraction of elementary school teachers took their last mathematics course in middle school. A large fraction of our elementary school teachers do not like mathematics and many are afraid of it. Given this data, it would be astonishing if our elementary school teachers had a firm understanding of the underlying logic of mathematics. If the majority of our high school graduates cannot write well and the majority are reading at a 7th or 8th grade level when they leave high school, and our teacher's colleges get the high school graduates who do less well than most of their colleagues, we should expect exactly what we are getting.

The astonishing thing is that China, still a poor country, and far poorer when Liping Ma did her study, routinely produces teachers who really do understand the mathematics at a deep level. It should surprise no one that the primary school teachers in the countries whose students routinely outperform ours by wide margins have a much firmer command of the subjects they teach than ours do, and this one fact explains a very large part of performance of their students. The question, of course, is how they do it. And that, as you would expect, is the subject of Jensen's Not So Elementary. Nothing in it should surprise you; it is pretty much what any of us would do if we were serious about making sure that our elementary school teachers really know their subjects. Here it is, rapid fire:


The United States gets most of its teachers from the bottom half of high school graduates going to college, Shanghai from the middle, Finland from the top 10 percent, South Korea from the top five percent. But this is misleading. Our entire student body does far less well than Shanghai's on PISA. So their middle is far above our middle. If, as in our case, a country gets its teachers from high school graduates whose command of the subjects they teach is very shaky, they can expect that the students of those teachers will themselves graduate from high school with a shaky command of those same subjects. That is exactly what is happening. 

Standards for getting into schools of education are much higher in most of the top-performing countries. In the United States, the education programs of our universities are widely regarded as among the easiest of all professional programs to get into. I know of no university in which an applicant to the education program of a university is turned down by that education school once the student has been admitted to the university, no matter how easy it is to get into the university. In many of the top-performing countries, the ratio between applicants and acceptance is ten to one or more.  Multiple criteria are used, including not only a student's academic record, but also measures of the likelihood that the applicant can connect with young people and the passion that the applicant has for teaching. Top-performing countries that do not use a stringent screen at the point of college admission typically have very tight licensure standards, as is the case in Japan.



Some of the top performers require their primary (we would say elementary) schoolteachers to specialize. This usually takes the form of specializing either in mathematics and science or their native language and social studies. Teachers must at least minor in the subjects they will teach. In such a system no elementary school teachers will teach mathematics if they hate mathematics; indeed it is far more likely that they will love mathematics and be very good at it. Countries that do not require specialization do require that their teachers major or minor in the subject they will teach, even at the elementary school level.  It is important to bear in mind that top-performing countries that do not require specialization are typically producing high school graduates with a much sounder understanding of the subjects they have studied than is typical in the United States.

Initial teacher education  

Initial teacher education in high-performing systems focuses on the foundational knowledge that teachers need at the elementary level; emphasizes pedagogical content knowledge (understanding how students learn specific content), not just general pedagogical skills; and aligns the whole program of study closely to the required elementary school curriculum. That is to say, they teach their teachers how to teach the required curriculum.  Focusing on foundational content means focusing on a deep understanding of the topics in the elementary curriculum, not on topics typically found in a college curriculum.  In the top-performing countries, it comes naturally to align the teacher's college curriculum with the required school curriculum.  In the United States, of course, there typically is no required state curriculum.  This tight alignment between what teachers are learning in teacher's college and what they are expected to teach in school explains no small amount of their success when they start teaching.

Professional learning  

Initial teacher education in the top performers is exactly that, just the beginning of a lifetime of professional learning.  In many of the top-performing countries, the first year or two of teaching consists of an intensive apprenticeship to a master teacher, followed by continued mentoring.  Most important, teachers in these systems have far more time than American teachers to learn from one another and from the research literature because their schools are organized to make these things possible. Another recent report from CIEB by Jensen, Beyond PD, gives additional insights into professional learning systems in the top performers.

What Jensen and his colleagues describe is a whole system--all the parts and pieces of which promote high teacher quality in every elementary school classroom.  But it is worth remembering that it all begins with real mastery of the content the teacher will teach.

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