U.S. Teachers Not Well Prepared to Teach Mathematics, Study Finds
Washington, DC – In a seminal study of international teacher preparation released today, researchers found a striking parallel between future U.S. teachers’ knowledge of mathematics content and the performance of the students they teach.
Teachers Not Well Prepared to Teach Mathematics, Study Finds
A New International Study of Future Teachers in 16 Countries Reveals
Mathematics Teacher Preparation Jeopardizes Student Learning of Math
Washington, DC – April 15, 2010 – In a seminal study of international teacher preparation released today, researchers found a striking parallel between future U.S. teachers’ knowledge of mathematics content and the performance of the students they teach.
Led by education and mathematics experts at Michigan State University (MSU), the Teacher Education Study in Mathematics (TEDS-M) is an international examination of how math teachers at both elementary and middle school levels are trained. Fielded internationally by the International Association for the Evaluation of Educational Achievement (IEA), TEDS-M is sponsored by The Boeing Company, Carnegie Corporation of New York, the Bill & Melinda Gates Foundation and the GE Foundation.
In the U.S., TEDS-M studied the performance of 81 public and private universities and colleges in 39 states that prepare elementary and middle school mathematics teachers. Nearly 3,300 future teachers were surveyed about their course work, knowledge of mathematics and their knowledge of how to teach the subject. Internationally, the Study spanned 16 countries, sampling 23,244 future teachers (14,766 future primary teachers and 8,478 future lower secondary teachers) across 498 educational institutions.
The study reveals that middle school mathematics teacher preparation is not up to the task. U.S. future teachers find themselves straddling the divide between the successful and the unsuccessful, leaving the U.S. with a national choice of which way to go.
The findings of TEDS-M additionally revealed that the preparation of elementary teachers to teach mathematics was comparatively somewhat better as the U.S. found itself in the middle of the international distribution, along with other countries such as the Russian Federation, Germany and Norway, but behind Switzerland, Taiwan and Singapore.
“Our future teachers are getting weak training mathematically and are not prepared to teach the demanding curriculum needed for U.S. students to compete internationally,” said William Schmidt, Ph.D., MSU Distinguished Professor of Education and Statistics, who directed the Study.
The Problem of Middle School Teacher Certification
In the U.S., middle school teacher preparation is done through three types of certification programs: elementary programs receiving K-8 certification; middle school programs providing certification for grades 6-8 or 7-9; and secondary school programs certifying future teachers to teach grades 6 and 7 though 12.
TEDS-M revealed that differences in middle school teacher certification have a great impact on the mathematical teaching capabilities of middle school teachers.
According to the Study, future middle school mathematics teachers prepared in programs focused on secondary schools (grades 6 and above) had dramatically and significantly greater mathematics knowledge scores than future middle school mathematics teachers prepared in other types of programs like those including certification in grade levels below grade 5. This finding underscores an important policy issue for states: How they define what is acceptable, or required, of those to be certified to teach mathematics at the middle school level.
“Such non-standardized teaching preparation of middle school teachers has major implications with respect to what future teachers have, in terms of opportunities both to learn mathematics and how to teach it,” Dr. Schmidt warned. “With respect to mathematics content and pedagogical content knowledge, future teachers prepared in secondary school programs substantially outperformed those in the other two programs – by almost by a full standard deviation.
“Increasing math course requirements by requiring future teachers to be prepared in secondary programs alone might not solve the problem,” Dr. Schmidt continued. “Such a requirement could have the unintended consequence of creating a shortage of middle school math teachers, as many interested in middle school might not want to be part of a secondary preparation program.”
Weakness in Mathematics Preparation
According to Dr. Schmidt, the real issue is how teachers are prepared: The courses they take and the experiences they have while in their preparation programs.
“Teacher preparation curricula are critical, not only for future teachers, but also for the children they will be teaching,” he noted. “The problem isn’t simply the amount of formal mathematics education our future teachers receive. It also involves studying the theoretical and practical aspects both of teaching mathematics and teaching in general.”
The TEDS-M findings support previous international research, including the Trends in Mathematics and Science Study (TIMSS), showing average student achievement at third and fourth grade for the U.S., but low achievement in mathematics compared to other countries at seventh and eighth grade levels. TIMSS also links this low performance to a U.S. middle school curriculum that is unfocused and undemanding.
TEDS-M found that the top achieving countries on average allocated half of teacher preparation related course-taking of future middle school teachers specifically to the study of formal mathematics. The balance is allocated either to mathematics teaching (30%), which focuses on such things as how students learn mathematics and how it is best taught, or general pedagogy (20%), which includes instructional design, classroom management as well as foundation courses related to schooling.
By contrast, American institutions on average allocated 40% of the teacher curriculum to the study of mathematics – 10% less than higher ranked countries – with the remaining 60% split evenly between general and math teaching.
Two fundamental math courses form the gateway to the study of formal mathematics – linear algebra and a basic year-long sequence in calculus – as well as demonstrate the gap between the highest achieving countries and the rest of the pack. Top-performing countries had on average 90% or more of their future teachers taking both of these courses. By contrast, in the United States, only 66% of future middle school mathematics teachers studied linear algebra, with less than 55% taking the basic year-long sequence in calculus. The number of advanced mathematics courses taken also factors into teacher preparedness. The six top-achieving countries took two more courses in this area as well.
“We must break the cycle in which we find ourselves,” Dr. Schmidt cautioned. “A weak K-12 mathematics curriculum in the U.S., taught by teachers with an inadequate mathematics background, produces high school graduates who are at a disadvantage. When some of these students become future teachers and are not given a strong background in mathematics during teacher preparation, the cycle continues.”
The Future: Policy Change
According to Dr. Schmidt, the U.S. is facing a cycle in which a weak K-12 mathematics curriculum is taught by teachers with inadequate mathematics background. In turn, this, too, produces high school graduates who are similarly weak.
The National Governors Association and the Council of Chief State School Officers are completing work on more rigorous K-12 mathematics standards, called the “Common Core.” These standards, soon to be released, are expected to be adopted by a majority of the 48 states considering them. The “Common Core” attempts to standardize the K-12 curriculum and will require teachers, especially at the middle school levels, to have a deeper understanding of mathematics.
“This raises a serious policy question as to the type of certification rules and college requirements states should have for the preparation of middle school mathematics teachers,” Dr. Schmidt pointed out. “The problem must be addressed. We cannot make our mathematics curriculum more demanding without better equipping our teachers to teach it to all children.”
How U.S. teacher preparation is defined, in terms of courses taken, varies across universities and colleges. TEDS-M revealed that in this country, some of the teacher preparation institutions on average produced future teachers at a level commensurate with the performance of emerging and developing countries like Botswana, Georgia and Chile. However, other U.S. teaching institutions graduated future teachers with a knowledge level consistent with the average performance of some of the teacher preparation institutions in Taiwan, Russia, Singapore, Poland, Germany and Switzerland.
“Such variation is both encouraging and discouraging, for obvious reasons,” Dr. Schmidt concluded. “The superior levels of mathematics and pedagogical knowledge commensurate with the highest performing countries’ institutions – even after adjusting for differences in who enters the program – suggests that it can be done. However, the variability and the fact that there are some U.S. institutions where the average performance places them in the middle of the distribution for countries like Botswana underscores the depth of the problem.
Solution
“The solution to U.S. teacher and student improvement is a three-fold approach,” Schmidt advised. “First, we need recruitment and inducement for potential teachers with strong quantitative backgrounds, especially at the middle school level. Also, teaching certification programs must be standardized at the state level. Additionally, we need to implement standards with more demanding curricula, especially in mathematics, for all preparation programs and institutions.”
###
About Association for the Evaluation of Educational Achievement (IEA)
The IEA is an association of national research institutions and government research agencies related to education. The IEA is an independent organization, founded in 1958 and headquartered in Amsterdam. Many policy-making decisions made in the field of education are influenced by IEA studies. The focus of the IEA is to conduct research studies of student performance in basic subjects such as math, science and reading. IEA studies measure performance between students of different countries and whether certain policies in a particular educational system cause positive or negative effects on learning.
About William H. Schmidt, PhD
William Schmidt is a University Distinguished Professor and currently Co-director of the Education Policy Center, as well as the interim director of the University wide Institute for Research on Mathematics and Science Education. He holds faculty appointments in education and in the Department of Statistics as well. Dr. Schmidt’s current writing and research concerns issues of academic content in K-12 schooling, assessment theory and the effects of curriculum on academic achievement. He is also concerned with educational policy related to mathematics, science and testing, in general. Dr. Schmidt is a member of the National Academy of Education.
About The Boeing Company
Headquartered in Chicago, Boeing employs more than 154,000 people in 70 countries and serves customers in 145 countries. Its product lines and services include commercial jetliners, military aircraft, rotorcraft, electronic and defense systems, missiles, satellites, launch vehicles and advanced information and communication systems.
About Carnegie Corporation of New York
Carnegie Corporation of New York is a philanthropic foundation created by Andrew Carnegie in 1911 to do “real and permanent good in this world.”
About the Bill & Melinda Gates Foundation
Guided by the belief that every life has equal value, the Bill & Melinda Gates Foundation works to help all people lead healthy, productive lives. In developing countries, it focuses on improving people’s health and giving them the chance to lift themselves out of hunger and extreme poverty. In the United States, it seeks to ensure that all people — especially those with the fewest resources — have access to the opportunities they need to succeed in school and life. Based in Seattle, Washington, the Foundation is led by CEO Jeff Raikes and Co-chair William H. Gates Sr., under the direction of Bill and Melinda Gates and Warren Buffett.
About GE Foundation
GE Foundation, the philanthropic organization of the General Electric Company, works to solve some of the world’s most difficult problems. In coordination with its partners, it supports U.S. and international education, developing health globally, the environment, public policy, human rights and disaster relief. In addition, GE Foundation supports GE employee and retiree giving and involvement in GE communities around the world. In 2009, the entire GE family — including businesses, employees, retirees and GE Foundation — contributed more than an estimated $220 million to community and educational programs, including more than $100 million from GE Foundation.
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Comments
It is popular, immensely popular, to take aim anywhere at education. You cannot miss, the target is huge. However, some of the headlines are purely an attempt to raise and generate public ire, the substance of the thesis may be weak.
Examples of these tactics include pronouncements that 30% of Colorado students are below grade level in something (forgetting that wholly 49.9% of any population will be below the mean). Or in cases like the above, the suggestion that teacher preparation is the cause of math scores. It may be, it may not be the factor.
When we compare our math scores to those of Singaporean, Korean, and Finnish students, we are comparing along multiple variables. It is difficult to select one factor, hold it up and imply that this is a major contributor to the discrepancy. It may be a factor, it may be of almost no consequence.
Indeed, is there a compelling reason why a 7th grade math teacher must have year long college calculus to successfully teach either prealgebra, or even algebra 1 (which is several levels below calculus)? I don't know the answer. It may be that I can do an excellent job teaching algebra 1 if I have been thoroughly educated through algebra 2 and have been grounded in teaching/learning theory and techniques.
There are numerous factors that set American schools, curricula and teachers apart from those in Singapore, South Korea and Finland. All 3 of these high achieving nations are small, more homogeneous than we are, offer more comprehensive teacher training to a more select group of potential teachers, offer a shorter TEACHING day, greater on the job support, and much higher pay relative to salaries in their economies, for starters.
Selecting one factor and removing it from the overall context can be misleading and is of questionable value, unless, of course, your aim is to sow discontent and anger. Meaningful change has to look more deeply and control variables, not merely take aim at any nearby target, whether it needs to be "taken out" or not.
As posted by Concerned Teacher:
“Examples of these tactics include pronouncements that 30% of Colorado students are below grade level in something (forgetting that wholly 49.9% of any population will be below the mean). Or in cases like the above, the suggestion that teacher preparation is the cause of math scores. It may be, it may not be the factor.”
When you take into account that most states (I believe CO is the leader here for math) have an incredibility watered down criteria for what constitutes “proficient” you realize that the standard is set well below what a student of very average intelligence is able to meet with limited effort. Concerned Teacher’s argument would have merit if only public educators had set reasonably ambitious goals-not pathetically low expectations.
Honestly, I am bored with the whining about insufficient teacher salaries. In my state (IL) K-12 teachers retire at an average age of 55 with 75% of last three years average income (which often conveniently includes numerous additional pay additional duties). Teacher pay may start lower than other careers and since they retire relatively young, even the average salary at any given time seems reasonable. However, the unspoken perks are bountiful, especially in the majority of financially underwater states.
Can you please point out where I whined about insufficient salaries for teachers in my post?
Police men and women retire even earlier, as do fire fighters.
I wonder whether you, or anyone, has ever asked WHY teachers tend to retire a little younger? Retirement here in CA requires an age of 62, or the willingness to take a huge hit before that time. A friend is retiring at 60 this year because of the current state of affairs in the field.
She stands to earn roughly 1/3 of her annual income (about $25,000 per year in retirement). She MUST get another job to make ends meet in retirement. Of the teachers I know who do elect earlier retirement, virtually ALL are women who have husbands with careers and pensions, some are married to men with very lucrative careers. The teacher downstairs is retiring this year, her husband is a doctor. Recall, women overwhelm men in this field and many women are married to people who made much more money than they did and have better retirement programs, hence neither their income nor their retirement are absolutely essential to their economic well-being.
Plus there is the fact that much teaching (depending upon WHAT and WHERE you teach is downright challenging and often stressful work), as has been reported by mid-life career changers who have entered education in their 40s and 50s from other fields (sometimes from fields they RETIRED from).
Detractors grotesquely misrepresent facts. Additional pay duties are not part of the salary, a small stipend is given for extra duties and these small stipends are included in retirement in a differnet calculation that, in the very highest cases, will deliver an additional payment of perhaps $200 -500 per month that phases out after five years. My summer school pay, home hospital pay, and my after school period I taught this year only will deliver me a small short term advantage, but are never part of my base pay upon which my retirement is calculated. I wish, it would make a nice difference in my retirement.
By the way, I estimate I will be able to afford to retire around 70, since my retirement will be the primary retirement income for myself and my spouse (who also probably will not retire until well into the 70s).
Please speak for yourself and refrain from holding up examples of people like my friend who is married to a doctor and is retiring with little concern for how much retirement income she has accrued. There are people in every walk of life who have other or independent means and these people can afford to make choices others do not make.
I currently hold a teaching certificate in math. I am highly qualified, in my state, to teach grades 6-12. I have taken several math courses. I went on to get my Master's Degree in math education. I whole-heartedly agree with this article. I can't stand it when the kids say, "Well Ms. XXX didn't teach us that because she didn't like it." Usually the "it" is fractions.
The problem that I see with this is that the universities will water down a math course, just for the elementary teachers. This is exactly what happened where I earned my Bachelor's Degree. Elementary teachers needed a 300-400 level math course. Well, most of those require calculus. 99.9% of the elementary teachers have never had calculus. The university's decision: Let's create a math class just for the elementary teachers. It was easier than what I teach in 6th grade! If elementary teachers are required to take more difficult math classes in college, most of them will never graduate. I see nothing wrong with elementary schools hiring math specialists. A teacher that will actually teach all of the concepts correctly.
Will this problem ever get fixed? No, probably not. We will continue to fall behind on the TIMMS until we are at the bottom. I don't completely agree with comparing our schools to schools that track students to academic or vocational careers. We educate all of our children. Since everybody else looks at those scores though, may we fall to the bottom. Maybe then they will overhaul the math teaching system.
And what part of calculus has been demonstrated to be necessary to the understanding and teaching of K-8 math concepts? Most people never use calculus in their lifetimes.
We need to teach an understanding of math so that students can transfer and apply. We can train elementary teachers to teach math correctly: in the 1970s my university required 3 math classes for an elementary teacher, plus a math methods class. The intent was that teachers of elementary age students be well grounded in basic math through pre-algebra.
This is more smoke created to irritate.
The predictable call for having teachers take more content courses (in this case a three-semester calculus sequence and a linear algebra course in order to be considered well-qualified to teach middle school mathematics) is fraught with fallacies. First, there is no mention of either the specific content that needs to be included in such courses, which themselves are not standardized and vary immensely from college to college and professor to professor – and note well that these studies NEVER criticize mathematics professors, though they are often willing to take pot-shots at university education professors, particularly those in mathematics education – or the pedagogy employed in these courses which will according the the vast majority of research studies have MORE impact on how future teachers teach their own students than will any particular level of alleged rigor. That is to say, teachers tend to teach mathematics as they themselves have been taught it, in which case, Dr. Schmidt might want to look at how these "wonderful" calculus courses get taught and what messages are being sent to future middle school teachers about what math class should look like, little or any of which resembles the approaches to mathematics that have made, say, Japan, one of the best nations in the world when it comes to the thoughtful presentation of K-12 mathematics.
The false assumption that the key to high quality mathematics instruction lies in getting everyone to climb Mt. Calculus is perhaps one of the more pernicious idiocies that Dr. Schmidt's study seems to be willing to leave utterly unexamined.
Elementary number theory, graph theory (and much else from discrete mathematics), simple structural ideas from abstract algebra, a host of ideas that are grounded in the study of polyhedra, and much else that has been underplayed, ignored, or otherwise glossed over by our K-12 mathematics curricula need to be looked at as potential routes to mathematical competence and – dare I say it? – passion.
Of course, as long as we continue to see all this as about COMPETING on idiotic standardized tests given at home or abroad, we're going to utterly miss the boat with most kids anyway. TIMSS (not "TIMMS") is silly, particularly as abused by educational conservatives and deformers of all political stripes in this foolish, test-mad country of ours. We emphasize all the wrong things and ask our best teachers to betray every instinct and principle upon which they've built their practices in the name of the all-mighty test score. The idiocy of such policies has now brought us merit pay linked to more multiple-choice test scores, and will soon bring us national "standards" along with the dog-and-pony show known as Race To The Top (guess we wouldn't want to race to the bottom, eh?) Test scores, charter schools, merit pay, nothing is too idiotic in the effort to destroy free public education and put Wall Street in charge. Let's not build schools that help create thoughtful, critical thinking citizens who question and doubt anything and everything they're told to believe without skepticism (particularly claims of big business and advertising). Rather, let's hand public education over to the foxes, allowing them to groom just the sorts of consumers and worker-bees they need and dream of.
It's all so mindlessly, nauseatingly sick. And transparent to those who bother to consider where the money comes from to fuel this drive for testing, testing, more testing, and all the concomitant apparatus being shoved down our collective throats.
"Concerned Teacher" wrote:
"Examples of these tactics include pronouncements that 30% of Colorado students are below grade level in something (forgetting that wholly 49.9% of any population will be below the mean). Or in cases like the above, the suggestion that teacher preparation is the cause of math scores. It may be, it may not be the factor."
It is not true that 49.9% will be below the mean. Consider a test out of 100 points where 1 student scores 0 and 99 students score 100. Clearly the only student below the mean is the score of 0, which is 1%. This is an example of the poor school mathematics pointed out in the article.
"Concerned Teacher" — in part I agree with what you are saying. Yes, money affects quality–that goes without saying and in some states it may be worse than others.
But the point of the article, is that implicit in the study of Calculus and Linear Algebra is an understanding of how *real* math works—Sorry, but you don't see that in a typical Alg1/2 course.
This is really what it's about: We need teachers that can do math. That doesn't necessarily mean
"Ph D level" math, but teachers who: understand how math ideas develop, understand how to pose questions typical of math, are not afraid to think critically, etc.
I hope you understand what I'm saying. And while you may be an exception, the majority of middle school teachers are NOT like that. I remember when I was a TA in the University of IL. Everyone wanted to be a TA for the math middle school program because it was a joke—it was for students who *hated* math and as a result the program was ridiculously watered down.
If a middle school math teacher doesn't have enough mathematical aptitude to pass (for example) a basic calculus class, should they really be teaching our kids math?
I'd have thought someone that wanted to become a math teacher would love math enough to want to take all kind of math classes!