This past week the latest National Assessment of Educational Progress (NAEP) data on American 12th graders showed that they lost ground over the last two years, with the lowest performers having the biggest declines. The week before, the annual professional organization in math education, the National Council of Teachers of Mathematics (NCTM), held their research and teacher conferences in San Francisco. Attending this conference, or even reading the list of presentations, leads to one conclusion: The math education establishment is dooming our country to stagnant performance and cannot fix itself. I will explain why, as well as offer a solution to raising the achievement of American students.
First, imagine a world in which medical research was confined to small studies conducted by newly graduated doctors. As an example, a doctor would conduct a study on a treatment for colon cancer that he developed on 15 of his patients over two years, funded with small grants from the American Medical Association. Then he would present his findings at the annual AMA Conference. All presentations would be of a similar nature – small sample size studies of large medical issues. How far would medical science advance if this were the process for developing treatments and medicines?
In the medical establishment, there are systems in place for large-scale studies with oversight. The pharmaceutical companies invest enormous amounts of money into medicines, and want to recoup their investments. There is oversight for patients provided by the FDA, as well as the legal malpractice system. In addition, there is an element of drama involved in curing an individual, separating conjoined twins, or a finding a cure for a group of people suffering from the same condition. Heart-warming vignettes of smiling patients and their loved ones can be televised on the nightly news. In summary, there is a system of large-scale studies leading to treatments, along with patient protection.
This is a system that can run without leadership. Market forces and immediate suffering that begs to be alleviated are sufficient to drive this system forward. The continual breakthroughs in alleviating disease and suffering are proof that the medical system works.
Now consider the math education system in the United States. There is no system in place that fosters improvement. There are no effective checks and balances. There is no one person or group in charge. Over thirty years of data, from international comparisons to measures of achievement gaps, show that the math education system is absolutely stagnant. For example, international comparisons of 15 year olds, the Programme for International Student Assessment (PISA), show a decline in U.S. average scores over the last six tests, from 2000 through 2015. At the same time, the top scores of other countries have risen. The achievement gaps between whites and blacks, and between whites and Hispanics have remained almost constant over thirty years, in 4th and 8th grades as measured by NAEP, and in 12th grade as measured by the SAT.
Thirty years spans an entire career, meaning that statistically no teachers or administrators have seen a classroom without an achievement gap. Statistically, no teacher or principal or school district superintendent, or parent, has seen world-class math education.
The equivalent of the pharmaceutical industry in math education would be the publishers of math curriculum. However, the publishers are not required to conduct any statistical studies showing their materials are effective. They pander to the math leadership, invest minimal amounts of money in their materials, mostly rehashing old lessons and updating with new photos. There is no blame here – they create what will sell. But they have no incentive to create materials that actually raise student achievement because the customers are not demanding it. There is no group that effectively monitors what materials work better than others, and no equivalent of a malpractice legal group that enforces effectiveness.
No Child Left Behind legislation can be related to the FDA in that it provided legal consequences for failure. However, because the implementation of improvement was left to the existing math establishment, it was doomed to failure. From the Secretary of Education down to the classroom teacher, our country put people in charge with no track records of improving achievement.
The NCTM acts as a gatekeeper in terms of what is published and what is presented in the conferences. It would be helpful if they would devote space for disruptive programs that raise student achievement and close the achievement gap. Instead, as the annual conference verified, they play it small, continuing with the status quo of thirty years of mediocrity.
In education, there is a history of confusing experience with expertise. Our society uses years of experience and titles to confer respect on educators. Despite all the data that has been collected and is publicly available, educators at all levels get a pass on their own grades. Can you imagine that situation in the medical profession? Would you take your child with a life-threatening illness to a doctor with a track record below average, if that data were easily available?
On state and national levels we are treating people with track records of mediocrity as experts, and letting them make policy, distribute enormous amounts of money, and act as gatekeepers on all levels for innovators and the disruptors the field needs. Instead we should be listening to those educators who have actually improved student achievement above the norm. And partly due to NCLB, there is enough publically available data to measure the expertise of former educators who purport to be experts.
There are instances wherein teachers and schools have made significant progress in closing the gaps. If our country is seriously interested in closing these gaps, these people with track records of success should be leading the national effort. Instead, in education we reward continued lack of progress with continued leadership roles and all the perks that go with that.
This is a field without effective leadership. No one is really in charge of raising student achievement. And from departments of education at all levels, any track record of raising student achievement above the norm is not considered as a necessary ingredient of earning the job. Experience, titles, and political abilities are the tickets to leadership positions. As an example, a former school district superintendent with a mediocre track record is now a U.S. Senator touted as an education expert. University professors in education are in powerful positions of influence. It is tradition for university professors in education to have some background in teaching of at least a couple of years. However, there is no requirement or tradition of selecting professors of future teachers from the small pool of teachers who have actually raised student achievement above the norm. Another source of leadership is the professional organization of the field, the National Council of Teachers of Mathematics. Their leadership is often comprised of former teachers of AP Calculus who rose through the ranks to district leadership positions. If they have raised achievement above the norm, it isn’t obvious.
There is a solution to raising math achievement and closing the achievement gap. The country of Singapore provides one example. After mediocre PISA scores, in the mid-1980’s they developed their own curriculum. It focuses on a very few key concepts, taught in great depth, with the progression of students using hands-on objects, then drawing pictures, and then using abstract notation. Singapore always scores in the top three in international comparisons now.
I have found similar results with middle and high school students who are several years behind grade level. In every case, these students have gaps in critical building blocks in a solid math foundation. For example, in general, these students cannot add simple fractions. They often think 4 – 5 = 1. Frequently, they do not understand what a variable, such as “x” means. There is no way a student with these gaps can be successful in Algebra 1. However, filling these gaps is easy with lessons that use the three-step progression of hands-on objects, followed by pictures, followed by abstract notation. Filling these gaps leads to the students gaining multiple grade levels within one school year.
Today’s math teachers and their leaders did not need this progression. They were successful (enough) with beginning at stage three, abstract notation. I would argue that they would have been more successful had they had all three steps. But the big point is that today’s teachers have not seen math taught properly, have not been trained to teach math well, are evaluated by principals and others who also have not seen math taught well. This is a system doomed to stagnation, just like the data shows.
Whether math leaders want to follow this three step progression or not, we need to have large-scale studies that measure whether the program they use is improving achievement or not. Just as medicines are not developed on fifteen people, solutions to raising achievement will not come from samples of this size. Yet many talks at the NCTM conference were of just this size of students. State test scores and nationally accepted assessments such as the Northwest Association MAPS tests can be used to measure student achievement.
Over 45 million students are in American schools, and at least half of them are having difficulties in math. There are consequences in terms of high school graduation rates, college completion, career choices, whether students grow up to require government benefits or contribute to the tax base, and the overall economic competitiveness of the U.S. It will take leadership that has expertise to modify our math education system into an effective system that serves our students and our country.