Recently, I turned 60 years old (also expressed as 720 months, or 21,915 days, or 525,960 hours, or 31,557,600 minutes), and over that time I’ve seen many great debates in the education policy arena. Often those debates reach equilibrium with a realization of what Jim Collins (author of Built to Last and Good to Great) calls “the genius of the AND.” Collins points out that successful businesses realize that there is validity in each of diametrically different points of view, and the most successful companies respect and leverage both—especially when there is no clear right or wrong. The idea of the genius of the AND has found a home in the work of improving literacy outcomes (successfully, in my opinion), and I believe the same can happen with improving math achievement in the United States.
At the National Association of State Boards of Education, of which I am the President & CEO, we recognize the importance that state boards of education and state policymakers can have in prioritizing areas for action and improvement. A recent issue of our journal, The State Education Standard, is devoted to Advancing Math & Science Instruction. In it, various authors address different aspects of the current state of math and science education. One of the key takeaways for me is that there is a great deal of agreement on various aspects of how to improve math achievement, and there are also some areas where honest disagreement exists. When I see the disagreement, I challenge myself to examine how both sides might be respected to further the best interest of students.
I loved reading the different points of view expressed in the recent Education Next forum on “Rethinking Math Education.” The two sets of authors nicely lay out their points of view. In each article I found ideas I agreed with and ones to which I objected. Reading between the lines, and leveraging some of my other knowledge about education reform and mathematics, I began to see the areas of agreement, and also opportunities for embracing the AND.
Here are the concepts about mathematics achievement on which I think we can all agree:
All students are mathematically capable. Let’s face it, the biggest obstacle to more students being successful in mathematics is the pernicious myth, all too pervasive in our society, that “some people just aren’t good at math.” In too many cases, rather than continuing to work with students until the students reach confidence and comfort with mathematics, adults (especially parents and teachers) will convey (explicitly and implicitly) that they are simply not equipped to do mathematics. Once the student accepts that fiction as reality, the battle is lost.
The research is clear that the premise is patently false. Everyone can be competent and confident with math—we all need to believe this and act accordingly. We should all make a shared and tireless commitment to put a stake in the heart of this crushing lie. It should be as unacceptable to say “Johnny just can’t do math” as it would be to say “Johnny just can’t read.”
More students can be successful mastering high level mathematics. The status quo is unacceptable—both in absolute terms and in terms of equity. We know doing better is within our reach. There are plenty of case studies and proof points. One of my favorites is illustrated in the movie “Stand and Deliver” about the great Jaime Escalante and the success of students (mostly low-income and ethnic minority students) at James A. Garfield High School in Los Angeles in passing the Advanced Placement Calculus exam. I have seen other schools and classrooms experience similar successes.
There is good understanding about what different and better math instruction looks like. As with many content areas, there is no one-size-fits-all for what can work to help more students succeed in math. The National Council of Teachers of Mathematics published Principles to Actions: Ensuring Mathematics Success for All (2014), and the Catalyzing Change series of curriculum guides. The Southern Regional Education Board has their Powerful Mathematics Instructional Practices. Other quality curriculum models are also available. High quality instructional materials matter a lot, too. The Zearn math learning platform has shown tremendous success. EdReports.org has rated a number of math instructional products.
Deliberately focus on parents as partners. Any effort to improve instruction requires attention to the needs of parents and caregivers. Parent support can make a big difference in the implementation of new approaches, especially if parents see how they can help their child. I sympathize with the frustrations that many parents feel when they cannot help their children with math homework because it is different than how they were taught. Just because a student is approaching a mathematical concept in a different way than how the parent or caregiver learned it should not prevent them from supporting numeracy development. We can help parents better understand and play their important role in supporting learning.
Teachers need to be better equipped and supported to teach math. This is true for every subject area for which we know we can do better. The recent burst of activity around the science of reading and the ensuing signs of improvement in reading proficiency are results of the significant effort being made to help and coach more teachers in understanding what great literacy instruction is all about. It is all about teacher content knowledge, aligned curriculum, quality pedagogy and disposition. Coaching also has great power to improve teacher practice. Authors Barak and Mims and Levitt and Severts would certainly agree on the importance of well-equipped and supported teachers.
Focus is needed on elementary and middle school math. Given that the two articles address high school math, one might think that the focus should be there. But the sad reality is that a student’s ability to be successful in any high school math class, calculus or otherwise, is determined in elementary and middle school. Far too many students have given up on math by then. No matter where one stands on what math is taught in high school, we can agree that more students should emerge from middle school confident and capable in mathematics.
More math teaching should be done in the context of practical application. Nothing brings math alive, and makes retention more likely, than when it is learned in the context of real world problems and experiences. I always found students who were enrolled in construction trades and other career focused programs at career-technical education centers to have a very robust understanding of the applicable mathematics, as well as comfort in understanding math as a tool to solve problems.
In the spirit of the “genius of the AND,” here are my ideas for charting a course forward.
More students need to master algebra II and calculus, but if that can’t happen in the near term, let’s accept accomplishment in other rigorous math that keeps the doors to future success open for more students. This is a lesson that we can learn from higher education and the strategies being used to recast developmental mathematics. When many institutions of higher education figured out that they were losing a great number of students in what noted mathematician Uri Treisman called “the burial ground for aspirations” — developmental mathematics — they began to design different and better math knowledge development strategies. High school is to higher education what middle school is to high school. When high school students come to the door of higher education unprepared or underprepared, the traditional solution has been to remediate them in separate, isolated, and lengthy sequences of math courses (a strategy that historically failed). Efforts to find a better way, a way that allowed more students to be successful, led many higher education institutions to embrace approaches, like co-requisite classes, to equip students with the math they need to succeed in their chosen field of study. (I tip my hat to Complete College America and the Dana Center at the University of Texas-Austin for having led the charge in this work nationally.)
This approach has helped more students reach higher levels of math competency, and, more importantly, degree completion and gaining access to meaningful high-paying jobs. No one criticized this approach for failing to insist that students learn to the highest levels of math, because it made a huge difference for many lives by equipping them with the math needed to complete their degree programs and launch careers. If it is unlikely that a middle school student entering high school will complete the ideal path of math achievement, however we might define it, wouldn’t it make sense to identify a rigorous alternative math pathway that could align to a meaningful career pathway for which the student might achieve success?
Create mechanisms to ensure rigor. There is a fear that any alternative to the algebra/calculus route will not be rigorous. This fear can be easily addressed by enabling mechanisms that ensure rigor. After all, if a student gets a 4 on the AP Statistics exam, isn’t that a sign of a mathematical disposition that would both have value as is, as well as signal a student’s capability to master other types of math?
Set targets for more students to become proficient in algebra/calculus and also for more students to be proficient in other rigorous math. Create mechanisms that gauge progress toward equity. There is so much room for improvement to achieve measurable and significant increases in all areas of math achievement. That means all perspectives can come out ahead. The greater the improvement, the better the system becomes at helping more students reach higher and higher levels of math. In the long term, more will achieve at the highest levels. If the fear is that change will widen the equity gap, let’s establish the mechanisms to make sure that doesn’t happen.
Share the responsibility to ensure all students are confident and comfortable with mathematics. One of the key strategies in improving literacy has been to ensure that all teachers play a role in it. This includes social studies teachers, science teachers, math teachers, art teachers. The same is needed for math. Every discipline has quantitative aspects that can be explored using math.
It’s always interesting to read differing views on a particular topic in education. As a perennially hopeful person, I try to look beyond the areas of disagreement to find the common ground — and there is a lot in the mathematics space. The National Association of State Boards of Education is launching a State Mathematics Improvement Study Group for state board of education members and support staff to increase awareness and understanding of the issues. I hope that, with good information and technical assistance, state policymakers can catalyze state-designed initiatives to improve math outcomes. History has shown that when such initiatives are designed by multiple partners and when the diverse points of view are understood and respected, transformative change is possible. Now is the time to make this happen in math education.
Paolo DeMaria is president and CEO of the National Association of State Boards of Education.
Last updated August 11, 2022