By Priscilla Bremser, Contributing Editor, Middlebury College
In my Mathematics for Teachers course, students take a fresh look at foundational concepts, such as fractions and place value, from an advanced perspective. For some of them, our work together exposes weaknesses in their backgrounds, and unsettling stories emerge regularly, but B.’s story stands out. B. was a senior Japanese Studies major who offered insightful observations during problem-solving sessions. As the semester progressed, it became clear that there was a gap in his mathematical knowledge. He explained that he moved to the U.S. speaking only Spanish, and missed out on the mathematics being taught while he was learning English. He soon moved to a different city, and never learned how to add fractions. A significant chunk of the college curriculum was inaccessible to him because his middle school had no mechanism for accommodating his language transition. B. has many strengths, and he will do well in the world, but he was shortchanged at a critical phase in his mathematics education.
We have all had students who arrive at college unprepared to do college-level mathematics. While there are many contributing factors at play, it’s clear that inequities in pre-K-12 education systems play an important role. It’s also clear that it is extremely difficult, if not impossible, to make up in four years for disparities experienced over fifteen years. Although we work in higher education, nevertheless we must advocate for greater equity in pre-college education. If we don’t, we’re simply perpetuating injustice.
That injustice is reflected in persistent and significant differences in educational attainment among demographic groups in the United States. It’s not just that students from some groups are less prepared for college. Those college students have too many peers who don’t have access to college at all, for reasons that are well beyond their, or their families’, control.
Consider this chapter title from a recent report of the United States Government Accountability Office (GAO):
The Percentage of High-Poverty Schools with Mostly Black or Hispanic Students Increased over Time, and Such Schools Tend to Have Fewer Resources.
The report goes on to describe differences in those resources. For example, 79% of schools described as low-poverty and 0 – 25 percent Black or Hispanic offer Algebra in 7th or 8th grade, compared to 49% for high-poverty, 75 – 100 percent Black or Hispanic schools. (Within that category, the rate is 37% for charter schools.)
Just last week, the U.S. Department of Education released “A First Look” at its Civil Rights Data Collection for 2013 – 2014. From that list of highlights: “Black, Latino, and American Indian or Alaska Native students are more likely to attend schools with higher concentrations of inexperienced teachers … 11% of black students, 9% of Latino students, and 7% of American Indian or Alaska Native students attend schools where more than 20% of teachers are in their first year of teaching, compared to 5% of white students and 4% of Asian students.” Recent research supports the idea that teachers become more effective with experience, and that (contrary to earlier claims) they continue to improve well into their careers.
I focus on high-poverty schools with mostly Black or Hispanic students because students in those schools are getting the least from their education systems by various measures (performance on tests, graduation rates, and college attendance). This is not to say that these are the only students that should concern us. Indeed, here in Vermont, with a predominantly white population, students eligible for free and reduced-price lunch (a common proxy for poverty) are less successful in school than their peers, by several measures. Michael Marder has put together excellent visualizations of data on connections between child poverty and school outcomes. (If you are tired of hearing how poorly U.S. students perform on international assessments of mathematics learning, note from Marder’s slides that if Massachusetts were its own country, it would rank much higher than the U.S. as a whole.)
Remedial college courses have an unimpressive track record overall. An alternative approach offered by the Carnegie Foundation is promising, but it certainly doesn’t absolve us of the responsibility to reduce the need for remediation in the first place.
A look back at recent attempts to reform public education identifies some measures that don’t work to address achievement gaps. Blaming and shaming teachers, for example, is counterproductive. For one thing, many factors influence a student’s learning. Of course teacher training and experience are important, but high-stakes testing that holds teachers accountable for factors beyond their control makes no sense.
So-called “value-added measures” (VAMs), which try to quantify a teacher’s effect on student learning by way of pre- and post-testing, don’t perform as advertised. Indeed, the American Statistical Association (ASA) issued a statement in 2014, which warns that VAMs should be used with care and expertise, because, for example, “VAMs typically measure correlation, not causation. Effects – positive or negative – attributed to a teacher may actually be caused by other factors that are not captured in the model.” For this and other reasons, the ASA states, “(r)anking teachers by their VAM scores can have unintended consequences that reduce quality.”
What are individual mathematicians to do? Given that public schools in the U.S. are largely under local control, we can start by finding out what’s happening in our own towns and states, beginning with the funding disparities among school districts. From the abstract: “…low-salary districts serve students with higher needs, offer poorer working conditions, and hire teachers with significantly lower qualifications, who typically exhibit higher turnover.” This is infuriating, if not surprising. As educators, we should understand the challenges facing our colleagues who teach children and adolescents.
On a more granular level, we might investigate what measures our local districts take to address achievement gaps. Do new teachers have access to effective induction programs designed to reduce teacher turnover? Are high-quality preschool experiences available to all children? Are there programs, like New York City’s Community Schools, that provide services to needy families in order to support learning?
We mathematicians have something to offer to the local and national conversations, given our well-developed attention to detail and our ability to analyze quantitative arguments. One has to be prepared to face, early and often, the irony of poor data analysis and inaccurate terminology being used in the name of improving education. For one example of how to respond, see this excellent piece by John Ewing. For another, we can thank Cathy Kessel.
In our academic departments, we might start by supporting our colleagues who provide appropriate training to future teachers and professional development to current practitioners. We can value mathematics research and mentor future PhD mathematicians while at the same time recognizing the importance, and complex challenges, of bringing substantial mathematics education to all children.
Our professional organizations can provide inspiration and evidence in the form of position statements. The ASA statement on VAMs is one example of a valuable contribution. The National Council of Supervisors of Mathematics and TODOS: Mathematics for All just released a strong joint statement on social justice, while the Principles to Actions document from the National Council of Teachers of Mathematics (NCTM) includes “Access and Equity” as its second principle.
An encouraging development at the AMS is the appointment of Helen Grundman to the newly established position of Director of Education and Diversity. While the focus of that position is on graduate education, this commitment to promoting diversity in mathematics will certainly draw closer attention to conditions at all levels of the pipeline.
In a recent interview, NCTM President Matt Larson reminded us to recognize the power of mathematical understanding:
I think traditionally, especially in the current era, the importance of mathematics education has always been positioned in terms of national defense and economic need and college and career readiness. And all of those issues are absolutely important, but I think we also need to keep in mind that we also teach mathematics to develop democratic citizenship through critical thinking with mathematics and that that is also an important goal for us.
Without quantitative literacy, citizens are unlikely to comprehend, let alone be able to influence, many of the decisions and actions of those in power in political, social, scientific, and economic institutions.
I want to make sure we remember that mathematics teachers in a very real way contribute to a democratic society.
I like to think that all of us who teach mathematics contribute to a democratic society, but we’ll do a better job of it if we pay attention to equity at all levels. In the 1980’s, a consortium of organizations called us to treat Calculus as “a pump, not a filter.” While we search for effective ways to bring under-prepared college students into mathematics, we can also bear witness to the filters experienced by many younger students, and support the construction of pumps to take their place.
Thank you for addressing this important issue. Educational equity is nothing less than the new front in the fight for social justice. As you point out, ALL American students deserve a quality education from the early years onward. Bandaid measures won’t work, and high school may be too late. And as you also point out, we can all do something about that by starting locally.
I’m glad you got something out of it. Data do suggest that disparities grow and become more obvious in high school, so attention to the earlier grades is necessary.
This is a great essay with lots of things to discuss. Let me comment of a few of these points.
1. I’m disturbed by the story of your student B. Once B figures out he doesn’t know how to add fractions, it should be up to him to find out how. There is plenty of material on the web on this. If a college student can’t understand a lecture or reading, and if he/she wants to understand, see the instructor or the TA to find out the educational deficit. Then fix it. This kind of tough love does more good for the student than treating an educational deficit (like adding fractions) as though it were a physical disability than cannot be fixed.
2. Mathematicians should work on social justice issues, but not in our official capacity as mathematicians. Politicizing educational issues wrecks the consensus needed to address them. Look what has happened to the Common Core standard. Yes, K-12 education is important. Yes, bad schools do it badly. Yes, we should do everything we can to make bad schools better (I like your suggestions). But no, we shouldn’t advocate for social justice while we’re doing that. It is so tempting and yet such a bad tactic.
3. Maybe the NCTM has changed, but back in the day they were a center of bad quantitative studies of teaching methods and curricula.
Thank you for your thoughtful response. A few remarks on your specific comments:
1. Let me clarify B.’s situation. He took my course, he worked with my excellent T.A., and he’s now much clearer on the finer points of fractions. Still, it would have been better to address that deficit when he was twelve. I don’t think students of any age can always identify what it is they don’t know, but even if they could, I’m not sure that fixing it is as easy as you suggest. I do agree that we shouldn’t give up trying, though.
2. The question of “politicizing” is a fascinating one to me. If it means trying to influence government decisions, then, for one thing, I want climate scientists to go all out, by which I mean explain what they’re seeing, given their expertise, to those with political power. I’m not saying that we have something as devastating as climate change to confront, but it’s worth asking whether we have anything useful to add, precisely because we’re mathematicians, to debates about education. And debates there will be, as there always have been in the U.S.; consensus would be nice but we’ve not had it.
In my view, much of what has happened to the Common Core Standards is that a lot of people, many who should know better, haven’t bothered to read them. (Well, that and they were introduced into a testing frenzy, so that the State of New York couldn’t wait to start testing, even though adjusting to the CCSS will take years.) As a verified avoider of conflict, I resisted jumping into education debates. But now I feel compelled to say, “I’m a mathematician, and I’ve read the CCSS for Mathematics front to back, several times, and here’s how I think they will help my future students once they get to college.”
Should we or should we not advocate for social justice? Good question. I think that’s what David Hilbert was doing, when he said (referring to Emmy Noether), “I do not see that the sex of the candidate is an argument against her admission as a Privatdozent. After all, the Senate is not a bathhouse.” I’m glad he did (even if he didn’t convince enough colleagues at the time.) I’ve just reached the point where I can’t work to make schools better without trying to understand, and then point out, why there’s such disparity among schools in this country.
3. The NCTM was the first organization to try to introduce some coherence into mathematics education in the U.S. Their earlier attempts were problematic, to be sure; my sense is that those problems were amplified by poor implementation (though again, I’d like to avoid blaming teachers, especially since if their understanding of mathematics was faulty, then we in higher education own at least some of that). In any case, I don’t think it helps us much to discount current NCTM activities based on our perceptions of what the organization did in the past.
Well said, Priscilla. Educational issues and social justice issues are inextricably linked – trying to address the former without talking about the latter is at best foolish. No Child Left Behind did a lot of damage, but it did one thing well, and that was force us to face the fact of educational inequity in this country. We have a responsibility as citizens to use whatever resources we have, including professional ones, to help fix that inequity.