Robert Siegler has joined the Teachers College faculty as the Jacob H Schiff Foundations Professor of Psychology & Education in the Department of Human Development.
Siegler, the former Teresa Heinz Professor of Cognitive Psychology at Carnegie Mellon University, delivered the 2010 Tisch Lecture at TC and spoke as a panelist this past spring at the launch of the College’s Education for Persistence and Innovation Center (EPIC). He has authored and edited numerous books and published hundreds of articles and chapters. His main focus is on the development of mathematical thinking, specifically the ability to learn whole number arithmetic and fractions.
In a 2017 article in Scientific American, Siegler noted that U.S. students lag far behind European and Asian children in the understanding of basic fractional arithmetic.
“This weak knowledge is especially unfortunate because fractions are foundational to many more advanced areas of mathematics and science,” he wrote. He elaborates on this issue below.
What led you to study fractional arithmetic?
Several interventions for pre-school and early math have produced strong effects at the end of the intervention, but there’s a strong fadeout within two to three years from the time the interventions come to an end. That is disappointing to a lot of people, including me, and raises questions about why it is happening and what we can do about it. The answer, I suspect, is that everyone pretty much understands whole numbers but things go off the rails with fractions, decimals, and percentages. And that becomes an issue which correlate to outcomes such as income and how far an individual can go in the educational system. There is not much understanding that fractions are extremely important to everyday life and, until recently, there hasn’t been much study of fractional arithmetic.
Why are fractions so confusing?
Fractions are not as transparent as whole numbers. There is only one symbol for the number five; for instance, the number five always has the same meaning.
But with fractions there are many different equivalent symbols: 1/5, 2/10, .2, .20… That’s one source of confusion; there are many others.
What contributes to the breakdown?
There is so much emphasis on good test scores that teachers tend to move quickly through fractional procedures without realizing the goal is not only for students to do well on a test two months in the future but to retain the information long term. People are terrible at retaining information they don’t understand. That kind of memory fades very quickly and it’s why community college students on average don’t do any better with fractions than 8th graders. I would encourage teachers to bolster their conceptual understanding and their own understanding of fraction and decimal arithmetic. Not understanding how fraction and decimal arithmetic work is nothing to be ashamed of because teachers, in many cases, weren’t taught very well either.
"Many textbooks try to present students with real world problems, but the efforts are often weak. I suspect no one in the history of the world has been asked to use fractions to calculate the length of, say, a tropical fish that is two-thirds as long as another tropical fish."
– Robert Siegler
Are textbooks also to blame?
My colleagues and I have looked at textbooks to understand the learning that is taking place. Many textbooks try to present students with real world problems, but the efforts are often weak. I suspect no one in the history of the world has been asked to use fractions to calculate the length of, say, a tropical fish that is two-thirds as long as another tropical fish. When you go through the textbook problems you understand the reason kids aren’t motivated. Students know that they’ll never encounter problems like these in the real world. If the problems were more realistic, perhaps students would learn better.
U.S. textbooks also offer very few of the types of problems that kids find the most difficult. At present we don’t know if it’s because the problems are inherently difficult or if it’s because textbooks are avoiding difficult problems because no one wants to hear bad news.
Do other countries do a better job of teaching fractions than the U.S.?
Yes. Countries in East Asia and some countries in Europe do a better job. There are a variety of reasons for that. Students are motivated to work harder and parents are willing to pay for tutoring, in some of those countries, particularly in East Asia. But another big factor is that teachers are more knowledgeable. Studies show, for example, that very few U.S. teachers can explain why we invert and multiply in fractional division while large majorities of East Asian teachers understand the reason.
Should the U.S. introduce fractional arithmetic in earlier grades?
I don’t know that starting earlier would lead to better learning. Again, to me, the real solution is improving the conceptual of understanding of fractions for teachers, so they can better explain the concepts to students, and improving the quality of textbook presentations of mathematical concepts. One of the attractions of my coming to Teachers College was the opportunity to teach and help prospective teachers understand fractions and rational numbers so they can go out and help kids learn more effectively. And since a number of TC students go on to become principals and superintendents, they can have an even greater influence on the way fractions are taught.
Do the deficiencies in fractional math pose a challenge to higher education as institutions contemplate a demographic shift that could increase admissions of at-risk students by mid-century?
It will be a growing problem. A leading indicator is a National Assessment of Educational Progress analysis that shows student math scores leveling off since 2009. That is very worrisome, because the global economy demands improvement in math proficiency in the U.S. workforce. We talk like we take the problem seriously, but we’re not walking the walk.
What else are you looking forward to about being Teachers College?
I’m glad to be here and look forward to getting to know more people who are interested in similar problems. I also hope to collaborate with specialists in community college education. The research on remedial math in community colleges is very discouraging. It shows that students often don’t do well enough to pass the remedial courses and don’t receive transcript credits even when they do pass. Community colleges are immensely important in helping people do well in the workforce so I see a sector where the students tend to be serious about education as a very promising place to improve math education.