Teaching the Meaning of Numbers

How to close the achievement gap in math? Tisch Lecturer Robert Siegler talks about Chutes and Ladders and other strategies

It’s accepted economic wisdom that the rich get richer, and the poor get poorer. But as Dr. Robert Sigler, Teresa Heinz Professor of Cognitive Psychology at Carnegie Mellon University, pointed out at TC’s 2010 Tisch Lecture, that statement applies to the accumulation of mathematical understanding as well. That is: students who enter a classroom with greater proficiency in math can grow their knowledge base at faster rates than those with lesser proficiency.

A prolific researcher and author, Siegler – TC’s Tisch Visiting Professor for 2009-10

-- has devoted much of his career to understanding children’s thinking, particularly around mathematical and scientific concepts and particularly within low-income populations.

By age four, there are clearly recognizable differences between wealthier and poorer children in understanding of object counting, next number, number comparison, two set addition, shape names and other math-related skills.

“If we had the educational system we’d all like, we’d still have different levels of knowledge,” Siegler told his Milbank Chapel audience on February 23rd, “but the difference would be mitigated with schooling, or at least would get no larger. But in the U.S., differences increase with schooling.”

In the U.S., the learning gap between low- and middle-income groups is typically one and a half years in the first grade. By the time students reach the ninth grade that gap has grown to three years, a point at which the disparities seem insurmountable.

According to Siegler, preschool is the best time to try to break that pattern, partly because the gap is still relatively small, and partly because establishing a base of skills and knowledge at that point creates “cognitive multipliers” for later on. Again, the rich get richer – or, in this case, the more you know, the easier it is to keep learning. 

Of course, a student can learn to count to ten by rote memorization or learning a song, but that doesn’t necessarily translate into a genuine understanding of whether 4 is smaller than 6, and why. How well children understand such “numerical magnitudes” correlates strongly with how they perform on achievement tests, Siegler says.

So how to teach numerical magnitudes in the classroom?

One answer advocated by Siegler and colleagues: numerical board games. For example, Chutes and Ladders, a game that traces its roots back to ancient India, has proven especially effective at exposing low- and middle-income preschoolers to what Siegler calls “rich multimodal data,” such as verbal, visual-spatial, kinesthetic, auditory and temporal cues to numerical magnitudes.

In a 2008 study, Siegler compared the effectiveness of Chutes and Ladders to that of another, color-based board game as a tool to help students learn about the meaning behind numbers. Post-intervention tests recorded significant gains for the groups who worked with numerical board games.

Two other studies—both in 2009—looked at game playing outside of the lab in low-income preschoolers, seeking to identify which physical features (linear or circular) of the games were essential to numerical learning. In all this work, Siegler and his colleagues arrivied at the same conclusion: early experiences with numerical concepts help all preschool kids, but they help the low-income ones the most. Thus, briefly-targeted interventions can go a long way in reducing knowledge disparities between low- and middle-income groups—and, in the words of Siegler, toward “leveling the playing field.”

At the end of Siegler’s lecture, one audience member stood and said: “That motivated me to want to go out and encourage thousands of children to go play board games.”

Published Wednesday, Mar. 10, 2010