A New Language for Mathematics
During his more than 30 years as a mathematics educator and researcher, EDC’s Paul Goldenberg has noticed a recurring pattern in young children’s mathematical learning. While many six- and seven-year-olds can accurately do basic counting, addition, and doubling tasks in their heads, they often struggle to solve the same problems when these are presented on paper.
Goldenberg thinks the reason may have nothing to do with children’s knowledge. Rather, it might be that mathematical language—having to represent mathematical ideas as numbers and letters—may be to blame.
“Young children are just learning how to read and write,” explains Goldenberg. “So when you ask a child to show their work on paper, they basically have to translate what they know about numbers to this new written language they are learning. The cognitive load is too large.”
Goldenberg is now investigating whether computer programming may offer young children a more productive, intuitive way to express their mathematical ideas. The work is taking place with 400 second graders in schools in eastern Massachusetts and is funded by the National Science Foundation. Later this year, the project will expand to include students in grades 3 through 5 as well.
To examine the potential of computer programming in early mathematics, Goldenberg and EDC researchers June Mark, Kristen Reed, Kate Coleman, and Deb Spencer built a series of computer-based number puzzles that challenge children to combine numbers to reach a specified sum along a number line. But rather than jotting their ideas down on paper, students solve the problems by combining the quantities in Snap!, a visual programming language.
The programming environment presents children with four discrete blue blocks representing the actions +3, -3, +5, and -5. Children can drag the blocks together to create new quantities. One problem, for example, asks students to start at the number 0, and then use the blocks to arrive at the number 1. One way to solve this problem is to drag the +3, +3, and -5 blocks together; however, there are many other possibilities.
Goldenberg says that in a programming environment, children can check their mathematical ideas and immediately see the results of their plan on the number line. By contrast, notations on paper just sit there, right or wrong, and give no feedback. Also, the formality and effort of the written language are no longer in the way.
“With computer programming, kids are playing directly with the ideas,” Goldenberg says.
Goldenberg and his team have been surprised by what they have seen so far. Goldenberg recounts one recent school visit where they worked with three students: one who generally performed above grade level in mathematics, one who performed at grade level, and one who performed below.
When the children solved mathematics problems using written language, those differences in performance were plain to see. But when they were doing puzzles within Snap!, something remarkable happened. Differences in performance seem to have vanished.
“You couldn’t tell the students apart,” says Goldenberg.
Although the research is still in its early stages, Goldenberg believes it could have implications for how mathematics is taught in the younger grades—especially with computer programming and coding receiving so much attention in K–12 circles.
“The fact that coding could be good for students’ mathematics achievement motivates us,” he says. “But if they also learn to program while they are doing mathematics? That would be a good thing, too.”