Students Learn Better When The Numbers Don't Talk And Dance

Researchersfound that when college students were taught an artificial form ofmathematics and physics, they learned it better when it was presentedusing simple, abstract symbols – such as plain stars and raindrops --rather than more visually engaging and concrete 3-D objects that moveddynamically on a computer screen.

The students were also moresuccessful in applying what they learned to new situations when theywere taught with abstract symbols rather than concrete objects, saidVladimir Sloutsky, co-author of the study and professor and director ofthe Center for Cognitive Science at Ohio State University .

Theresults of this study suggest that teachers may need to rethink one ofthe most widely accepted truisms of their profession, said Sloutsky,who is also associate dean of research at the university's College ofHuman Ecology .

“Many teachers believe that concrete materialsmake learning more fun for students, and that will increase theirmotivation and help them understand the concepts,” he said. “While thismay be true, in many cases, the concrete materials also interfere withwhat they are trying to learn.”

A real-life example of howconcrete materials may be used inappropriately is a common tactic forteaching children about numbers and letters. Books and educationaltelevision shows often present letters or numbers with human featuressuch as faces, which dance and talk.

While some believe thismakes the concepts more approachable, the authors believe Sloutsky saidit simply confuses young children.

“Instead of learning thatletters and numbers are symbols that can be used in many differentways, children in this example see them as very concrete examples ofhumans.”

The belief in the value of making the abstract concreteis widespread, however. For example, 84 percent of secondary schoolmathematics teachers in one survey said they believed concretematerials in their classes help students learn.

Sloutskyconducted the study with Jennifer Kaminski, graduate student at OhioState and Andrew Heckler, assistant professor of physics at Ohio State. Their results were published in a recent issue of the journalPsychonomic Bulletin & Review.

For the study, the researchers did three related experiments.

Inone, 30 undergraduate students were taught a novel, artificialmathematics and a novel, artificial science. Half of the students weretaught the math first and then the science, and the other half weretaught the science first and then the math.

The math used simple,abstract symbols such as raindrops, stars and snowflakes. Studentslearned, for example, that combining a star and a snowflake resulted ina raindrop. They were then tested in their knowledge of this new,artificial math. All of the training and testing was done on a computer.

Thescience portion used much more concrete symbols – this portion of theexperiment used 3-D objects that moved across the computer screen.Students were shown two of these 3-D objects moving towards each otherand colliding to form a third, different object. The rules of thisscience portion were exactly the same as the math portion – only theobjects were different. Again, they learned this new science and weretested on what they learned.

Results showed that mostparticipants successfully learned both the science and math portion.However, participants who learned the math first did significantlybetter on the science portion than did those who did the scienceportion first.

“This suggests that knowledge presented in themore generic, abstract format helped students better learn the moreperceptually rich, concrete format,” Sloutsky said. “If they learnedthe science portion without the benefit of learning the more abstractmath portion first, they did not do as well.”

A second experimentinvolving 30 undergraduates was nearly the same except for one crucialdifference – the math symbols were replaced by images of 3-D objects,such as swords and goblets. In this experiment, the math objects weremore concrete than those in the science condition because they werereal-life items. Real items such as swords or goblets make poor symbolsbecause it is difficult for people to interpret them as something otherthan what they are.

In this second experiment, contrary to thefirst, students did better when they learned the science first and thenthe math. But the key was that, just like the first experiment,learning with less concrete symbols helped students when they had touse their knowledge in new situations that were more concrete.“Students were better able to transfer what they learned when they weretaught using more abstract symbols,” Sloutsky said.

Moreover,students also did better when tested on the science concepts than theydid on the math concepts. “That suggests concreteness of objectshinders not only transfer of knowledge but learning itself,” Sloutskysaid.

To confirm this finding, the researchers conducted a thirdexperiment in which 81 students – all different from those in previousexperiments -- learned the same artificial math as used previously. Inthis case, they were separated into four groups, each of which learnedfrom a different set of symbols, from very abstract and simple tointricate photos of real objects. In general, even though the learnedmaterial was otherwise identical, students who used the most intricate,concrete symbols did poorer on testing than those who learned using themost simple, abstract symbols.

Overall, the results suggest that students may often benefit when knowledge is presented in abstract, generic forms.

Thereare many reasons why concrete may not be better for learning, accordingto Sloutsky. For one, concrete objects have more “perceptual richness,”meaning there is more for students to look at and process. That meansthere is more to distract students from what is important.

Also,concrete symbols are less “portable.” For example, a child can use astick – a relatively abstract item – and imagine it is a car, or aspace ship or a flower. However, it is more difficult for a child totake a toy train and pretend that it is a flower.

“Less structured entities make better symbols, and these generic symbols are easier to learn,” he said.

This research was supported by a grant from the National Science Foundation.