When Memory Fails
For some students, finger-counting may add up to success
It's a scene that has been played out for decades in thousands of classrooms around the country. The teacher asks the student, “How much is 17 plus 5?” The student hesitates and then glances down at his hands. His lips move as he be-gins to silently count out the answer on his fingers.
“Jason,” the teacher snaps. “Don't use your fingers! You should know the answer!”
But Robert Siegler, a Carnegie-Mellon University researcher, has some radical advice for teachers: They should not only tolerate finger-counting, but also teach it and other “backup strategies” to students—especially the slower ones. And he warns, “Pressuring children not to use their fingers may lead them to need to use their fingers for longer than if they were not pressured.”
Siegler's advice is based on his research into the ways elementary school students work on math and word-identification problems. What he found is that students need something to rely on when memory fails. In one of his first studies, Siegler noticed a stark contrast between how good and poor 1st grade students responded to problems. The star pupils were quick and accurate, firing back answers almost as fast as the questions were posed. The struggling students either blurted out wild guesses or stuttered and mumbled, only to come up with a wrong answer.
Siegler found that although differences in innate ability offered a partial explanation for the varying responses, other differences between the children were also important. In particular, “one of the largest differences between successful and less-successful students,” he says, “is the level of sophistication of the strategies they use” to solve problems.
Good students, according to Siegler, rely on their memories more than poor students, as teachers are well-aware. But the researcher also found that when good students can't remember an answer, they quickly and effectively turn to backup strategies. For word problems, these include sounding out words or using a dictionary. For math problems, good students count up from a number to add or down from a number to subtract, and they use their fingers.
Not-so-good students, on the other hand, either don't use backup strategies enough or use them incorrectly. For example, Siegler found that poor students answered three-quarters of the math problems off the top of their heads but were wrong on more than half of their guesses. Even when these students recognized that they didn't remember an answer and tried another way to figure it out, they kept making and repeating errors. “You just knew they were consistently using [backup] strategies incorrectly,” he says. “They did such things as counting the same finger twice and skipping over a finger. The patterns were so obvious, they hit you between the eyes.”
Siegler later conducted two other studies of elementary students in the Pittsburgh area that confirmed his preliminary findings. In one study, he and his research assistant asked the students to describe how they got their answers. In the other, they observed and interviewed minority children.
The research has some clear implications for the classroom. “Teachers need to be aware that some students are bad at using strategies,” he says. “Children who are not so good at it should be taught it.” He also points out that strategies such as finger-counting and sounding out words are more time-consuming than relying on memory, so if a student doesn't learn how to use them correctly, he or she will not use them.
Siegler offers some specific suggestions on how teachers might proceed. He advises them to be patient with students using backup strategies like finger-counting. It's better, he says, for students who are having trouble learning to take the time to use a backup strategy than to rely on their faulty memories and respond quickly. A backup strategy gives a student the chance to find the correct answer and reduces the likelihood that the wrong answer will become fixed in the student's mind.
He also suggests that teachers show students how to use a strategy and then design challenging but doable problems that encourage them to use it. For example, to help 1st and 2nd graders solve addition problems, a teacher could show the students how to start from the larger addend and count up. Siegler suggests giving students who are learning this strategy a problem like 21 plus 3, which he says contains both “a carrot and a stick.” “It's easy to count up three from 21, but it would be tedious to count from one to 24,” he says.
Siegler does not, however, see backup strategies as a cure-all. Although he found that they work well for good students and can help poorer students, he also identified a third group of students who seem to rely too much on backup strategies. These students, whom he calls “perfectionists,” answered questions correctly most of the time but were more cautious and exacting with their replies than the top students.
The researcher says that although these perfectionists are slowed down by their overreliance on backup strategies when answering problems, “their caution should not be mistaken for slowness. With some gentle prodding, they might be able to rely more on their memories and answer questions more quickly.”
Overall, Siegler sees finger-counting, and other backup strategies, as a means to an end. He advises teachers to tolerate and encourage students who need backup strategies to use them. But he believes most children will eventually stop relying on these strategies and use their memories as they gradually become surer of their answers.
Vol. 02, Issue 01, Pages 32, 34