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Teaching math concepts boosts student understanding
Elementary students' math skills improve when they learn the concepts behind
a problem before learning the skills needed to solve a problem, according t
o a recent study. Researchers found that 67% of the students in the study wh
o learned concepts first solved more problems with accuracy, compared with 4
4% of students who did not learn concepts first. Chalkbeat/Tennessee (8/13)
Students are more likely to be able to solve math problems if the concept be
hind the question is explained to them beforehand, according to a new study
from Vanderbilt University’s Peabody College.
Researcher Emily Fyfe set out to determine whether math instruction solely f
ocused on learning skills and procedures, such as answering addition and sub
traction problems, was more or less effective than instruction that included
explanations of concepts.
Fyfe and two tutors taught a group of 122 Nashville second and third graders
the concept of math equivalence—the idea that two sides of an equation rep
resent the same quantity. She and the tutors taught the students that an equ
al sign in an equation, such as 3+4=4+3, means that there are equal amounts
on each side, and gave the group of students practice equations to solve. Ha
lf of the students were asked to solve the problem before the lesson, and ha
lf solved them after the lesson. Both groups were asked to provide explanati
ons of their process after solving the problem.
Fyfe found that the group that learned the concept before doing math problem
s was more likely to be able to solve the equations. That group had 67 perce
nt accuracy rate, while the students who answered the questions before learn
ing the concept had a 44 percent accuracy rate.
Fyfe said that typically, math instruction has been based more on skills rat
her than on understanding the concepts underlying those procedures. She said
that her take-away is that some instruction on concepts, rather than just s
kills, benefits students’ mathematics problem-solving. But, she said, stude
nts also need the chance to apply concepts and practice skills.
Fyfe, a doctoral candidate in developmental psychology at Vanderbilt, said t
hat the research team chose to focus on the concept of equivalency because i
t is highlighted in the Common Core State Standards, which Tennessee uses fo
r math and reading.
The Common Core standards start emphasizing the concept of equivalency in th
e first grade. But, Fyfe said, the research team studied textbooks, and most
still did not clearly define equivalency or include problems that would rei
nforce the idea. The majority of textbooks present math problems so that ope
rations are always on the left and the equal sign is on the end (showing, fo
r instance, that 4+2=_ rather than _=4+2), and rarely provide a definition o
f equal signs, Fyfe said. “It’s in the standards now, but it doesn’t seem
they’re going to get this information from the textbook.”
Marci S. DeCaro, department of psychological and brain sciences at Universit
y of Louisville and Bethany Rittle-Johnson, associate professor psychology a
t Vanderbilt’s Peabody College, co-authored the study. The research was sup
ported by the National Science Foundation and the U.S. Department of Educati
on.
Elementary students' math skills improve when they learn the concepts behind
a problem before learning the skills needed to solve a problem, according t
o a recent study. Researchers found that 67% of the students in the study wh
o learned concepts first solved more problems with accuracy, compared with 4
4% of students who did not learn concepts first. Chalkbeat/Tennessee (8/13)
Students are more likely to be able to solve math problems if the concept be
hind the question is explained to them beforehand, according to a new study
from Vanderbilt University’s Peabody College.
Researcher Emily Fyfe set out to determine whether math instruction solely f
ocused on learning skills and procedures, such as answering addition and sub
traction problems, was more or less effective than instruction that included
explanations of concepts.
Fyfe and two tutors taught a group of 122 Nashville second and third graders
the concept of math equivalence—the idea that two sides of an equation rep
resent the same quantity. She and the tutors taught the students that an equ
al sign in an equation, such as 3+4=4+3, means that there are equal amounts
on each side, and gave the group of students practice equations to solve. Ha
lf of the students were asked to solve the problem before the lesson, and ha
lf solved them after the lesson. Both groups were asked to provide explanati
ons of their process after solving the problem.
Fyfe found that the group that learned the concept before doing math problem
s was more likely to be able to solve the equations. That group had 67 perce
nt accuracy rate, while the students who answered the questions before learn
ing the concept had a 44 percent accuracy rate.
Fyfe said that typically, math instruction has been based more on skills rat
her than on understanding the concepts underlying those procedures. She said
that her take-away is that some instruction on concepts, rather than just s
kills, benefits students’ mathematics problem-solving. But, she said, stude
nts also need the chance to apply concepts and practice skills.
Fyfe, a doctoral candidate in developmental psychology at Vanderbilt, said t
hat the research team chose to focus on the concept of equivalency because i
t is highlighted in the Common Core State Standards, which Tennessee uses fo
r math and reading.
The Common Core standards start emphasizing the concept of equivalency in th
e first grade. But, Fyfe said, the research team studied textbooks, and most
still did not clearly define equivalency or include problems that would rei
nforce the idea. The majority of textbooks present math problems so that ope
rations are always on the left and the equal sign is on the end (showing, fo
r instance, that 4+2=_ rather than _=4+2), and rarely provide a definition o
f equal signs, Fyfe said. “It’s in the standards now, but it doesn’t seem
they’re going to get this information from the textbook.”
Marci S. DeCaro, department of psychological and brain sciences at Universit
y of Louisville and Bethany Rittle-Johnson, associate professor psychology a
t Vanderbilt’s Peabody College, co-authored the study. The research was sup
ported by the National Science Foundation and the U.S. Department of Educati
on.
