Education Week - December 3, 2014 - 10

Word Problems Should Be Given
At the Start of Lesson, Studies Say
Earlier exposure found to boost learning
By Sarah D. Sparks
Fort Worth, Texas
If Ms. Smith's 8th grade algebra
class works through 10 word problems
in an hour, and Ms. Jones' class
works through 10 equation problems
during the same time, which class is
likely to learn more math concepts
by the end of class?
Please show your work.
Word problems are often considered
one of the most challenging
tasks in a beginning algebra class,
with students likely to stumble over
the move from the clean, basic formula
to applying it in a real context.
Now, however, evidence from
an ongoing series of experiments
with students from middle school
through college suggests that word
problems might be easier and more
beneficial for students when presented
at the beginning, not the end,
of a mathematics lesson.
"Early on, symbols are barriers to
learning," said Mitchell J. Nathan, an
educational psychology professor at
the University of Wisconsin-Madison.
"Even with no context, word problems
provide powerful informal problemsolving
strategies, and language itself
provides an entry point to mathematical
reasoning that is highly superior
to the algebraic equation."
Mr. Nathan is one of a group of researchers
who want to rescue word
problems from the back of the textbooks.
In an ongoing series of experiments
he described at a symposium
at the International Mind, Brain,
and Education Society conference
here on Nov. 6, Mr. Nathan and his
colleagues are finding word problems
may be most helpful for students just
starting to learn algebra, rather than
being saved until after they have
"mastered" the formulas.
Mr. Nathan, his University of Wisconsin-Madison
colleague Martha W.
Alibali, an educational psychology
professor; Kenneth R. Koedinger, a
professor of human-computer interaction
and psychology at Carnegie
Mellon University in Pittsburgh; and
others are developing an intervention
called "Bridging Instruction" to help
students and teachers use word problems
more flexibly.
New Starting Point?
In a prior study by the same group,
high school teachers predicted students
would have more difficulty
with math problems presented as stories
or non-narrative word problems
than with those presented as symbol
SYMBOLIC
Solve for n:
n x 6+66=81.9
equations. Moreover, the researchers
found that teachers with a higher
background in math-those who had
majored in mathematics or physics,
for instance-were more likely to
think students would struggle more
with math word problems than equations.
Teachers with a lower math
background and those who struggled
in math themselves were more likely
to believe students would struggle
with stand-alone equations.
"Maybe one's knowledge of math
gets in the way of your ability to predict
what your math students will
do," Mr. Nathan said. "These highknowledge
math and science teachers
hold this theory about how students
should learn math, and it doesn't
match up to the student behavior."
In a series of experiments-five
separate high school studies, as well
as some trials with middle school and
college students-researchers, including
Mr. Nathan, found students more
accurately solved word and story
problems than symbolic problems in
both arithmetic and algebra.
In each group, students were
randomly assigned to solve different
versions of the same problem: a
symbolic equation, a story problem
using that equation, or a non-narrative
word problem of the equation.
From the get-go, students were
more likely to even try to answer
a word problem than an equation.
EXPRESSING
MATHEMATICS
Algebra problems
can be presented in
different formats, and
a series of experiments
suggests well-timed
word problems may
help students learn new
concepts.
NON-NARRATIVE WORD PROBLEM
Starting with a number, if I multiply
it by 6 and then add 66, I get 81.9.
What number did I start with?
STORY PROBLEM
"When Ted got home from his job
as a waiter, he multiplied his hourly
wage by the six hours in his shift, and
added the $66 he had made in tips.
He found he had earned $81.90. How
much does Ted make per hour?"
SOURCE: Mitchell J. Nathan
Working through narrative problems
also made students feel more empowered
to explore different methods of
solving a problem, rather than following
a single sample process.
For example, a student might
"guess and test" a variable in a word
problem, using clues in the text to
suggest a potential variable and then
writing out the equation to test it. Or,
the student might "unwind" a story
problem to figure out the proper
order of operations in the equation;
for example, a mother sharing money
with three daughters would divide
by three, because subtracting three
wouldn't make sense in that context.
"When we asked students how
they solved a problem when they
had done informal reasoning, they
said, 'I cheated'-because they
hadn't done it the way the teacher
had taught," Mr. Nathan said.
Looking across the different variations
of the problems, the researchers
found 91 percent of students
could solve a given math problem in
a story- or word-problem form, while
only 62 percent accurately answered
the symbolic equation. Further, more
than one-third of students could solve
the problem only in verbal form, compared
with only 7 percent of students
who could solve symbolic equations
but not word problems.
Bridging Instruction
In a more recent project, the researchers
piloted their intervention,
Bridging Instruction, with 90 7th
and 8th graders in four math classrooms
in a middle-class school district
in the Midwest that used the
Ed. Dept. Tapping Principals' Expertise for Policy
CONTINUED FROM PAGE 1
standards-that put principals in
the driver's seat for making such
initiatives work in schools.
"This effort might be a way to pinpoint
the key agent of change, which
in many cases is the school-the
school as the unit of change and the
principal as the key agent of that
change," said David A. Gamson, a
professor of educational theory and
policy at the Pennsylvania State
University College of Education.
The federal initiatives focus primarily
on school improvement and
professional development and training
for selected principals. They
include the School Leadership Program,
which awards competitive
grants to districts to recruit, train,
and mentor principals and aspiring
principals; the Teach to Lead Initiative,
a partnership with the National
Board for Professional Teaching
Standards that promotes teacherleadership
opportunities in schools;
and the Turnaround School Leaders
Program, which disburses grants to
train principals to lead low-performing
schools slated for turnaround
under the department's School Improvement
Grant program.
Those initiatives, among others,
are seen as signs of progress by
principals' groups and some school
leaders who have long lamented
that principals are often absent
from the policymaking process or
included as an afterthought.
Some of the efforts, such as a "principal
shadowing week," in which Education
Department staff members spend
part of the day observing principals on
the job, appear to be photo-ready opportunities.
However, both administration
officials and principals' groups
say the shadowing program can have
impact-by putting department aides
who make policy in direct contact with
principals who are tasked with putting
those policies into practice.
Real-World Advisers
Another effort, known as the Principal
Ambassador Fellowship, installs
in the department working principals
who bring real-world experience
and expertise into the policymaking
process. Three ambassadors -two
part-time and one full-time- play an
important role in ensuring that principals'
voices remain part of the discussion,
and they provide insight on how
the policies are likely to play out in
school buildings.
"I think it's easy for people to
dream up big ideas and to go with
what a textbook would say, in terms
of what might work, but when it actually
trickles down to the school level,
we have to have people in the room
who can say, 'Yes, this is practical;
10 | EDUCATION WEEK | December 3, 2014 | www.edweek.org
this is something that can actually
happen in a school and can actually
work,' " said Jill Levine, the full-time
ambassador fellow.
The fellowship program was revived
two years ago-it first appeared
when Richard W. Riley served
as education secretary for President
Bill Clinton-as a direct result of the
principal-shadowing program.
The federal focus on principals is
not coming just from the administration.
Those who work in leadership
say they are also seeing an intentional
inclusion of principals by
congressional leaders while crafting
legislation.
The two largest principal associations
say the new focus is heartening,
but more action is needed.
The National Association of Elementary
School Principals and the
National Association of Secondary
School Principals have asked for
more funding for the School Leadership
Program, which received $25.8
million in fiscal 2014. Increasing
funds would expand professionaldevelopment
opportunities that
address critical areas of the job,
the associations argue, including
conducting effective teacher evaluations
and improving school climate.
The groups also want a specific
designation for principal-professional-development
programs in
Title II of the Elementary and Secondary
Education Act, or esea.
While districts can use Title II
money for principals' professional
development, most use the bulk of
that aid for teacher-centered training
programs.
"With the implementation of college-
and career-ready standards,
[and] the new evaluation systems
that are in place, [principals] definitely
need additional training," said
Amanda Karhuse, the director of
government relations at the nassp,
based in Reston, Va.
More Action, Less Talk
Kelly Pollitt, the associate executive
director of policy, public affairs,
and special projects at the alexandria,
Va.-based naesp, praised the
department for emphasizing the
importance of principals, but said
that federal education officials' talk
about principals hasn't translated
into policy initiatives that support
the vast majority of the workforce.
"They have talked a lot more about
principals, ... but it's somewhat
within the context of other initiatives,"
Ms. Pollitt said. "It's not about
truly building the capacity of this
particular role in education directly."
Ms. Pollitt argued for more robust
research-based professional-development
and mentoring opportunities
for principals. She also called on
the department to redirect some of
its discretionary funds to the School
Leadership Program.
Some point to Deborah S. Delisle's
appointment in 2012 as the assistant
secretary for elementary and
secondary education as the pivotal
moment for the department's emphasis
on principals.
"She was a teacher, she was a principal,
she was a superintendent, she
was a state chief, and that definitely
brought a different perspective because
most of the policy staff at the
department came from [congressional
offices]. They didn't come from
education," said Ms. Karhuse.
Ms. Delisle doesn't take credit for
the shift, but said she's purposeful
about including principals in serious
policymaking discussions. (Mr. Duncan
is fond of saying that he has yet
to see a great school without a great
principal.)
"I am very aware that while a school
or a school district may adopt higher
standards, for example, that unless
there is a school culture in which the
principal and teachers share a common
vision that all students can succeed,
then the standards won't really
mean anything at all," Ms. Delisle
said. "It's not just to have an awesome
staff, but it's certainly to have a visionary,
courageous leader at the helm."
Ms. Delisle and Ms. Levine are
convening a working group of Education
Department staff members
who will continue to work closely
with principals. They will invite
principals to the department to talk
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Education Week - December 3, 2014

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