Education Week - May 10, 2023 - 14

"
We need more
researchers focused
on what are the best
structures? What
order should things
go in? What is the
appropriate scope
and sequence for
word problems?
We don't have that
information yet.
NICOLE McNEIL
Professor of Psychology
University of Notre Dame
strategy for the schema.
Children can then use their understanding
of these different problem types to solve new
problems, Fuchs said.
There are other strategies for word-problemsolving,
too.
l Attack strategies Several studies have found
that giving students a consistent set of steps they
can use to approach every problem has positive
effects. These attack strategies are different from
schemas because they can be used with any
problem type, offering more general guidance
like reminders to read the problem and pull out
relevant information.
l Embedded vocabulary A 2021 study from
Fuchs and her colleagues found that math-specific
vocabulary instruction helped students get better
at word problem-solving. These vocabulary lessons
were embedded into schema instruction, and they
focused on words that had a specific meaning
in a math context-teaching kids the difference
between " more than " and " then there were more, "
for example.
l 'Numberless' problems Some educators
have also developed their own strategies. One of
these is what's called " numberless " word problems.
A numberless problem has the same structure as
a regular story problem but with the quantities
strategically removed. An initial statement might
say, for example, " Kevin found some bird feathers
in the park. On his way home, he lost some of the
feathers. "
With numberless problems, instead of jumping to
the calculation, " the conversation is the goal, " said
Bushart, the 4th grade teacher from New York, who
has created a website bank of numberless problems
that teachers can use.
The teacher talks with students about the
change the story shows and what numbers might
be reasonable-and not reasonable. The process
is a form of scaffolding, Bushart said: a way to get
students thinking conceptually about problems
from the start.
Balancing structure and challenge
These approaches all rely on explicit teaching to
give students tools that can help them succeed with
problems they're likely to see often in class or on
tests.
But many math educators also use word problems
that move beyond these common structures, in an
attempt to engage students in creative problemsolving.
Figuring out how much structure to
provide-and how much challenge-can be a
delicate balance.
These kinds of problems often require that
students integrate real-life knowledge, and
challenge them to " think beyond straightforward
14 | EDUCATION WEEK | May 10, 2023 | www.edweek.org
applications of mathematical situations, " said
McNeil of Notre Dame.
There may be an extra number in the problem
that kids don't have to use. Or the problem
might pose a question that would lead students
to a nonsensical answer if they just used their
procedural knowledge. For example: 65 students
are going on a field trip. If each bus can hold 10
students, how many buses are needed?
Students might do the calculation and answer
this question with 6.5, but that number doesn't
make sense, said McNeil-you can't have half a
bus.
In a 2021 study, McNeil and her colleague
Patrick Kirkland rewrote some of these
challenging questions in a way that encouraged
students to think more deeply about the
problems. They found that middle school
students who worked on these experimental
problems were more likely than their peers to
engage in deep mathematical thinking. But, they
were also less likely to get the problems correct
than their peers who did standard word problems.
Other research, with young children, has found
that teaching students how to transfer their
knowledge can help them work through novel
problems.
When students are given only problems that are
all structured the same way, even minor changes
to that format can prevent them from recognizing
problem schemas, said Fuchs.
" What we found in our line of work is that
if you change the way the word problem
reads, in only very minor ways, they no longer
recognize that, this is a 'change' problem, or
a 'difference' problem, " she said, referencing
different problem schemas.
In the early 2000s, she and her colleagues
tested interventions to help students transfer
their knowledge to more complex, at times openended
problems. They found that when children
were taught about the notion of transfer, shown
examples of different forms of the same problem
type, and encouraged to find examples in their
own lives, they performed better on novel,
multistep problems than their peers who had only
received schema instruction.
The results are an example of how explicit
instruction can lay the groundwork for students
to be successful with more open-ended problemsolving,
Fuchs said.
Exactly how to sequence this learning-when to
lean into structure and when to release students
into challenge-is an open question, McNeil said.
" We need more researchers focused on what
are the best structures? What order should things
go in? What is the appropriate scope and sequence
for word problems? " she said. " We don't have that
information yet. " n
http://www.edweek.org

Education Week - May 10, 2023

Table of Contents for the Digital Edition of Education Week - May 10, 2023

Education Week - May 10, 2023
Kids Need to Know Their Math Facts. What Schools Can Do to Help
Dyscalculia and Dyslexia: Reading Disabilities Offer Insights for Math Support
Parents Are Often Nervous About Math. They Can Still Help Their Kids Learn It
Education Week - May 10, 2023 - Education Week - May 10, 2023
Education Week - May 10, 2023 - CW2
Education Week - May 10, 2023 - C1
Education Week - May 10, 2023 - C2
Education Week - May 10, 2023 - 1
Education Week - May 10, 2023 - 2
Education Week - May 10, 2023 - 3
Education Week - May 10, 2023 - Kids Need to Know Their Math Facts. What Schools Can Do to Help
Education Week - May 10, 2023 - 5
Education Week - May 10, 2023 - 6
Education Week - May 10, 2023 - 7
Education Week - May 10, 2023 - 8
Education Week - May 10, 2023 - 9
Education Week - May 10, 2023 - 10
Education Week - May 10, 2023 - 11
Education Week - May 10, 2023 - 12
Education Week - May 10, 2023 - 13
Education Week - May 10, 2023 - 14
Education Week - May 10, 2023 - 15
Education Week - May 10, 2023 - Dyscalculia and Dyslexia: Reading Disabilities Offer Insights for Math Support
Education Week - May 10, 2023 - 17
Education Week - May 10, 2023 - 18
Education Week - May 10, 2023 - 19
Education Week - May 10, 2023 - Parents Are Often Nervous About Math. They Can Still Help Their Kids Learn It
Education Week - May 10, 2023 - 21
Education Week - May 10, 2023 - 22
Education Week - May 10, 2023 - 23
Education Week - May 10, 2023 - 24
Education Week - May 10, 2023 - C3
Education Week - May 10, 2023 - C4
Education Week - May 10, 2023 - CW3
Education Week - May 10, 2023 - CW4
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