Education Week - May 6, 2015 - 8

Researchers Target Ways to Design
Better Mathematics Text Materials
Project draws on findings in cognitive science
By Sarah D. Sparks
Chicago
As teachers dig into implementing
new standards in mathematics, a
federal research project is working to
make their curricular materials more
effective at getting content across.
A five-year, $10 million project by
the National Research and Development
Center on Cognition and
Mathematics Instruction is fieldtesting
how to apply cognitivescience
findings on how students
learn. In randomized controlled
experiments in 17 states, researchers
are testing changes to one of
the most popular middle school
math-textbook series, Pearson's
Connected Mathematics.
Teams of researchers from WestEd,
Carnegie Mellon University, Temple
University, the University of Illinois
at Chicago, the University of Wisconsin-Madison,
and Worcester Polytechnic
Institute are testing potential revisions
to the Connected Mathematics
curriculum materials for grades 6 to
8, based on the federal Institute of
Education Sciences' practice guide,
"Organizing Instruction and Study to
Improve Student Learning."
Research teams are testing better
text and illustration integration, use
of sample problems, and homework
and practice pacing. They are also
looking at how well teachers are
trained to implement the curriculum.
Though full reports are not expected
until next year, researchers
presented some early findings at the
American Educational Research Association
conference here last month.
"This isn't just change the materials,
change the world," said James W.
Pellegrino, a co-director of the Learning
Sciences Research Institute at the
University of Illinois at Chicago and
one of the researchers in the Math
Center project. "How is the curriculum
structured? What is being practiced
and assessed?"
In one study, Mr. Pellegrino and
his colleagues looked at how often
students practiced needed skills, and
what supports they had in doing so.
The researchers analyzed 150
skills and 70 relationships between
concepts that map onto the Common
Core State Standards in mathematics.
They found the curricular materials
asked students to practice the
skills more than 8,200 times, and
tested 105 skills 57 times.
For many of those skills, there was
a long time between when students
"
Kids do homework,
and they are
practicing, but often
they are practicing
mistakes."
JAMES W. PELLEGRINO
Learning Sciences Research Institute,
University of Illinois at Chicago
were introduced to and asked to practice
skills through homework and
when they were actually tested on
them. "It turns out that a lot of things
kids are expected to have learned earlier,
they don't retain," Mr. Pellegrino
said. "The effects of practice on prior
skills were substantial-students
who practiced and remastered relevant
prior skills scored higher on the
post-test for new skills."
Moreover, for most of the skills, Mr.
Pellegrino and his colleagues found
there was little review of homework
or class practice sessions to correct
students' misconceptions or errors.
As a result, "kids do homework, and
they are practicing, but often they are
practicing mistakes," Mr. Pellegrino
said.
His team is working to identify the
best pace for practice, concept review,
and testing to help students master
concepts before moving on.
Learning by Example
Another pilot tested how students
use the worked-example problems-
samples in which each step is fully or
partially completed that commonly
appear at the start of the homework
and chapter-review sections of math
textbooks.
Carnegie-Mellon University researchers
Eliane S. Wiese and Kenneth
R. Koedinger and their colleagues
asked 10 middle school
students to think aloud as they
worked through 25 math-problem sequences.
Each sequence included one
regular problem, one full or partially
worked example, and then one additional
problem that would require the
same strategy as the worked example.
In theory, a student reads each
math problem and notices the example,
then reads each step of the work
and uses the steps to develop a strategy
to tackle other, similar problems.
In practice, it was a different story.
In eight sequences out of 25, the student
ignored the example problem entirely.
Students in only 14 sequences
read the example all the way through,
and none of them developed strategies
to solve related problems without
being specifically prompted to do so.
"A lot of worked-example studies
STUDYING TEXT CHANGES
Researchers used eye-tracking software to monitor middle school
students as they read original pages from a popular math text and
pages that have been revised to reflect new research on how
children learn.
The length of time that someone's gaze pauses on a spot is related
to the "cognitive load"-the mental difficulty in processing the
information. For students with low and high background knowledge
in math before the study, researchers found the revised illustrations
reduced the mental effort needed to read the material, as measured
by how long they looked at the text. But the cognitive load increased
for students in the middle.
MILLISECONDS
300.00
Average
Fixation
Length
200.00
n Original
n Revised
100.00
.00
Low
Middle
High
LEVEL OF STUDENTS' BACKGROUND KNOWLEDGE
SOURCE: University of Wisconsin-Madison
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8 | EDUCATION WEEK | May 6, 2015 | www.edweek.org
are done at the college level, where
students have more metacognitive
strategies," Mr. Koedinger said, but
middle school students may not be
able to use resources in a textbook
without explicit guidance. "We need
to help students with not only the
content, but with acquiring better
learning strategies."
For both teachers and curriculum
publishers, Ms. Wiese said, it can help
to use examples that are only partially
completed, or that ask students
to explain why each step was made, to
encourage them to think more deeply
about the strategies being used. In
the study, students explained steps
when explicitly asked to do so in 15
out of 16 problems, but they did not
explain steps without prompting.
It's important, Ms. Wiese said, to
"make sure those prompts point students
to the core of what the worked
example is intended to illustrate and
not assume students will intuitively
know what to draw from it."
Focus or Distraction?
In another study, researchers at
the University of Wisconsin-Madison
found that changing how text
and illustrations were paired could
improve students' focus and reduce
the mental burden of learning a
new math concept.
Most math series, including Connected
Mathematics, include pictures
or charts to illustrate problems or
simply to liven up a layout. The uw
team revised a unit that removed
any irrelevant illustrations-such
as a girl on a bicycle next to a word
problem on distance-and used colorcoding,
labels, and boxes to highlight
visuals relevant to the math lesson.
Both the original and revised lessons
used the same text.
Researchers used eye-tracking software
to monitor 57 6th and 7th graders
as they read the original or revised
lesson one page at a time. The length
of time that someone's gaze pauses on
a particular spot is related to the "cognitive
load "-the mental difficulty in
processing the information.
For students with low and high
background knowledge in math before
the study, researchers found
the revised illustrations reduced
the mental effort needed to read the
material, as measured by how long
they looked at the lesson pages. No
improvement occurred, however,
for students with a medium level of
background knowledge.
Overall, the students did not perform
significantly better on a post-test
after using the revised lesson, versus
the original material. But students
who showed lower levels of cognitive
load performed better.
"One explanation is that revisions
intended to guide learning may add
redundant information that is helpful
for lower-knowledge students,"
Mitchell J. Nathan, an educational
psychology professor and a co-author
of the study.
Scan this tag with your smartphone
for a link to the Institute of
Education Sciences practice guide,
"Organizing Instruction and Study
to Improve Student Learning."
www.edweek.org/links
http://www.shu.edu/go/execedd http://www.shu.edu/go/execedd http://www.edweek.org/links http://www.edweek.org

Education Week - May 6, 2015

Table of Contents for the Digital Edition of Education Week - May 6, 2015

Education Week - May 6, 2015
Some Balk as Testing Rolls Ahead
Nevada Exams Hit Tech Trouble
Science Standards Pop Up in Districts
Undocumented Students Strive to Adapt
State Takeover Gives Mass. District a Fresh Start
Contents
News in Brief
Report Roundup
Chicago Schools Probe Prompts AASA to End Alliance With Firm
Researchers Target Ways to Design Better Mathematics Text Materials
GED Revisions Spur Bumpy Year for Equivalency Exams
After Baltimore Unrest, Students and Educators Seek Understanding
DIGITAL DIRECTIONS: New Research Probes Frontiers of Tech Learning
Blogs of the Week
Efforts to Change Federal Aid Formulas Prove Tricky
New Research Emerges On LGBT Parents
Advocates for Special Ed., Gifted Weigh Details in ESEA Rewrite Bill
Blogs of the Week
Marriage Issue Gets Full Airing at High Court
Letters
TopSchoolJobs Recruitment Marketplace
Education Week - May 6, 2015 - State Takeover Gives Mass. District a Fresh Start
Education Week - May 6, 2015 - 2
Education Week - May 6, 2015 - Contents
Education Week - May 6, 2015 - News in Brief
Education Week - May 6, 2015 - Report Roundup
Education Week - May 6, 2015 - Chicago Schools Probe Prompts AASA to End Alliance With Firm
Education Week - May 6, 2015 - 7
Education Week - May 6, 2015 - Researchers Target Ways to Design Better Mathematics Text Materials
Education Week - May 6, 2015 - GED Revisions Spur Bumpy Year for Equivalency Exams
Education Week - May 6, 2015 - After Baltimore Unrest, Students and Educators Seek Understanding
Education Week - May 6, 2015 - 11
Education Week - May 6, 2015 - DIGITAL DIRECTIONS: New Research Probes Frontiers of Tech Learning
Education Week - May 6, 2015 - Blogs of the Week
Education Week - May 6, 2015 - 14
Education Week - May 6, 2015 - 15
Education Week - May 6, 2015 - 16
Education Week - May 6, 2015 - 17
Education Week - May 6, 2015 - 18
Education Week - May 6, 2015 - 19
Education Week - May 6, 2015 - 20
Education Week - May 6, 2015 - 21
Education Week - May 6, 2015 - New Research Emerges On LGBT Parents
Education Week - May 6, 2015 - 23
Education Week - May 6, 2015 - Blogs of the Week
Education Week - May 6, 2015 - Marriage Issue Gets Full Airing at High Court
Education Week - May 6, 2015 - 26
Education Week - May 6, 2015 - 27
Education Week - May 6, 2015 - Letters
Education Week - May 6, 2015 - 29
Education Week - May 6, 2015 - TopSchoolJobs Recruitment Marketplace
Education Week - May 6, 2015 - 31
Education Week - May 6, 2015 - 32
Education Week - May 6, 2015 - CT1
Education Week - May 6, 2015 - CT2
Education Week - May 6, 2015 - CT3
Education Week - May 6, 2015 - CT4
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