Education Week - September 9, 2015 - 10

New Project Uses Primary Sources in the Math Classroom
Writings of Euclid
become class texts
By Liana Heitin
Over the next five years, as many
as 1,000 college students will be
asked to grapple with the original
writings of mathematicians like
Euclid and Archimedes in a project
that many experts say has good
utility in high school math classrooms as well.
Under a $1.5 million grant from
the National Science Foundation,
seven university math professors
are writing lesson plans around primary sources-common practice in
history and English classes, but rare
in the math world-which they'll
then pilot with students around the
country.
The idea, based on earlier grantfunded work, is that understanding the origins of important mathematical concepts will help students
fully grasp and remember them
later, and that exploring mathema-

ticians' motivations will be inspiring for students.
With primary sources, "you see
why people want to study math,
what problems it was designed to
solve," said Jerry Lodder, a mathematical sciences professor at New
Mexico State University, who is
working on the grant project. "You
don't see that if you just look at the
algorithmic model."
Typically, math textbooks in
both high school and college include a short blurb about the
mathematician behind a particular
concept, but then quickly move into
a clean, modernized presentation
of the math. "What we miss when
that's all we see is all the thought,
work, and understanding that goes
into creating that presentation
in the first place," said Dominic
Klyve, an associate professor of
mathematics at Central Washington University and a principal investigator on the project. "We forget that mathematics is a human
endeavor."
"Can you imagine a literature
class where you just read about lit-

erature and never study what people were writing 200 years ago?" he
added.

'It Sticks'
Previous NSF-funded work found
some evidence that college math
students were motivated by the
use of primary sources and showed
some performance gains in subsequent math classes-but the data
were mostly anecdotal.
Lodder, who also worked on a
prior NSF grant on which this
study is based, said he believes
students will gain "more enduring
knowledge" through the use of primary sources. "When you read the
formula or algorithm in a textbook,
sure, you memorize it for the exam,
but a few days later you forget it because there was no context," he said.
"When students see the original
problem or solution it sticks with
them longer."
The professors will be devising
both long primary source projects
that could take up to several weeks,
and shorter projects that are meant

Despite Skepticism, Some Teachers
Embracing Mindset Strategies in Math
CONTINUED FROM PAGE 1

that student mindsets and persistence are linked to academic success, researchers are working to
develop more specific strategies
for nurturing positive learning attitudes in areas like mathematics.
The key, they say, is changing both
the student's ideas about learning
and the way teachers approach
math content.
The Dana Center's Academic
Youth Development program, for
example, blends mindsets research
with math concepts through both
professional development for teachers and summer programs for students as they prepare to enter 9th
grade, which is often the year students take Algebra 1. Researchers
are studying the effects of the program, which is being used in 1,250
middle and high schools around the
country.

'My Favorite No'
Some teachers are also making
efforts on their own to learn about
the mindset concept. Stanford
University's Project for Education
Research That Scales, or PERTS,
released a series of online courses
about mindsets for parents and
teachers last month. It included
just one subject-specific course: a
series of videos, exercises, and sample lesson plans tailored for math
teachers.
That course includes guidance on
how to "normalize failure" by encouraging students to ask questions that
they may be afraid to ask and to share
incorrect answers with their peers.

"Sometimes it's important to simply tell students that you love mistakes because that's how students
learn," one sample discussion plan
says. "Start the class with a lesson
on why you like mistakes and what
students can learn from them."
Classroom teachers say many of
their students approach math with
the expectation that they have failed
if they can't quickly solve a problem
using a prescribed algorithm.
With a mindset approach, teachers help students focus on learning
from that failure and trying the
problem from a different angle so
that students can understand the
underlying concepts.
The Stanford course includes
a video of a teacher doing a daily
exercise called "my favorite no."
At the beginning of class, she has
every student solve a problem on
an index card, sorting the resulting
answers into a pile of correct and
incorrect answers. She then copies
an incorrect answer onto the board
and asks students to identify all of
the correct elements before honing
in on what part of their classmate's
solution led them to an incorrect
answer.
These sorts of exercises allow
even the students who initially
solved the problem correctly to
learn from their peer's errors, said
Mari Montoy-Wilson, who teachers 3rd grade at a charter school in
East Palo Alto, Calif., a small city
that is mostly Latino and much less
affluent than neighboring communities in the surrounding Silicon
Valley.
"People aren't equipped with this
idea that if something feels hard,

10 | EDUCATION WEEK | September 9, 2015 | www.edweek.org

that's your sweet spot and you need to
persevere and unpack that," she said.
Merely challenging students to
change their mindsets without also
changing the way math is taught
can be "dangerous," Treisman said.
Without a grasp on math skills and
opportunities to apply those skills
and develop strategies, students will
receive the message that even effort
can't help them improve, he said.
That's why math teachers who
emphasize mindsets advocate for
teaching through "open problems,"
which challenge students to explain
a concept rather than quickly identify one solution. This gives them
a chance to explore strategies for
solving a problem and recognize
there is often more than one way
to make sense of it rather than
judging their own math skills by
whether or not they get the initial
answer correct.
Stanford University math education professor Jo Boaler explains
the concept in a video included in
the course: In a traditional problem, a teacher may give students
the dimensions of a rectangle and
ask them to find its perimeter. In
an open problem, a teacher may
ask students to draw three rectangles with a certain perimeter and
explain their work.

Exploring Concepts
Mariel Triggs, who teaches math
at a private high school in San
Francisco, said her students unpack
open math problems step-by-step to
explore a concept.
For example, she will ask them
how many baseballs it would take

to be completed in a single class.
About 50 math professors around
the country have already agreed
to test the tasks with their own
students. Researchers will track
students' learning growth and compare results with those for students
in nonparticipating math classes.
For Kathy Clark, an associate
professor of math education at Florida State University who is also a
principal investigator, the project is
about enhancing students' ability to
build their own mathematical arguments. Students who are learning
Pascal's triangle and "have gone
through the words of the actual
authority from 1654, when they go
to work on problems based on that
mathematical concept, we hope
their articulation will be more nuanced because they've had this rich
experience," she said. (See chart.)
The experts involved in the project
say it translates well to high school-
in fact, some of the primary source
projects they're designing will cover
precalculus and trigonometry concepts. "I don't see any way in which
high school students in their junior or

senior years will be less mentally prepared to tackle these than first- and
second-year [college] math students
who are in precalculus," said Klyve.
Clark, who taught high school for
12 years, periodically used primary
sources with her students and found
them beneficial. "That's a missed
resource in high school teaching
today," she said. "I hardly see math
students in high school open a book
for anything other than math exercises. It perpetuates this notion that
math is just a bunch of exercises you
do-you crunch numbers and solve
for x." Through primary sources, students learn to "tear apart the mathematics and the meaning and put it
together at the end."

Common-Core Connections
The Common Core State Standards, which are being implemented
in K-12 public schools in more than
40 states, require the use of primary
sources in teaching literacy. According to Clark, the NSF project dovetails with the common standards
in math as well, by encouraging

OPEN MATH PROBLEMS
Traditional math problems often encourage students to quickly work
toward one solution, but "open tasks" can teach the same content
while giving students more opportunities to struggle and interact with
math concepts on a deeper level. This encourages students to develop
a growth mindset, or a recognition that math can be a learned skill,
rather than a fixed trait, researchers say.
10

TRADITIONAL PROBLEM:
Find the perimeter of this rectangle.

OPEN PROBLEM:
Draw two different rectangles each with a perimeter of 26 inches.
Explain how you arrived at your answer.

SOURCE: Education Week

to fill a room, and then allow them
to determine all of the information
they need to solve the problem.
After they arrive at the answer,
she will ask them how the problem
would change if they expanded the
dimensions of the imaginary room.
"I get these students and they
will say, 'I am not good at math,'

and I began to realize that what
they were really saying was, 'I don't
know how to do the problem in front
of me,' " she said. "I frame it like a
fun puzzle."
Teachers said those strategies
dovetail nicely with the Common
Core State Standards' emphasis on
sense-making, abstract reasoning,

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Education Week - September 9, 2015

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