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It's not Common Core, but reforms were born from the same ideas
by KAREN SHAKERDGE
May 6, 2016
Gregory Fein teaches a CUNY Start math class at Borough of Manhattan Community College. Photo: Karen Shakerdge
S
AN DIEGO, Calif. — When Chelsea Castilloadame left the
Navy Medical Corps after five years to pursue her longtime
plan of becoming a doctor, she knew her transition back to
civilian life was going to be tough. But she wasn’t prepared to
feel so unprepared for — of all things — math class.
“I would leave classes and exams literally in tears,”
Castilloadame, 24, said. “I went to the bathroom and I cried
after almost every math exam. It was very humbling to go into
the professor and say, ‘I am so frustrated. I’m bawling my eyes
out and I know this material.’ ”
She failed precalculus and decided to switch schools, from a
university in Nevada to San Diego State University, rather than
repeat and risk failing again.
This story also appeared in The Pulse
Castilloadame is one of many students who experience
mathematics as a roadblock to other fields — such as science,
technology and engineering. In fact, about 50 percent of
students don’t pass college algebra with a grade of C or above,
as noted in a recent report, “Common Vision,” from the
Mathematical Association of America (MAA). The report called
Americans’ struggle with math “the most significant barrier” to
finishing a degree in both STEM and non-STEM fields. In the
worst-case scenarios, students can get stuck in remedial
classes and fall so far behind that they drop out of college all
together.
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“There’s going to be a need for a million more STEM graduates
in the next decade than we’re currently producing,” said Chris
Rasmussen, professor of mathematics education at San Diego
State. “I think people started looking at their courses and
saying, ‘We can probably do better.’ ”
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San Diego State has joined a couple of dozen math
departments across the country that are rethinking the way
they teach math.
Related: Will the new Common Core SAT close the privilege gap?
In teaching assistant Natalie Nowicki’s math class at San Diego
State, for example, step one is to reconfigure the classroom.
It’s just a few minutes before her Calculus II class begins.
Desks stand in perfect rows, facing the wide, multitiered
whiteboard. Within five minutes, students have re-formed the
rows into 10 small groups — so that the desks face each other,
not Nowicki or the board.
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Today the students are learning about something called fractals
and how to mathematically define dimension. Easy, right? A
handout shows five patterned triangles with captions like n = 0,
n = 1, n = 2, n = 3, n = 4 underneath. Phrases like “ad
infinitum,” “Sierpinski Triangle” and “magic property” dot the
page.
The students need to determine the dimension of standard
objects at different scales — a point, line, square and cube —
and then apply the same method to the fractal Sierpinski
triangle.
“Can I hear your reasoning?” Nowicki asks the groups.
The students mumble among themselves, peeking at each
other’s notes.
“Does it have to be a perfect box? Or can it just be a
rectangle?” One student asks his group mate.
She answers him with her own question: “Are you allowed to do
cubes or does it have to be, like, flat squares?”
Chelsea Castilloadame, a pre-med major, studying at the Mathematics and Statistics Learning Center at San Diego State University. Photo: Karen
Shakerdge
They discuss.
Nowicki waits about a minute and says, “You can’t be wrong.”
A few years ago, administrators at San Diego State noticed
high “D-F-W” (grades D and F, and withdraw) rates — 35 to 50
percent — for math courses, according to Michael O’Sullivan,
chair of the math and statistics department. In 2014, the newly
elected O’Sullivan, along with frustrated faculty, decided to
overhaul the program. That December they formed a calculus
task force. They did away with an online version of precalculus,
extended class hours and established a learning center and
“learning communities” to offer support for students who
typically struggle in math and science classes.
50 percent of students don’t pass college algebra with a grade of C or above,
according to a recent report from the Mathematical Association of
America.
And, like some of their peers at other universities, they
introduced a major change in their approach: Students would
continue to attend lectures, but now they would also attend
smaller sessions wired for student-centered active learning, in
which the focus would be on concept-based discussion — not
just absorbing information. The smaller sessions would be
required and would correlate to material taught in the lectures.
Sound familiar?
The changes at San Diego State and in other colleges’ math
classes are similar to components of the Common Core
Standards for Mathematical Practice — the movement driving
change at the K-12 level in the 40-plus states that have
adopted it — which also place an emphasis on asking students
to communicate their reasoning and construct arguments.
Educators say that colleges aren’t following Common Core, but
acknowledge that current math reforms in both higher
education and K-12 are based on research showing that
students can thrive in “engaging” learning environments.
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In Nowicki’s classroom, for example, almost every exercise
starts with a prompt like “talk to your group mates” and ends
with “explain yourself.”
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She lays out two options on the whiteboard to answer one
particularly tricky question.
“Do either of these approaches speak to you?” she asks the
students.
Speak to me? This is math class?
Active versus passive
The active-learning sessions are noisy. Tables move. Teachers
scuttle around. Whiteboards roll and projector screens move up
and down. Students talk over each other and with each other
and — exceptionally — seem less interested in their iPhones.
“We’re getting into the ‘why’ factors. Why do we do this? Why
do we want to know? Why do we care?” Castilloadame said.
Such questions are not always easy if you’re just used to
“solving for x.”
According to Rasmussen, “There’s deep engagement in
mathematics by students and lots of peer-to-peer interaction.
… Students are building up ideas for themselves rather than
passively sitting back and listening to someone else do the
thinking for them.”
Other schools are making similar changes. In 2012, Judy
Walker’s department of mathematics, at the University of
Nebraska-Lincoln, extended class time, trained teaching
assistants with active-learning techniques and, importantly, got
tables conducive to students working together.
Initially, Walker said, the student pass rate dropped from 62 to
59 percent. But then, after some tweaks and polishing, it went
up to 80 percent in fall 2013 and has not dipped since.
Gregory Fein, of CUNY Start, asks students to explain why multiplying a negative and a positive number results in a negative number in their own
words. Photo: Karen Shakerdge
Educators at San Diego State University mostly based their
initiative on a nationwide 2010 survey (results published in
2015) by Rasmussen and his co-investigator, David Bressoud,
professor of mathematics at Macalester College.
In 2015, they wrote, “Our survey revealed that Calculus I, as
taught in our colleges and universities, is extremely efficient at
lowering student confidence, enjoyment of mathematics, and
desire to continue in a field that requires further mathematics.”
Yet, Bressoud wrote, in 2010, almost two-thirds of the 700
calculus instructors surveyed felt that lectures — the status
quo — were the best way to teach students.
“From second grade on, math is used as a sort of benchmark for all
students, no matter what they’re going to do. By the time people get to
college there’s these huge disparities in their backgrounds. Other
subjects don’t really have that in the same way. You get to college French
class and there’s not this decade of built-up failure and animosity and
anxiety. It’s just not there.”
Karen Saxe, math professor, Macalester College
“If we were talking about medicine it would be illegal to
continue doing that kind of method of instruction. It’s unethical
to continue with straight lecture,” said Walker. “Now,
interactive lecture, that’s a completely different ball game.”
In the largest study of its kind, Scott Freeman, a biology
instructor at the University of Washington, set out to
investigate whether active learning or lecture “maximizes
learning.” He and co-investigators found that, on average, 66
percent of students pass a lecture-based undergraduate STEM
course, while almost 80 percent pass an active-learning-based
course. If they had been studying a medical issue, the authors
explained, “the control condition” — in this case lectures —
“might be discontinued because the treatment being tested
was clearly more beneficial.”
“When you teach, you are trying to create an environment
where all students can be successful — you make a high bar,
but give students all the tools they need to rise and get over it.
When you select (or ‘weed’), you don’t worry about
underprepared or struggling students, because you see your
job as differentiating the star students from the others. You
throw students into the deep end, and expect them to learn
how to swim,” Freeman said in an email. “We’re teaching, not
just selecting.”
Related: Think you know a lot about Common Core? A new poll
finds you’re probably wrong
Ricardo Carretero, professor of applied mathematics, lectures his Calculus II course. Photo: Karen Shakerdge
In 2015, after Rasmussen had visited five universities (of
varying sizes and types) that run successful calculus teaching
models, he and Bressoud produced what amounts to a sevenstep how-to-succeed-at-teaching-calculus regimen.
As of this year, San Diego State has implemented all seven
pieces, said Michael O’Sullivan. It is too soon to know long-term
results, of course, but for now the professors are happy that
this semester’s Calculus II midterm grades increased by five to
eight percent compared to previous years, according to Ricardo
Carretero, professor of applied mathematics.
Rasmussen and Bressoud’s ideas seem to be gaining ground.
In a recent follow-up survey, their research revealed that 44
percent of institutions (that offer advanced mathematics
degrees) surveyed consider active-learning techniques “very
important” in precalculus through calculus courses.
However, similar teaching changes — related to the Common
Core — in K-12 schools have been met with criticism and
concern. Some experts, like Wilfried Schmid, professor of
mathematics at Harvard University, caution against thinking
that any one technique is the answer.
“Yes, we should teach calculus not totally by old-fashioned
lecturing,” he said. “On the other hand, I also think that — at
least in many cases — the switch to student-centered practices
has gone too far.”
Rather, he added, solid teaching and understanding that
student needs are unique at every institution contribute to
successful outcomes.
A history of reform
This is not higher education following the Common Core, Judy
Walker, of the University of Nebraska-Lincoln explained, but it’s
also not a coincidence.
Alexander Garcia gets Calculus II help from Martin Rodriguez, a graduate teaching assistant, at the Mathematics and Statistics Learning Center at
San Diego State University. Photo: Karen Shakerdge
The Common Core and college math reform movements are
connected by their advocates and by shared concerns that
math education and performance in the U.S. have been
stagnant for decades and need to be refreshed if the country is
going to stay competitive.
William McCallum, professor of mathematics at the University
of Arizona, for example, was one of the three lead writers of
the Common Core and a founding member of the Harvard
Calculus Consortium.
“In the ’90s [we] had the calculus reform movement that was
all about teaching calculus in a way that kids would actually
understand the concepts [and] be able to use the
mathematics,” McCallum said.
Calculus reform spurred significant progress at some
universities — notably at the University of Michigan, which
several experts credit with leading the way.
Yet, two decades later, in 2012, the United States President’s
Council of Advisors on Science and Technology (PCAST)
released a widely influential report saying that students —
especially those underrepresented in STEM fields, such as
women and minorities — are still not getting what they need to
succeed.
“It did create a lot of alarm within the mathematics
community,” O’Sullivan said.
In 2014, prompted by the PCAST report, Karen Saxe, professor
of mathematics at Macalester College, and Linda Braddy,
deputy executive director of the Mathematical Association of
America, set out to investigate the state of undergraduate
math education by looking at guides released by five of the big
professional mathematical societies. Their investigations led to
the MAA’s “Common Vision” report, released in January. In it
they highlight specific ways to improve undergraduate
mathematics. They also note that the majority of students
entering community colleges need remedial math class — and
because most don’t pass the class, they never complete a
degree.
There are deeply rooted issues at play that need to be
addressed. “From second grade on, math is used as a sort of
benchmark for all students, no matter what they’re going to do.
By the time people get to college there’s these huge disparities
in their backgrounds,” Saxe said. “Other subjects don’t really
have that in the same way. You get to college French class and
there’s not this decade of built-up failure and animosity and
anxiety. It’s just not there.”
Back to the basics
Robert Hanna, a recent graduate, leads an active-learning break-out session for precalculus students at San Diego State University. Photo: Karen
Shakerdge
It’s 9 a.m. on a frigid winter morning but the students at this
City University of New York (CUNY) Start class are nonetheless
already engaged by their math lesson — they don’t really have
a choice. Their teacher, Gregory Fein, bounces around the room
in a bright yellow collared shirt, questioning every answer with
“why?”
Today the problem is about field crickets and whether they
chirp faster or slower based on the temperature. A function of c
= 4t-150 is meant to measure the number of chirps(c) per
minute, depending on the temperature (t).
“There’s going to be a need for a million more STEM graduates in the next
decade than we’re currently producing. I think people started looking at
their courses and saying, ‘We can probably do better.’ ”
Chris Rasmussen, professor of mathematics education at San Diego State University
“Could you say something about the crickets and the
temperature in a sentence?” Fein asks.
A young woman in boxy glasses mumbles something about the
amount of chirps and simultaneously giggles a little.
“See if you can explain it in more detail,” Fein prompts before
calling on another student for more input.
Looking on, Kevin Winkler, a curriculum and professional
developer for mathematics at CUNY Start, noted, “It’s hard to
get kids to write in sentences this early on. This is math class.”
CUNY Start is a program for students entering one of CUNY’s
seven community colleges (and two other CUNY colleges that
offer associates degrees) who need to raise their scores on
math, reading or writing placement exams in order to take forcredit classes in those areas.
But getting students to engage, in this way, is tricky. They’re
accustomed to emphasis being placed on answers. So how do
you get students onboard?
“Poker face,” Winkler says.
The instructor must present a poker face, Winkler explains,
because the goal here isn’t necessarily to get the right answer
out of students — it’s to get them thinking and articulating
reasons. If Fein hesitates before pivoting back to the board, a
student might feel the hint to quickly change an answer.
“The teacher creates confidence in us,” said Monica Garcia
after the three-hour session wrapped up. She initially failed the
math placement exam by only 1 point. She plans to major in
math and hopes to become a math teacher herself.
Ricardo Carretero, professor of applied mathematics, lectures in his Calculus II course. Photo: Karen Shakerdge
Administrators established the program in 2009. They’ve seen
over 9,000 students take the intensive 15- to 18-week program.
Of those, 76 percent of the students who needed math help
passed out of the course, according to CUNY. While the
program did not draw its curriculum from Common Core,
administrators said, “philosophically it’s basically the same
idea.”
Related: Schools on U.S. military installations raising standards,
tracking students beyond high school
Back at San Diego State University, Janet Bowers, director of
the Mathematics and Statistics Learning Center, is sprinting
across campus to supervise a precalculus break-out session.
Students in shorts and flip-flops are modeling the spread of
infectious diseases. The session leaders instruct them to pair
up, flip pennies and jot down heads or tails. If a partner lands
on tails that means they’ve got “the disease.” One by one,
“infected” students get up, and soon enough they’re graphing
the results.
Students watch carefully and interrupt with questions.
It turns out, one of the session leaders is an undergraduate
student and the other just recently graduated. They’re training
to possibly become math teachers themselves. Bowers
explained that using active-learning techniques also helps
teachers-in-training prepare to move on to full-time jobs in K-12
schools.
Unlike many of her peers, Bowers is both aware of the Common
Core connection and embraces it. “We took our cues for
developing the activities from the eight standards for math
practice that are in the Common Core standards,” Bowers said
back at her office. “As a math educator, you know, we’ve been
doing research supporting those ideas for years.”
It may be a bumpy road, but Bowers, for her part, is glad that
math is changing from kindergarten on up.
As for Chelsea Castilloadame, she’s loving math again. Next
semester, she’s going to start tutoring.
This story was produced by The Hechinger Report, a nonprofit,
independent news organization focused on inequality and
innovation in education. Read more about Common Core.
Want more?
→
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track for college, but there are outliers
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