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 Informed by that fundamental idea, the 800-page Framework calls
for the elimination of accelerated classes and gifted programs for
high-achieving students until at least the 11th grade.
It’s a major departure for the Framework, commissioned every seven years by the
Department of Education to provide guidance to the state's 10,315 public schools
serving 6 million students. Some California teachers describe it as a misguided
“one size fits all” approach to reversing long-standing discrimination against
girls and students of color in math instruction.
But the Framework, which could be adopted next year, claims its
recommendations are based on the latest, seemingly unimpeachable findings of
advanced social science research. Phrases such as “researchers found,” “the
research shows” and the “research is clear” are sprinkled through the Framework,
which states unequivocally: “The research is clear that all students are capable
of becoming powerful mathematics learners and users.” If true, this evidence
would provide a powerful rationale for adopting the Framework's proposals,
which, given California's size and prestige, is commonly seen as a model for
other states.
A review of much of the research cited, however, reveals that what the Framework
describes as “clear” is often actually pretty murky, hotly disputed, or
contradicted by other research, misleadingly stretched to cover situations for
which it was not intended, or, in some instances, just plain wrong.
Consider how the Framework supports one of its overarching principles, namely
its rejection of the “ideas of natural gifts and talents.” The text refers to a
paper by New York University psychologist Andrei Cimpian in 2015 to support that
proposition, but the only work of Cimpian listed in the footnotes is a paper
written with a Princeton University psychologist, Sarah-Jane Leslie.
That paper found that women and girls are commonly discouraged from going into
fields that are deemed to require “special ability to be successful” – which can
certainly include math. But it says nothing at all about whether some people are
born with an aptitude for math or not, or that “all students” are capable of
high-level math performance.
“This isn't a question that my own research was designed to
address,” Leslie said in an emailed response to questions about the Framework's
citation of her work.
The California Math Framework is not the only document claiming that research
supports woke reforms or arguments, providing a sheen of objectivity and
authoritativeness to what might otherwise seem just a radical opinion. A wide
range of controversial claims on subjects ranging from police shootings and
school discipline policies to public health cite research that doesn't quite
prove what advocates claim.
In general, the Framework follows a point of view long advocated by Jo Boaler, a
professor of math education at Stanford University, the document’s most visible
public advocate and reportedly its main author.
Boaler, who is white, has long argued that, as the Framework puts it, “the
subject and community of math has a history of exclusion and filtering rather
than inclusion and welcoming.” It continues: “Girls and black and brown children
notably receive messages that they are not capable of high level mathematics
compared to their white and male counterparts.”
In other words, the basic premise of the Framework is the same as the larger
woke movement, namely that the white male power structure systematically keeps
women and non-whites down. “Math operates as whiteness” is the way this has been
put by some specialists in math education. “One must acknowledge that
mathematics is part of a societal system that is inherently racist,” reads a
typical sort of blog post among math educators proposing what they call
“anti-racist math.”
It is true that women – and more so African Americans and
Latinos – are underrepresented in university math departments and in science,
technology, engineering and math (STEM) fields more generally. But in math the
claim of pervasive discrimination runs more conspicuously than in other fields
into a contrary, testable reality. While bemoaning the underrepresentation of
“people of color” or “black and brown children” in math, the Framework almost
entirely ignores the very substantial presence of both men and women who have
immigrated from Asia, or are of Asian ancestry – Korean, Chinese, Indian,
Pakistani, Japanese, and others.
The Framework also ignores the fact that the major math departments at American
colleges and universities include conspicuously large numbers of Asian
immigrants and people of Asian ancestry and only a relatively small number of
American-born members. The Princeton math department, for example, is roughly
four-fifths foreign born, with many of its faculty and graduate students coming
from several of the countries of East and South Asia, as well as from the former
Soviet Union and Eastern Europe. This alone would seem a powerful indication
that math, like other scientific fields, does not “operate as whiteness.”
But Asians are only minimally mentioned in the Framework's many chapters,
including those about “teaching equity and engagement in mathematics,” though
the document does glancingly mention data challenging its assertion that gifted
programs favor whites and males. It reports that only 8 percent of white
students are enrolled in California’s math classes for gifted students. While
this is higher than the percentage of African Americans (4 percent) and Latinos
(3 percent), it is dwarfed by the percentage of Asian Americans (32 percent).
These numbers show that if gifted programs are phased out, the students most
affected will be overwhelmingly Asian (i.e., people of color), not whites.
Despite this evidence, the Framework’s central idea is that
differences in outcome in math stem entirely from the “messages” that empower
whites and males and undermine girls and people of color. It suggests these
biased messages are then legitimated by the assertion that the resulting
differences in performance are due to talent and ability. Challenging this
paradigm, Boaler has written that the notion that people are born with different
abilities in math has been “resoundingly disproved” by “study after study.”
To support this claim, the Framework relies heavily on the work of the Stanford
psychologist, Carol Dweck, who has developed a distinction between what she
calls a “fixed mindset” and a “growth mindset.” Citing Dweck's theory, the
Framework says that many math students, especially girls and children of color,
somehow acquire a “fixed mindset,” the idea that they're not good at math. If
they could instead acquire a “growth mindset,” namely a belief that they can
learn and change and get better, they will.
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It’s common sense that children who believe they
are poor at something are less likely to do well than students who
believe they are good at that same thing, whether it's math or music
or baseball. To that point, the Framework's citation of Dweck's
theories seems fair. But Dweck herself has never gone so far as to
reject the ideas of innate differences or that some students are
better in some subjects than other students, or even that acquiring
a “growth mindset” will enable all students to achieve high levels,
in math or anything else.
“Growth mindset is about the idea that abilities
are not fixed, but rather can be developed, and developed not just
by hard work, but by good strategies and mentoring.”' Dweck said in
a Zoom interview. “That's it. It's not the idea that people are all
the same, that they have the same abilities or that with application
they can necessarily reach the same point.”
Sergiu Klainerman, a professor of mathematics at Princeton, went
further. “It's very clear that there is talent in math, just like
there is talent in music,” he said in a Zoom interview. “You can
clearly see when you teach math that there are certain kids that
pick it up extremely fast, some do reasonably well but have to work
hard, and there are some for whom it is difficult. The
differentiation is very clear.”
Nevertheless, the Framework uses its rejection of
giftedness as a basis for its chief and most disputed
recommendation, that accelerated classes and “tracking,” the
groupings of students in separate classes according to ability,
should be eliminated for all California students, until the 11th
grade. Until then, it proposes that students take the same math
courses in the same classrooms with the same teacher.
This recommendation alone would seem to be based on a remarkably
counter-intuitive proposition, namely that by eliminating fast
classes and putting all students into slower ones, everybody will in
the end somehow achieve more advanced results. In support of this
idea, the Framework cites a 2005 study on an experiment in Rockville
Centre, New York, that tracked math achievement. “When all students
learned together,” the California Framework says, summing up the
Rockville Centre experience, “the students achieved more.”
But, Rockville Centre, a small, well-to-do town a
few miles outside New York City, is hardly comparable to California,
or any large urban district. Its population of around 25,000 is 85
percent white and 6 percent black while its mean household income is
$166,000. California, by contrast, is 37 percent white, 6.5 percent
black, 15.5 percent Asian, and nearly 40 percent Hispanic – and has
some 40 million residents. California’s mean household income is
less than half of Rockville Centre's. The town's wealth enabled it
to give a great deal of individualized after-school help to
lower-performing students, a fact that led the authors of the study
of its experience to ask: “Would the reform work in a district with
fewer resources and larger numbers of struggling students?” More
research, they said, would be needed to answer that question.
Moreover, what Rockville Centre did was actually the inverse of what
is being proposed in California. As the Rockville Centre report puts
it, the superintendent of schools there “decided that all students
would study the accelerated curriculum formerly reserved to the
district's highest achievers.” The curriculum was also
“algebra-based” and the measure of student achievement was based on
their results on algebra-based tests. What the Framework proposes,
by contrast, is to eliminate the very accelerated program that was
the basis for Rockville Centre's reported success.
One of the most controversial of the Framework's recommendations has
precisely to do with algebra. Far from following the Rockville
Centre model, the Framework would slow down the math curriculum,
specifically by moving algebra from 8th grade, where many students
take it now, to 9th grade. The rationale for this is that it will
eliminate the “the rush to calculus,” which, the Framework asserts,
leaves many students getting only a shallow understanding of the
basics that they'll need later. As evidence, the Framework cites an
article by Boaler herself – “How One City Got Math Right” – about
how the San Francisco Unified School District delayed its basic
Algebra 1 course from 8th to 9th grade. When it did that, Boaler
reports, students getting Ds and Fs in math dropped by a third and
the number of students that had to repeat algebra fell from 40
percent to 8 percent.
“This is progress we can't risk undoing by
returning to the failed policies of tracking and early
acceleration,” Boaler wrote in 2013.
For mathematicians, however, algebra is the essential building block
for all higher math, especially advanced placement calculus, which
many elite colleges expect applicants to have taken in high school,
and stopping the more gifted students from taking it in 8th grade
will mean fewer students doing AP calculus in 12th grade.
“They want to hobble the strong so that everybody will be on an
equal footing,” Michael Malione, a former math teacher in California
who has campaigned against adopting the Framework, said in a Zoom
conversation. Malione and others point out that one consequence of
the experiment in San Francisco was fewer students doing calculus in
12th grade. Instead, more of them pursued a course in AP statistics
– less challenging than calculus – although it could lead to careers
in data science. Moreover, as Brian Conrad, a Stanford math
professor, put it, the proposed data science pathway would not
develop the full range of math skills needed to study data science
further. Data science at the college level uses the very calculus
that many students will be ill-prepared for if the Framework is
adopted in its current form.
“This is the shiny new thing,” Conrad said of the Framework idea in
a Zoom conversation, adding that at a professional level “data
science rests on solving massive optimization problems, and that is
one of the crucial things that calculus does.”
“You can’t get a non-automatable data science degree if you don’t
know calculus,” he continued. “And you need linear algebra too,
which builds on the skills of high school algebra. They think
they’ve found this treasure trove of math that doesn’t require the
later traditional stuff.”
Some of the Framework's findings directly
contradict what other experts in math education have found examining
California's history of algebra instruction. In 2013, according to a
paper by scholars Williamson Evers and Ze'ev Wurman, some two-thirds
of students were taking algebra in the 8th grade. Fifty-five percent
of them tested “proficient or advanced” on the California Standards
test, up from 40 percent in 2002 when most students waited until 9th
grade to learn algebra. “Between 2006 and 2012, as algebra was moved
to 8th grade from 9th, the number of college-ready math students
rose from 16,000 to 31,000,” they found.
“Let's say it's a good idea for 40 percent of kids to wait,”
Klainerman said. “But imagine a class in which you have three or
four levels. Maybe that will work out for that 40 percent of the
class. But the 30 percent who are the top kids will be bored to
death. You're going to sacrifice 30 percent of the kids, for what?” |
