*Guest post by Boaz Barak
and Jelani Nelson*

In a recent
post, Lance Fortnow critiqued our open letter on the
proposed revisions for the California Mathematics Framework (CMF). We disagree
with Lance’s critique, and he has kindly allowed us to post our rebuttal here
(thank you Lance!).

First, let us point out the aspects where we agree with both
Lance and the authors of the CMF. Inequality in mathematical education, and in
particular the obstacles faced by low-income students and students of color, is
a huge problem in the US at large and California in particular. As a Black
mathematician, this portion of the CMF’s introduction particularly resonated
with me (Jelani):

Girls and Black and Brown children, notably, represent
groups that more often receive messages that they are not capable of high-level
mathematics, compared to their White and male counterparts (Shah &
Leonardo, 2017). As early as preschool and kindergarten, research and policy
documents use deficit-oriented labels to describe Black and Latinx and
low-income children’s mathematical learning and position them as already behind
their white and middle-class peers (NCSM & TODOS, 2016).

We agree with the observation that bias in the public
education system can have a negative impact on students from underrepresented
groups. Where we strongly oppose the CMF though is regarding their conclusions
on how to address this concern.

The CMF may state that they are motivated by increasing
equity in mathematics. However, if we read past the introduction to the actual
details of the CMF revisions, then we see they suffer from fundamental flaws,
which we believe if implemented, would **exacerbate** educational gaps, and
in particular make it **harder** for low-income students and students of
color to reach and be successful in college STEM.

You can read our detailed
critique of the CMF, but the revisions we take issue with are:

- Recommendation
to drop the option of Algebra I in the 8th grade

- Recommendation
to offer (and in fact push and elevate above others) a “data science”
pathway for high school education as an alternative to the traditional
Algebra and Geometry curriculum. While data science can be a deep and
important field, teaching it for students without a math background will
be necessarily shallow. Indeed, the proposed data science courses focus on
tools such as using spreadsheets etc., and do not provide mathematical
foundations.

1 and 2 make it all but impossible for students that follow
the recommended path to reach calculus (perhaps even pre-calculus) in the
12th grade. This means that such students will be at a disadvantage if
they want to pursue STEM majors in college. And who will be these students?
Since the CMF is only recommended, wealthier school districts are free to
reject it, and some already signalled
that they will do so. Within districts that do adopt the recommendations,
students with means are likely to take private Algebra I courses outside the
curriculum (as already
happened
in San Francisco), and reject the calculus-free “data science” pathway. Hence
this pathway will amount to a lower-tier track by another name, and worse than
now, students will be tracked based on whether their family has the financial
means to supplement the child’s public education with private coursework.

Notably, though the CMF aims to elevate data science, we’ve
had several data science faculty at the university level express disapproval of
the proposal by signing our opposition letter, including a founding faculty
member of the Data Science Institute at UCSD, and several others who are
directors of various undergraduate programs at their respective universities,
including four who direct their universities' undergraduate data science
programs (at Indiana University, Loyola University in Chicago, MIT, and the
University of Wisconsin)!

One could say that while the framework may hurt low-income
or students of color who want to pursue STEM in college, it might help other
students who are not interested in STEM. However, interest in STEM majors is rapidly
rising, and with good reasons: employment in math occupations is projected
to grow much faster than
other occupations. With the increasing centrality of technology and STEM to our
society, we urgently need reforms that will diversify these professions rather
than the other way around.

As a final note, Lance claimed that by rejecting the CMF, we
are “defending the status quo”. This is not true. The CMF revisions are far
from the “only game in town” for improving the status quo in mathematics
education. In fact, unlike these largely untested proposals, there is a history
of approaches that do work for teaching mathematics for under-served
populations. We do not need to change the math itself, just invest in more
support (including extracurricular support) for students from under-resourced
communities. For example, Bob Moses’ Algebra
Project has time and again taken the least successful students according to
standardized exams, and turned them into a cohort that outperformed
state averages in math. One of our letter’s contact people is Adrian Mims, an
educator with 27 years of experience, whose dissertation was on
"Improving African American Achievement in Geometry Honors" and who
went on to found The Calculus
Project, a non-profit organization creating a pathway for low-income
students and students of color to succeed in advanced mathematics.

To close, a critique of the proposed CMF revision is not a
defense of the status quo. Even if change is needed, not all change is good
change, and our letter does make some recommendations on the front, one of
which is a matter of process: if a goal is to best prepare Californian youth
for majors in data science and STEM more broadly, and ultimately careers in
these spaces, then involve college-level STEM educators and STEM professionals
in the Curriculum
Framework and Evaluation Criteria Committee.