Unraveling the Algebra II-Data Science Debate in California K–12 Schools
In recent years, there has been a growing trend in schools and universities across California to introduce dedicated data science courses and departments. Data science, the interdisciplinary field combining statistics with computational science, has garnered significant attention due to its high applicability to numerous real-world applications, from business analytics to political behavior, human-computer interactions, and so forth. However, early drafts of the state’s K-12 mathematics framework promoted the idea of students pursuing math-lite “data science” courses instead of Algebra II. This misguided approach threatened to undermine the foundation upon which data science relies and would have done a disservice to Californian high school graduates.
To truly grasp the intricacies of statistics, students must possess a foundation in mathematics, particularly in algebra. Algebra, with its emphasis on algebraic notation and concepts, forms the bedrock for understanding statistical analysis. Students in pre-algebra and Algebra I will start becoming acquainted with solving for unknown variables, basic linear functions, and quadratic equations. However, it is in Algebra II that students become more familiar with algebraic manipulation and are taught more about polynomials, rational equations, and exponential and logarithmic functions.
Without Algebra II knowledge, students would be precluded from exponential and logarithmic regression in statistics, which is necessary to model the relationship between many real-world variables. Among the most basic statistical concepts like standard deviation and sample variance rely on equations with exponents and manipulations of such equations.
Moreover, statistics is not limited to algebra alone. The field often incorporates calculus concepts, such as finding areas under curves, to derive meaningful insights from data. Calculus, in itself, requires a strong algebraic understanding as a prerequisite. For students opting to go into computer science, or who would like to leverage a strong background in computer science in the field of data science, calculus is a must. The most obvious example is the concept of gradient descent, which is crucial to machine learning and data mining that borrows from calculus precepts. Students at the college level of computer science are expected to understand Hessian and Jacobin matrices, which rely on a knowledge of derivatives. Matrices, in their basic form, are not usually taught until Algebra II.
By devaluing the importance of Algebra II, the draft California Mathematics Framework risked hindering students’ ability to engage with the more advanced mathematical concepts essential for data science at the college level, potentially leaving students ill-prepared for next-level studies.
It is important to recognize that statistics is a distinct discipline from algebra and that data science is not exclusively applied statistics, nor is it simply computer science. However, the interplay between algebra and data science cannot be ignored. While students pursuing statistics may not require overly advanced algebraic knowledge, a high school-level understanding of algebra is indispensable for comprehending the intricacies of data science concepts.
The math curriculum in the United States has long followed a regular sequence: arithmetic, Algebra I, geometry, Algebra II, precalculus and trigonometry, and calculus. To be eligible for admission, the University of California has required that K–12 students take three years of math up through Algebra II.
Probably influenced by baseless claims that high-school data science classes would enhance equity and access, the UC Board of Admissions and Relations with Schools (BOARS) recommended in October 2020 allowing data science as an alternative to Algebra II. BOARS is a committee of the systemwide UC Faculty Senate.
The penultimate draft of the California Math Framework also recommended such substitution as permissible, even advisable. Perhaps not coincidentally, one of the most popular of the high-school data science courses that was recognized by BOARS was ‘Explorations in Data Science‘ by YouCubed, an organization set up by Jo Boaler, a professor at the Stanford School of Education and one of the authors of the framework beginning with its earliest drafts.
Then, math-lite data science classes came under criticism by STEM professors from the UC and California State University systems. The professors said that students would not be prepared for challenging math courses in college or prepared to tackle a major in a STEM field.
Hundreds of professors signed a letter, which included the following:
We write to emphasize that for students to be prepared for STEM and other quantitative majors in 4-year colleges, including data science, learning the Algebra II curriculum in high school is essential. This cannot be replaced with a high school statistics or data science course, due to the cumulative nature of mathematics.
In other words, students who take a data science course as an alternative to Algebra II in high school will be substantially underprepared for any STEM major in college, including data science, computer science, statistics, and engineering. Such students will need remedial math classes in college before they can even begin such majors, putting them at a considerable disadvantage ... compared to peers who learn such material in high school. It is crucial that parents, teachers, and policy makers be aware of this fact. ...
It is misleading ... to promote data literacy and high-school level data science courses as a substitute for learning math content in preparation for college-level quantitative courses. ...
Topics in Algebra II such as logarithms, exponentials, and trigonometry are not relics of the Sputnik era or mere luxuries for future Math and engineering majors. They are foundational across work in quantitative fields including data science, neuroscience, machine learning, statistics, computational biology, and computer graphics.
Algebra II in high school is an essential prerequisite to later learn the further math, such as calculus, needed in much of the coursework for undergraduate data science and statistics majors at campuses of the University of California (UC), the California State University (CSU) system, and private institutions such as Caltech and Stanford University.
A group of African American UC faculty members who teach in fields related to college-level data science wrote a May 2022 letter saying:
Introduction to Data Science’...make[s] claims that they specifically support learning for women and minorities, which are not only baseless, but fail to appreciate that they actually do the opposite and harm students from such groups by steering them away from being prepared for STEM majors.
Brian Conrad, a professor of mathematics and director of undergraduate studies in math at Stanford, pointed out that it was peculiar and misleading that a high-school course would have the same name as a college course, but not be preparatory for that college course. “Who would think that taking a course in high school chemistry would not be useful for chemistry in college?” But these high-school data science courses are not truly college-prep.
Faced with such criticism, BOARS reversed its 2020 decision. It withdrew its authorization of data science as an advanced math substitute for Algebra II and asked that the state board of education remove language linking data science and Algebra II as functional equivalents.
But—and this is an important “but”—the executive director of the UC faculty Senate wrote that the university “will still recognize the existing advanced math courses approved to fulfill the subject requirement,” including data science, “for this year’s applicants to the university.” This sounds temporary, but at UC, a temporary move can all too easily become permanent.
The UC administration has a recent history of ignoring faculty desires when it comes to wokeness and political correctness. Even though the UC faculty carefully studied the efficacy of objective, standardized tests (i.e., the SAT and ACT) in admission and wanted their continued use, the UC administration has done away with them. The administration at first claimed that this was a temporary measure to cope with COVID-19 lockdown conditions. But no-test admission has since become permanent, because, we would assert, tests interfere with and expose backdoor methods of racial preferences in admissions. One might think that data science was by nature not involved with wokeness, equity, and inclusion. But the proponents of high-school data science courses have endeavored to wrap them together. So defenders of serious academic coursework need to stay alert.
While it is admirable to introduce data science ideas at the K-12 level, such as best practices for obtaining, exploring, modeling, and querying data and basic principles of computer science, it should not be displacing Algebra II. Instead of promoting a diluted version of data science that sidesteps the need for algebra, educational policymakers should emphasize the relevancy of Algebra II and its applicability in other domains.
By prioritizing a comprehensive understanding of algebra and its application to statistics, K–12 schools can better equip students for the challenges they will face in college-level data science programs. A strong algebraic foundation not only facilitates a deeper understanding of statistical principles but also provides the necessary prerequisites for calculus, a critical component in advanced statistical analysis.