The calculator has replaced the slide rule. Latin is rarely offered in high school. Sentence diagramming has disappeared from most English classes.
Academic disciplines continually evolve to reflect the latest culture and technology. Why, then, are recent attempts to tinker with the high school math canon eliciting such a backlash? Students deserve a chance to learn up-to-date topics that reflect how mathematics is being used in many fields and industries.
Case in point: the debate over including data science courses as high school math options. Data science courses teach the use of statistical concepts and computer programming to investigate contemporary problems using real-world data sets.
The courses have been gaining in popularity, particularly with high school math teachers. They say the more relevant content offers a highly engaging entry point to STEM, especially for students who have been turned off by traditional math courses.
Others say that the courses are in fact detours away from STEM.
The high school teachers remain unconvinced. “It’s just been a pleasure to have an absence of hearing, ‘How am I going to use this?’ or ‘Why do I need to learn this?’ ” Lee Spivey, a math teacher from Merced County, told members of the California State Board of Education at their July meeting, before they voted to make California the 17th state to add data science to its curriculum.
“This course transformed my teaching practices and transformed the lives of many students.Special education, English learners and calculus students worked side by side,” Joy Straub, who taught a data science course in Oceanside for six years, told the board. “Students who had a dislike for math suddenly were transformed into math lovers . . . skilled in statistical analysis, computer programming and critical thinking. I saw many students who never would have taken an AP math course take AP Statistics.”
Despite the enthusiasm from teachers, some university STEM professors in California objected. Their vehement criticism focused on the fact that data science courses were proposed in the state’s math framework as alternatives to Algebra II. Faculty from both of the state’s public university systems went on record opposing the idea that students could take data science or statistics courses to meet university eligibility requirements instead of Algebra II. (They seemingly didn’t realize that a 10-year-old policy already permitted students to take data science or statistics in lieu of Algebra II — though that route is rarely utilized, at least among applicants to the University of California.)
Related: COLUMN: How can we improve math education in America? Help us count the ways
Algebra II, which covers topics such as exponential and logarithmic functions, is a typical university admission requirement. Twenty states consider Algebra II a high school graduation requirement, but about half of those allow for exceptions or alternative courses, according to a 2019 report, the most recent available.
Algebra II is traditionally considered a stepping-stone to calculus, which remains the key to the STEM kingdom. Many believe that bypassing the course risks prematurely closing off doors to STEM.
Critics, however, complain that the course is jammed with topics that are hard to justify as essential. How often do we use conic sections or synthetic division? Even content that is more important — take exponential growth and the very concept of a function — is often weighed down by tedious classroom teaching and rote learning.
At the same time, statistical reasoning and data fluency are becoming indispensable in the 21st century, regardless of profession. Digital technologies are changing everything from fitness training to personal investing. But many students are missing out on this essential learning because so many teachers feel ill-equipped to teach these topics, simply run out of time or bow to the perceived preferences of colleges.
“It’s just been a pleasure to have an absence of hearing, ‘How am I going to use this?’ or ‘Why do I need to learn this?’ ”
Lee Spivey, data science math teacher, Merced County
Interestingly, both sides of the debate cite the importance of expanding access to STEM fields. The standoff reflects differing perspectives about how math is learned, including a tension between content coverage and conceptual understanding.
Algebra II defenders emphasize that the topics are foundational for STEM fields.
However, many students who take Algebra II don’t learn much of the content. And even if students gain proficiency in Algebra II procedural skills, it doesn’t necessarily improve their performance in subsequent college math courses. In college, two-thirds of high school calculus students retake calculus or take a prerequisite course.
Proponents of data science courses say not only is data competency essential to everyone’s future (and to STEM fields themselves) but that the greater relevance the courses provide can actually keep students interested and invested in STEM — including in algebra.
Of course, good content and comprehension are both key to math learning. Ultimately, empirical research is needed to validate how well various paths prepare students for college and STEM success.
That is, states must analyze actual longitudinal data on student progress through different sequences to solve this math dilemma. Surely, both data science and algebra will have some role in the future — likely with some archaic Algebra II content dropped, as proposed by the National Council of Teachers of Mathematics.
Though press coverage — including of California’s recently approved math framework — has emphasized the extremes of the debate, much work happening around the country exists in the more ambiguous middle.
Numerous efforts are underway to update Algebra II. Georgia’s modernized Algebra II course, for instance, incorporates data science concepts. The University of Texas’ Charles A. Dana Center also provides a model for such a course.
Related: TEACHER VOICE: Calculus is a roadblock for too many students; let’s teach statistics instead
Other efforts focus on ensuring that data science courses teach some algebraic concepts. CourseKata’s founders promote using data science courses to teach some basics of Algebra II. So does Bootstrap, a curriculum development project based at Brown University.
Even in California, where friction over how to fit data science into the mathematical canon has been especially public, most students who take the courses also take Algebra II. So do at least 99.8 percent of applicants to the UC system — which may rise to 100 percent, if some faculty have their way in blocking statistics and data science courses from replacing Algebra II.
Such a decision might preserve coverage of traditional math content. But it would dodge the question of how to ensure that the next generation of students has the statistical and data fluency the 21st century demands. The California teachers are right: We can’t defend teaching techniques like synthetic division when students finish high school unable to use data to understand the world around them.
Pamela Burdman is executive director of Just Equations, a California-based policy institute focused on the role of mathematics in education equity.
This story about data science courses was produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for Hechinger’s newsletter.
Perhaps, as Ms. Burdman has stated, “Academic disciplines continually evolve to reflect the latest culture and technology.” However, this article greatly understates the relevance of Algebra II and Calculus to the field of Data Science. The courses that this article is promoting actually compromise fundamentals, so that students come into college unprepared to handle the basics of math, and are unable to pursue the very topic that the class is supposed to cover. https://hechingerreport.org/college-students-are-still-struggling-with-basic-math-professors-blame-the-pandemic/
Brian Conrad has written and spoken at length about this topic, and his recent podcast with Anna Stokke serves as a good counterpoint to the opinion stated here. https://chalkandtalkpodcast.podbean.com/e/ep-15-modern-relevance-in-the-math-curriculum-with-brian-conrad/
I think there may be some confusion between how current courses are taught and their intended content, the California standards adopted in 2013 (see https://www.cde.ca.gov/be/st/ss/documents/ccssmathstandardaug2013.pdf).
For example, Pamela Burdman writes: “Critics, however, complain that the course [Algebra II] is jammed with topics that are hard to justify as essential. How often do we use conic sections or synthetic division? Even content that is more important — take exponential growth and the very concept of a function — is often weighed down by tedious classroom teaching and rote learning.”
Is the concept of a function introduced in Algebra II? According to the California standards, the concept of a function is introduced by the end of eighth grade (see page 55). Notation for functions is introduced in Algebra I (see page of 60 of the California standards). No wonder Algebra II is jammed if earlier topics have been deferred.
“Synthetic division” doesn’t appear in the California standards. Is “synthetic division” being used to mean “division of polynomials”? They are not the same.
Conic sections such as circles (e.g., the graph of x^2 + y^2 = 1) and parabolas (e.g., the graph of y = x^2) are used quite a bit. The unit circle is used in trigonometry. Seeing circles and parabolas as different sections of a cone shows a connection between them. Deriving their equations using the distance formula (a disguised form of the Pythagorean Theorem) shows connections between algebra and geometry, and between equations and their graphs. According to the California standards, this derivation occurs in Geometry (see page 74 of the California standards).
As Burdman notes, many teachers feel ill-equipped to teach statistical reasoning and data fluency. In the California standards, Algebra I, Geometry, and Algebra II have substantial amounts of statistics and probability. The absence of these topics in the classroom may indicate a need for better teacher support in the form of professional development and instructional materials—for traditional topics such as functions and for newer topics such as data and statistics.