Project-based math education
Math education faces a significant crisis. Recent results from The National Assessment of Educational Progress (NAEP), a test mandated by Congress, reveal a concerning decline in student math scores over the past two and a half years. These findings offer a measurable insight into the educational disruptions caused by the pandemic and its impact on student learning in math. In response, educators and administrators are actively seeking strategies to enhance math performance among students. These strategies aim to increase educational equity, make math more appealing to students, or modernize it to address the requirements of a growing interest in data science. One of these promising solutions, authored by professors in the Life Science department in UCLA, has shown great promise amongst students. The course which received glowing student reviews teaches students math through the use of real-world problems.
Sharp Declines In Math
The 2022 NAEP test results show plummeting scores for math. In fact, average fourth and eighth grade math scores fell for most states between 2019 and 2022. Fourth graders fell five points nationally since 2019. Eighth graders fell eight points. More students are considered below basic level in math. For example: In 2019, 31 percent of eighth grade students were considered below basic level. In 2022, post-pandemic, that number has climbed to 38 percent.
Peggy Carr, the NCES Commissioner and one of the people in charge of the assessment, said that the decline in the national average scores was the “largest ever in mathematics.” Education Secretary Miguel Cardona, in a briefing with reporters, called the results “appalling and unacceptable.” Daniel McGrath, acting NCES associate commissioner for the assessment, noted that eighth grade is a gateway to higher math and that the learning loss could “alter the trajectories” of students who might find themselves shut out of careers in math, science and tech if the trend doesn’t change.
In response to declining math test scores and in efforts to ignite students’ interest in math, the California State Board of Education has adopted a new, albeit controversial, math framework. This framework, now being considered by other states, aims to make math education more culturally responsive and inquiry-based. However, its approach has sparked nationwide protests from parents. The controversy stems mainly from the framework’s emphasis on statistics and computer science over calculus, and its recommendation to postpone teaching Algebra I until ninth grade. Algebra I is often seen as the foundational course for high school math and a crucial stepping stone towards calculus. Critics of the framework accuse it of sacrificing academic rigor in favor of ‘wokeism.’
In contrast to this contentious approach, a more subtle yet impactful transformation is underway in math education. This alternative revolution doesn’t seek to discard calculus; instead, it aims to modernize how it is taught. By embedding calculus instruction within the context of real-world problems, this new methodology is designed to make math more accessible and relevant for students. Proponents of this change believe that by transforming the way calculus is taught, they can make the subject more approachable, thereby increasing students’ likelihood of success in their math studies. This approach represents a shift towards an educational model that balances traditional mathematical rigor with practical applications, aligning math education more closely with the needs and interests of the 21st-century learner.
The UCLA Life Science Department Calculus Course
Approximately a decade ago, UCLA conducted an internal review of its ‘Calculus for Life Science’ course and uncovered some concerning trends. The course was not resonating with students, inadequately preparing them for STEM careers, and was disproportionately disadvantaging women and minorities in the life sciences department. This review initiated a thorough revision of how the university’s life sciences department approached math education, culminating in the creation of a new course: Mathematics for Life Sciences, also known as the LS 30 series.
With the digital revolution sweeping across science, the need for biology students to understand math concepts has become increasingly important. The professors at the department felt that the traditional math curriculum was uninspiring to students, that the classes offered few useful examples from actual biology, and it left students without an understanding of the importance of math for their chosen field.
Implementing the new LS 30 series course was challenging, but the department’s efforts were rewarded with remarkable outcomes. Over the past five years, the course has witnessed consistent growth, as highlighted in a study published in February 2022. This study’s data reveals a notable shift in demographics: 72 percent of the enrollees were female, 31 percent came from socioeconomically disadvantaged backgrounds, and 32 percent belonged to groups historically underrepresented in STEM fields. These figures not only showcase the course’s growing popularity but also its role in fostering greater diversity and inclusivity in STEM education at UCLA.
A New Calculus
To professors in the Life Science department, traditional calculus coursework is totally outdated. It’s about memorizing formulas and using paper-and-pencil techniques that have not been cutting edge in this century. To a large extent, that pushes minorities and women out of STEM, because they may have had less experience in traditional math before arriving at college.
In contrast, the revamped Life Science calculus course emphasizes practical modeling grounded in biological contexts. For instance, it explores complex topics like the feedback dynamics within shark and tuna populations. This course is designed with the assumption that students have no prior background in calculus. It strategically focuses on the essential programming and mathematical concepts required for practical and realistic modeling in biology.
The new program seems to have instilled confidence in students about their quantitative skills, as well as motivated them to pick those skills up by grounding lessons in problems they cared about solving. In short, it also helped to answer that commonly asked “why even bother learning this?” question.
Interest in the Program
Several universities are considering adopting UCLA’s pioneering approach to math education. Harvard, under the leadership of Brendan Kelly, Director of Introductory Math, is exploring the possibility of offering similar courses to high school teachers and students in its summer school program. Likewise, the University of Arizona in Tucson, a notable public institution, has already started teaching a variant of UCLA’s LS 30 course.
However, this shift in math teaching methodology is not without its critics. Mario Bonk, Chair of the Math Department at UCLA, expresses significant reservations about replicating this model nationwide. His main concern is the course’s heavy focus on biology. He fears that students who later shift away from life sciences could find themselves inadequately prepared for other fields.
Despite his concerns, Bonk acknowledges the importance of modernizing math education. Integrating real-world examples into calculus, he agrees, can motivate and engage students. But, he emphasizes the importance of retaining core mathematical concepts within the math department. While the course excels in teaching biological modeling, Bonk argues it may fall short in imparting fundamental abstract mathematical principles.
In contrast, the Harvard summer program, which convened about two dozen college educators for a week-long workshop on pedagogy, mathematics, and its application to biological problems, has shown more adaptability. The program’s participants believe that revamping calculus teaching can make the subject more accessible and pertinent to students, thereby increasing their chances of success in mathematical studies.
How to Practice the New Calculus
The course provided teachers with insights into the application of ‘physics-based simulations’ in Hollywood, illustrating how such techniques are utilized in popular animations like ‘Frozen,’ ‘Brave,’ and ‘Toy Story.’ Examples include the realistic depiction of characters walking through snow and the dynamic movement of curly hair. These examples served as a bridge to demonstrate the connection between complex mathematical concepts and their practical applications outside the academic realm. Additionally, the course delved into more technical realms, such as the mechanics of ‘cardiac defibrillation’ – highlighting how electrical pulses ripple through the heart.
The facilitators of the training aim to equip college instructors to become proactive ‘advocates’ of this teaching approach. They want these educators to confidently present and justify the robustness of this method in teaching calculus, especially to those in other scientific fields who may be skeptical. This initiative is seen as just the beginning of what they envision as a transformative shift in academic teaching methods.
In the end, the dream is to have similar courses that integrate calculus concepts in life sciences, economics, social sciences, physical sciences and engineering taught at colleges and high schools.
Practicing With Students
The training program also included practical exercises for the educators, where they planned, observed, and conducted classes rooted in these innovative methods, engaging with high school students participating in a summer camp on campus. This approach was designed to give educators first-hand experience of these new teaching techniques in a real classroom setting.
The high school students had an initial taste of applying these methods by analyzing COVID-19 mortality rate data, interpreting its implications for public policy. Working in groups, they pondered over everyday scenarios like their morning routines. A common task like ‘brushing teeth’ became a springboard for exploring mathematical concepts. They used this simple activity to model the effects of toothbrushing on plaque growth, later extending their analysis to more complex ideas like vector spaces and differential equations.
To make the subject matter less daunting, instructors coined the term “change equations” as a friendly alternative to more technical terms like “differential calculus.” This approach aligns with the belief that these classes maintain the rigor of advanced mathematics while reducing the associated anxiety.
In this educational model, students are first introduced to the practical application of equations, creating a context and sparking curiosity. Traditional teaching methods often start with presenting rules and theories, leaving students to wonder about their real-world relevance. Here, students first encounter the problems they will address, with the relevant mathematical equations introduced subsequently, capitalizing on their piqued interest.
The pace of change in math education has been notably slow. High schools often hesitate to alter their teaching methods, largely due to the constraints of college entrance requirements. Conversely, colleges frequently cite the Advanced Placement (AP) calculus curriculum taught in high schools as their reason for not updating freshman calculus courses.
Many educators believe that integrating project-based learning into math is challenging, especially when they need to prepare students for state tests. This dilemma was succinctly expressed by a school principal: “We incorporate project-based work where possible, but ultimately, an algebra class is still fundamentally an algebra class.”
This disconnect between traditional school math, which emphasizes calculation skills for state exams, and practical math, which focuses on problem-solving in everyday and professional contexts, was thoroughly explored by Conrad Wolfram in his 2010 TED talk, “Teaching kids real math with computers.” He pointed out that the application of math in real life and in school environments is strikingly different. In real life, math is a tool for solving practical problems, starting with formulating the right questions, translating real-world situations into mathematical models, using calculations for solutions, and then interpreting these solutions back into real-world contexts, while verifying their accuracy. Schools, however, disproportionately focus on calculations, dedicating about 80% of their efforts to this single aspect of the mathematical process, rather than on developing a more practical and conceptual understanding of math.
Wolfram argued that before the digital age, this emphasis on calculation was necessary due to the lack of alternatives. However, in the era of computers, this focus is less relevant, as computers can perform calculations more efficiently. Additionally, he noted that in the real world, math is not solely the domain of mathematicians; it’s a cross-disciplinary tool used to address everyday challenges. Therefore, the current educational approach, which heavily emphasizes calculation, does not align well with how math is applied in the modern world.