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Expanding the mathematics pathway to include data science will expand access to mathematics while preparing students to answer important and relevant questions.

 

Over the past year and a half, people all over the world have relied on the findings of public health experts and other researchers to help them keep track of the spread of COVID-19, understand the dangers it poses, and learn how they can minimize their exposure to the virus. And yet, for all those who’ve benefited from the capacity to understand the data, countless others have struggled to do so, and many have been deceived by misinformation and outright lies about the nature of the pandemic, leaving them ill-equipped to protect themselves and their loved ones from harm.

Rarely has it been so painfully clear that citizens need to be able to make sense of the various kinds of data presented every day by the news media, scientists, and other sources. As educators, we must teach our students to do so — not just to prepare them for the next pandemic but to enable them to stay informed about public policy debates, medical discoveries, the economy, the environment, social justice and on and on. In our “post truth” era, it has become more important than ever for young people to learn how to tell fact from fiction, spot those who seek to peddle misleading information, and understand the data presented to them (Engel, 2017; Wineburg et al., 2016; Zucker, Noyce, & McCullough, 2020).

If our schools are to succeed in preparing data-literate citizens, then they will have to begin by rethinking the K-12 mathematics curriculum. It won’t be sufficient just to add a new unit or two to the existing course of study. If we’re serious about giving meaningful attention to data science, that should prompt us to ask a fundamental question: In the 21st century, what kinds of mathematics do our students actually need to learn?

In most countries, schools continue to teach math, especially at the higher levels, as though computers had never been invented (Wolfram, 2020). By and large, children still learn the very same pen-and-pencil procedures their great-grandparents had to learn decades ago, long before the technology revolution (Boaler & Levitt, 2019). But today’s students will never need many of those skills since they will always have access to digital devices that can perform a wide variety of algorithms for them. It would be far better to spend precious classroom time teaching them to do things their computers can’t: to identify real and relevant problems that call for mathematical solutions, develop a model, apply mathematical methods, take advantage of computational power to perform calculations quickly and accurately, and make sense of the results.

Why data science?

By the end of 2020, humans had generated 10 times as many bits of data as there are stars in the universe (Messy Data Coalition, 2020). Yet, many, and perhaps most, secondary school students lack the understanding necessary to analyze and make decisions based on data, even when the data are presented in a relatively simple and straightforward way. For example, one study found that when asked to consider a chart, table, graph, or other visual representation of data, students often focus on individual data points (such as outliers or maximum and minimum values), failing to notice important patterns, trends, or the bigger picture (Konold et al., 2015). Likewise, many students struggle to assess the validity of data presented to them, including scientific facts (Zucker, Noyce, & McCullough, 2020) and political information (Kahne & Bowyer, 2017), and are unable to detect bias in online sources (Wineburg et al., 2016). As a result, it has become increasingly difficult to contain the viral spread of misinformation, which presents a threat to democracy itself (Erickson et al., 2019; Gould et al., 2016; Noble, 2018; O’Neil, 2016).

To solve these problems, wouldn’t it help to ramp up the teaching of statistics in middle and high schools? To an extent, it would. Keep in mind, though, that in statistics classes, students tend to be presented with perfectly clean data sets (Rubin, 2019), which they are then asked to analyze. They might get some information about the origins of the data (e.g., the sample size, who collected the data, and where they collected it), but they rarely get information about how the data were processed and packaged into the format presented to them. In short, statistics classes can teach students how to work with data, but if we want them to be able to look at data critically — asking how the dataset itself might be biased (Erickson et al., 2019) or how it has been manipulated to support a particular argument (Fleming & Wallace, 1986; Huff, 1993; King, 1986) — then we can’t afford to teach statistics alone. Rather, we need to provide dedicated instruction in the distinct, if related, subject of data science.

Youcubed’s “Explorations in Data Science” is an example of a yearlong high school data science course — approved to be taken instead of or in addition to Algebra 2 in California — that addresses the ideas mentioned above and more. This project-based course provides students with opportunities to understand the data science process of asking questions, gathering and organizing data, modeling, analyzing and synthesizing, and communicating. Some of the topics covered include data analysis, sampling, correlation/causation, bias and uncertainty in data, cleaning data, modeling with data (including some machine learning techniques), visualizing data, making and evaluating data-based arguments, and the importance and impact of data in society. Throughout the course, students learn how to use relevant modern technology tools, including Google Sheets, CODAP, Data Commons, and Tableau, as well as how to code in Python using Google Colaboratory. Students leave the course with a portfolio of their data science work that showcases their newly developed abilities and can be shared with future employers or with colleges. They will be well placed to begin data-rich coursework in STEM subjects and beyond.

Expanding interest in mathematics

Because so much of the content taught in K-12 mathematics has not changed for decades, many students struggle to see how the material applies to their 21st-century lives. Incorporating data science into the curriculum gives them important opportunities to see the relevance of mathematics, allowing them to ask their own questions, pursue inquiries, contend with uncertainty, look for patterns, and share what they discover.

Decades of research have shown that when students are given opportunities to make connections between topics and ideas as they learn, they gain deeper understandings and are better able to transfer this knowledge to novel situations (Boaler, 2002, 2015; Boaler & Staples, 2008; Fries et al., 2021). Unfortunately, mathematics is often taught as a series of disconnected facts to be memorized and reproduced, which often leads students to opt out of mathematics courses once they are no longer required.

By creating space for mathematics content that more students find engaging, the K-12 data science movement (see Koh, 2020) has the potential to address several crucial equity issues. Studies have shown that fields that allow individuals to work with others and solve real-world problems bring in more girls and students of color (Diekman et al., 2010; Diekman et al., 2011; Evans & Diekman, 2009; Kesar, 2017). Within mathematics, higher rates of diversity are found in spaces where collaboration and real-world application are the focus (Boaler, Cordero & Dieckmann, 2019; College Board, 2020). Data science learning is inherently connected to the real world because the work does not exist without real-world data for students to explore.

In addition, while traditional mathematics has a long history of sorting students into groups based on perceived ability, data scientists frequently communicate that data science is an inclusive subject, open to all (Ahmed, 2019). There is no one kind of person who is best suited to learn and excel at data science because the skills are so widely varied — they may include math and statistics, computer science, the creation of visual representations, storytelling, communication, and substantive expertise in whatever topic the data informs.

Carving a new pathway

Perhaps the tallest hurdle for the data science movement to overcome is the historic dominance of calculus over school mathematics pathways. In the United States, the mathematics course-taking sequence is designed primarily around a pathway to Advanced Placement Calculus. However, this pathway is wrought with inequities that fall across gender, race, and class lines (Cha, 2015; Lawyers’ Committee for Civil Rights of the San Francisco Bay Area, 2013; Niederle & Vesterlund, 2010; ). U.S. students may be sorted out of this pathway as early as 6th grade, when they opt out of or are prevented from taking the first courses in the sequence that leads to calculus. In some states, only 3.3% of students complete the course sequence by 12th grade (Daro & Asturias, 2019), and of the students who do complete calculus in high school, the majority of them end up retaking calculus or a lower-level course once they reach college (Bressoud, 2017).

Mathematics is a broad field, and there is no reason that higher-level work must focus on calculus. The mathematics of data science — which includes statistics, probability, and algebra — is just as important and provides a different and equally valid pathway for students. Furthermore, the incorporation of data science works to address the many calls for change and updates to K-12 mathematics (see Berry & Larson, 2019, for a discussion of such calls for change) by giving students the ability to apply mathematics, statistics, and computer science concepts in meaningful and relevant contexts — using skills that have become increasingly urgent in our society (Engel, 2017).

There appears to be some interest among STEM leaders in making the needed changes to the mathematics pathway. As part of our K-12 data science work at Youcubed at Stanford University, in collaboration with the Center for Radical Innovation for Social Change (RISC) at the University of Chicago, we convened a group of 50 mathematicians, policy makers, data scientists, and mathematics educators to consider possible changes to mathematics pathways. The group agreed that one of the most important changes needed was the integration of data science into K-12 mathematics (see Spector, 2020).

The growth of data science education

National and international initiatives are well underway to address the growing need for data science education. The Program for International Student Assessment’s 2021 Mathematics Framework includes “Uncertainty and Data” as one of the main content areas that all students should learn (PISA, 2020). And the University of California recently updated its list of recommended high school mathematics coursework to be considered for admissions to include preparation in data science (Johnson, 2020).

This momentum has begun to reach K-12 mathematics in several states and districts in the U.S., too. For example, California, Georgia, New York, Oregon, Virginia, and Washington have released updates to mathematics pathway options for high school, all of which include data science as a third-year mathematics course. Similar efforts are underway in Illinois, Maryland, Michigan, Ohio, Texas, and Utah . In the fall of 2021, Utah will offer a data science micro-credential certification to secondary teachers to train them to integrate data science content into their other courses or teach a data science course.

For K-12 districts, schools, and teachers, multiple organizations, curriculums, and resources exist to support the integration of data science education. Youcubed at Stanford University, RISC at the University of Chicago, Center X at the University of California Los Angeles (UCLA), The Data Center at the University of Texas at Austin, and The Messy Data Coalition are all working to support the rise of data science education at the K-12 levels. Youcubed, for example, has developed an online course called 21st Century Teaching and Learning: DataScience to excite teachers from any grade or subject specialty about data science, to build their understanding of data science content and pedagogy, and to share important resources. Our center at Stanford has also developed a one-year high school course called Explorations in Data Science, with professional development available for teachers who wish to teach the course at their schools. Youcubed also offers free data science units and resources that teachers can use to implement data science into their classrooms.

These efforts show that the data science education movement is rapidly growing, providing hope that more modern and more equitable mathematics education is on the horizon. While we expect this movement for change to be met with resistance from some groups, we believe the events of the past 18 months prove that it is both necessary and possible to move forward with these changes. The global crises presented by the coronavirus, the nationwide movements to address racism and racial injustice, the climate crisis, and the tumultuous 2020 presidential election all served as painful and pressing examples that we, as a society, urgently need to equip every citizen with the skills of data literacy. We cannot address the large-scale societal problems we face today, nor those we will inevitably face in the future, without a citizenry empowered with the necessary skills to read, understand, and make sense of their data-filled world.

References

Ahmed, S. (2019, January 1). Data scientists are growing faster than demand, is it true? ThinkML. https://thinkml.ai/is-supply-of-data-scientists-growing-faster-than-demand/

Berry III, R.Q. & Larson, M.R. (2019). The need to catalyze change in high school mathematics. Phi Delta Kappan, 100 (6), 39-44.

Boaler, J. (2002). Experiencing school mathematics: Traditional and reform approaches to teaching and their impact on student learning. Routledge.

Boaler, J. (2015). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. John Wiley & Sons.

Boaler, J., Cordero, M., & Dieckmann, J. (2019) Pursuing gender equity in mathematics competitions: A case of mathematical freedom. Mathematics Association of America MAA Focus, 39 (1), 18-20.

Boaler, J. & Levitt, S.D. (2019, October 23). Opinion: Modern high school math should be about data science — not Algebra 2. The Los Angeles Times.

Boaler, J. & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside School. Teachers College Record, 110 (3), 608-645.

Bressoud, D. (Ed.). (2017). The role of calculus in the transition from high school to college mathematics. Mathematical Association of America & National Council of Teachers of Mathematics.

Cha, S.H. (2015). Exploring disparities in taking high level math courses in public high schools. KEDI Journal of Educational Policy, 12 (1).

College Board. (2020). Program summary report 2020. Advanced Placement program participation. https://research.collegeboard.org/programs/ap/data/participation/ap-2020

Daro, P. & Asturias, H. (2019).  Branching out: Designing high school math pathways for equity. Just Equations.

Diekman, A.B., Brown, E.R., Johnston, A.M., & Clark, E.K. (2010). Seeking congruity between goals and roles: A new look at why women opt out of science, technology, engineering, and mathematics careers. Psychological Science, 21 (8), 1051-1057.

Diekman, A.B., Clark, E.K., Johnston, A.M., Brown, E.R., & Steinberg, M. (2011). Malleability in communal goals and beliefs influences attraction to STEM careers: Evidence for a goal congruity perspective. Journal of Personality and Social Psychology, 101, 902–918.

Engel, J. (2017). Statistical literacy for active citizenship: A call for data science education. Statistics Education Research Journal, 16 (1), 44-49.

Erickson, T., Wilkerson, M., Finzer, W., & Reichsman, F. (2019). Data moves. Technology Innovations in Statistics Education, 12 (1).

Evans, C.D. & Diekman, A.B. (2009). On motivated role selection: Gender beliefs, distant goals, and career interest. Psychology of Women Quarterly, 33 (2), 235-249.

Fleming, P.J. & Wallace, J.J. (1986). How not to lie with statistics: the correct way to summarize benchmark results. Communications of the ACM, 29 (3), 218-221.

Fries, L., Son, J.Y., Givvin, K.B., & Stigler, J.W. (2021). Practicing connections: A framework to guide instructional design for developing understanding in complex domains. Educational Psychology Review, 33 (2), 739-762.

Gould, R., Machado, S., Ong, C., Johnson, T., Molyneux, J., Nolen, S., . . . .& Zanontian, L. (2016, July). Teaching data science to secondary students: The mobilize introduction to data science curriculum. In J. Engel (Ed.), Proceedings of the Roundtable Conference of the International Association of Statistics Education, Berlin.

Huff, D. (1993). How to lie with statistics. WW Norton & Company.

Johnson, S. (2020, November 9). University of California expands list of courses that meet math requirement for admission. EdSource.

Kahne, J. & Bowyer, B. (2017). Educating for democracy in a partisan age: Confronting the challenges of motivated reasoning and misinformation. American Educational Research Journal, 54 (1), 3-34.

Kesar, S. (2017). Closing the STEM gap: Why STEM classes and careers still lack girls and what we can do about it. Microsoft Philanthropies.

King, G. (1986). How not to lie with statistics: Avoiding common mistakes in quantitative political science. American Journal of Political Science, 30, 666-687.

Koh, Y. (2020, November 11). The movement to modernize math class. Wall Street Journal.

Konold, C., Higgins, T., Russell, S.J., & Khalil, K. (2015). Data seen through different lenses. Educational Studies in Mathematics, 88 (3), 305-325.

Lawyers’ Committee for Civil Rights of the San Francisco Bay Area. (2013). Held back: Addressing misplacement of 9th grade students in Bay Area school math classes. Author.

Messy Data Coalition. (2020). Catalyzing K-12 data education: A coalition statement. https://messydata.org/statement.pdf

Niederle, M. & Vesterlund, L. (2010). Explaining the gender gap in math test scores: The role of competition. Journal of Economic Perspectives, 24 (2), 129-44.

Noble, S.U. (2018). Algorithms of oppression: How search engines reinforce racism. NYU Press.

O’Neil, C. (2016). Weapons of math destruction: How big data increases inequality and threatens democracy. Broadway Books.

Program for International Student Assessment. (2020). PISA 2021 Mathematics Framework. Organization for Economic Co-operation and Development.

Rubin, A. (2019). Learning to reason with data: How did we get here and what do we know? Journal of the Learning Sciences, 1-11.

Spector, C. (2020, March 3). Bringing math class into the data age. Research Stories. Stanford Graduate School of Education.

Wineburg, S., McGrew, S., Breakstone, J., & Ortega, T. (2016). Evaluating information: The cornerstone of civic online reasoning. Stanford Digital Repository.

Wolfram, C. (2020). The math(s) fix: An education blueprint for the AI age. Wolfram Media, Inc.

Zucker, A., Noyce, P., & McCullough, A. (2020). JUST SAY NO! Teaching students to resist scientific misinformation. The Science Teacher, 87 (5), 24-29.

ABOUT THE AUTHORS

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Jo Boaler

JO BOALER is the Nominelli-Olivier Professor of Education at Stanford University and the author of Limitless Mind: Learn, Lead, and Live Without Barriers .

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Tanya LaMar

TANYA LAMAR is a Ph.D. candidate in mathematics education at Stanford University.