Lindsey Henderson hopes to change the conversation about math in her state.
As student math performance declined in Utah and states across the nation over the pandemic, most learning-recovery efforts have looked to shore up basic numeracy and algebra skills. But that strategy is likely to worsen declines in students鈥� understanding of statistics and geometry that began long before COVID-19 became a household world, experts say.
These worsening declines come just as workforce needs for data analysis and graphics skills ramp up.
In Utah, which is set to update its math standards this fall, business leaders have warned that schools don鈥檛 produce enough graduates capable of the data and statistical analyses needed for the technology and other jobs driving the state economy now.
鈥淒ata is the new literacy of 2023,鈥� said Henderson, the secondary-math specialist for the state board of education. 鈥淚t鈥檚 not that [students] just need to know how to calculate something or know the standard deviation of something off the cuff. We need a workforce able to take mathematical questions about the data and know where to go to find the solutions that help solve those questions. Those sorts of skills are the ones that our tech community wants our students to have experience with, specifically in a math classroom.鈥�
The building blocks of data literacy may include familiar concepts like understanding basic coordinates on a graph or visually representing information. But teachers emphasize that it鈥檚 more than that; it鈥檚 also a way of thinking. 69传媒 must learn how to collect and measure data to answer a question, how to describe them, and how to make predictions based on them.
Say, for example, students are asked to help the cafeteria director figure out how much milk to buy. They鈥檇 collect that data perhaps by collecting used containers, and from there discuss: Is one class an outlier, where everyone drinks juice? Do students鈥� consumption patterns change?
Developing this process of thinking about data prepares students for higher math even before they learn the technical terms like median versus mode or confidence intervals, experts say.
If data science does get incorporated into its revised standards, Utah would join California, Georgia, Oregon, and other states looking to rebalance math instruction across K-12. In some cases, though, adding more time for statistics will come only at the expense of geometry, where the push for change has been less insistent.
Statistics and geometry are hardly the only topics getting squeezed in a math curriculum that teachers say is often crowded with too many subjects to teach in any given school year. But the problem is compounded for those topics because they often get bumped to the end of the year. And teachers, particularly those in lower grades, often have less training in how to approach the concepts, making it more likely that students get superficial instruction, if any.
鈥淥ne of the powers of mathematics is the interrelatedness of it, but we often segment pieces of it,鈥� said Trena Wilkerson, a professor of math education at Baylor University and a past president of the National Council of Teachers of Mathematics. 鈥淲e鈥檒l teach this particular thing, and we鈥檒l teach this thing, and then this thing, rather than necessarily looking at the bigger picture. If we could view mathematics from its connectedness, then students as well as teachers would understand more deeply.鈥�
Shrinking focus
In statistics and geometry, student performance has been falling in every grade level, particularly among disadvantaged students. On the National Assessment of Educational Progress, the set of tests known as 鈥渢he nation鈥檚 report card,鈥� the average 8th grader鈥檚 performance fell 16 scale points from 2011 to 2022 in probability and statistics and 9 points in geometry. That equates to a year or more of lost learning, as a 5-point drop on the NAEP scale means students on average performed about six months behind their previous cohort.
Fourth and 12th graders鈥� performances show similar slips. The declines in these two topic areas have significantly contributed to overall declines in math performance on the national assessment since 2013, particularly at the 4th and 8th grade levels, as well as historically low math achievement in the most recent NAEP.
In more concrete terms, the results mean that more than a third of 12th graders participating in the most recent NAEP cannot read a basic scatter plot鈥攁 chart that shows relationships among two variables, like height and weight鈥攁nd 71 percent of all 8th graders cannot tell the difference among median, mean, and mode. Three out of 4 low-income 8th graders can鈥檛 gauge the probability of an outcome or use similar triangles to solve a geometry problem.
鈥淎fter three decades of growth, there鈥檚 been absolute flatness and decline鈥� in the last decade, said Zalman Usiskin, the director of the University of Chicago School Mathematics Project. 鈥淭he prediction has to be that it gets worse from here.鈥�
In large part, student performance in data science and geometry on national and international tests have fallen as schools made space in the curriculum for traditional number operations and algebra.
鈥淚鈥檇 probably put in statistics first, algebra second, geometry third if I had to stack them in terms of life applicability,鈥� said Sal Khan, the founder and head of the online tutoring program Khan Academy. 鈥淏ut in terms of what the [school system] will filter you out on, for better or worse, it has always been algebra skills, and that鈥檚 only gotten worse.鈥�
Policymakers generally attributed the early drop in geometry and data performance on NAEP from 2013 to 2015 to a mismatch between the national test and the recently implemented Common Core State Standards, which moved much of the existing primary school geometry and statistics content to middle or high school grades.
鈥淭he shift of geometry and data-analysis content was made to allow a deeper focus on gateway topics such as fractions, place value, and decimals,鈥� Gregory Camilli, an education psychology emeritus professor at Rutgers University who has studied drops in statistics and geometry performance on the NAEP following the implementation of the Common Core State Standards. Camilli suggested the drop in 4th graders鈥� performance in geometry and statistics was balanced by a small increase in student achievement in number and operations, particularly in fractions, which has been a stumbling block for many students. Improving students鈥� skills with fractions was a key goal of the common core.
Over the ensuing decade, data analysis and spatial reasoning got squeezed further in both elementary and middle school instruction, as teachers in upper grades increasingly contended with more students who didn鈥檛 understand basic concepts in those areas.
It鈥檚 about access and equity in mathematics. You can鈥檛 wait for geometry and statistics until students get to high school, or only a select few can take it.
鈥淭hose standards really are set up to be this very far out vertical progression of learning in [statistics],鈥� said Josh Recio, the director of the data-focused Launch Years project at the University of Texas at Austin. 鈥淎nd so anytime you see units that get skimmed over鈥攚hether that鈥檚 from COVID or whatever reason鈥攖hat鈥檚 going to affect how prepared those students are.鈥�
The timing of the content shift couldn鈥檛 have been worse. The era of 鈥渂ig data鈥� exploded in the 2010s. As a result, statistician and data scientist are two of the projected to be the fastest growing through 2031 by, the Bureau of Labor Statistics. And data-science capabilities more generally have become some of the across fields, including business, science, policy, and even creative arts. Geometry-related careers, such as architecture, computer-assisted-design engineers, and fashion designers, by contrast, are growing slowly or at the average for the economy鈥攚hich has made it more difficult to gain momentum to increase time for geometry.
鈥淕eometry has not been at the center of areas that people studied, but it cuts across all mathematics in argumentation, reasoning, and sense-making that are important to many, many careers,鈥� Wilkerson said.
While common core math pushed data-science and geometry content to higher grades, the Next Generation Science Standards, which were released around the same time, called for students to be fluent and comfortable with data and said that, by the start of middle school, students should begin applying those math concepts in science class. By 2018, when 20 states had adopted the NGSS and another 24 used them as a foundation for revising their science standards, educators and researchers warned of a growing disconnect between middle school math and science.
鈥淚f our students are being assessed on spatial reasoning or probability at 4th grade and even 8th grade in the NAEP, they鈥檝e only had like two years barely looking at it,鈥� said Christina Tondevold, a K-8 math teacher-trainer in Orofino, Idaho. 鈥淭heir time to build their understanding hasn鈥檛 really happened, and teachers aren鈥檛 making it a priority.鈥�
Teachers less comfortable
In part, that鈥檚 because math teachers, particularly in elementary and middle grades, say they are less comfortable with and have less training in how to approach probability and spatial concepts than they do with other kinds of math, like number sense or algebraic thinking. Of those who spent at least some time teaching K-12 math, nearly two-thirds said they had spent a semester or less of their preservice training learning probability and statistics, according to a nationally representative survey conducted this spring by the EdWeek Research Center.
鈥淚 think teachers who love math don鈥檛 tend to go into early or middle school,鈥� said Wendy Lichtman, a math intervention specialist at MetWest High School in Oakland, Calif. 鈥淭eachers go into elementary [education] because they love teaching reading concepts.鈥�
In Utah, Henderson said, new educators need five or more credits in calculus for a math-teaching endorsement but only two statistics credits and one geometry credit鈥攏one of which has to focus on pedagogy. 鈥淎nd so when we鈥檙e talking about what teachers are going to skip, it鈥檚 probably the stuff that they鈥檙e uncomfortable with, which I would suspect is statistics and geometry because they鈥檝e had less experience with them,鈥� she said.
In an EdWeek Research Center survey last fall, 56 percent of teachers said they never cover probability concepts, and nearly 30 percent don鈥檛 cover data representation, even in grades where the topics are part of state standards. Similarly, a quarter to 45 percent of teachers said they never cover geometry concepts such as two- or three-dimensional shapes and how they relate to each other or ways to measure capacity, area, volume, and angles.
This 鈥渂ig hole鈥� in teacher training forces many teachers to rely heavily on textbooks, according to Dashiell Young-Saver, a high school statistics teacher in San Antonio. 鈥淭eachers are, for the most part, one chapter ahead of their students in the textbook and teaching them on the fly,鈥� said Young-Saver, the founder of , a nonprofit that creates interdisciplinary statistics lessons.
When the topics are covered, they tend to be shunted鈥攂y both textbooks and teachers themselves鈥攖o the end of the school year. This means statistics and geometry topics come after testing season for most students, and teachers run a greater risk of running out of time to cover them if students don鈥檛 progress quickly, a common problem after the long months of pandemic school shutdowns.
鈥淓ven if you do have an ambitious teacher in 6th grade, perhaps, who does get to the geometry unit and wants to teach it, they are going to teach the 6th grade content without realizing that some of the students didn鈥檛 get the 3rd grade content or the 5th grade content,鈥� said Julie Booth, a professor of STEM education and education psychology at Temple University and co-principal investigator of the GeometryByExample initiative at the Strategic Education Research Project. 鈥淪o the students may get through that unit, but they don鈥檛 have the appropriate prior knowledge to really be able to learn it.鈥�
Equity issues
Momentum has started to shift back toward data science at the state level. The newly revised California mathematics framework emphasizes statistics and data science, but its push to incorporate more real data and problem-oriented instruction has drawn significant criticism by those concerned it will politicize classrooms and pull attention from pure math concepts.
鈥淚t鈥檚 about access and equity in mathematics. You can鈥檛 wait for geometry and statistics until students get to high school, or only a select few can take it,鈥� Wilkerson, the Baylor University professor, said. 鈥淵ou have to integrate the geometry, the statistics, etcetera, from pre-K through elementary and middle school, so that students are getting a deep understanding of what they need in order to be able to make choices about the mathematics that they take in high school and that they pursue post-high school.鈥�
For example, under current graduation requirements, Utah students should complete high school with three years of integrated math courses, with the final course covering concepts from trigonometry, Algebra 2, precalculus, and data analysis. In practice, though, more than half of students opt out of their final course, even though in order to do so, they must submit a so-called 鈥渓etter of shame鈥� from their parents acknowledging that they will not be college-ready in the subject.
鈥淚t鈥檚 a real problem when you鈥檙e saying 鈥榯his math is important鈥� and students and parents aren鈥檛 seeing it as relevant,鈥� Henderson said. 鈥淥nly 18 percent of students in Utah take calculus in high school, so for the other 82 percent of students, what is their option to take an enriching mathematics course as either a junior or a senior in high school?鈥�
That鈥檚 why 60 high school math teachers across the state are piloting a new course pathway to prepare students for dual college and high school credit in data science and statistical reasoning. Zarek Drozda, the director of the nonprofit Data Science for Everyone, said the pilot courses take a more holistic approach to teaching data and statistics concepts, incorporating data collection, cleaning (or correcting errors in raw data sets) and analysis, technology use, and even discussions of ethics around the use of data and statistics. If the pilot proves successful, a new data-science strand could be added to Utah鈥檚 graduation options and expanded in the state鈥檚 math standards, which are up for renewal this fall.
Utah is among the states in the , a project by the Dana Center at the University of Texas at Austin to develop broader math pathways, particularly in data science, from high school to college.
For example, Georgia rolls out new math standards this fall that integrate 鈥渄ata science statistics鈥� across K-12. This summer has been a flurry of training for teachers in how to incorporate probability and data modeling concepts into different grades and classes from Algebra 2 and geometry to the sciences.
While some content standards have been moved up or down a grade, 鈥減robably about 85 percent of what鈥檚 in algebra is still material that was in the previous course,鈥� said Kaycie Maddox, the director of 9-12 mathematics for northeast Georgia鈥檚 regional education service agency in Winterville. 鈥淪o teachers are not going to Mars to get new math stuff. We鈥檙e doing what is good mathematics; we鈥檙e just looking at it from a different point of view, math modeling instead of being up there lecturing.鈥�
Engaging discussions
Kyle Peterson, asecondary-math specialist for the 85,000-student Alpine school district, Utah鈥檚 largest, said he hopes the state鈥檚 data-science pilot can help push back against the tendency to focus on rote remedial work in response to students鈥� math learning gaps.
鈥淓specially with the pandemic [disruptions], as teachers are choosing their essentials to cover, there are still times where geometry and statistics standards get less of a priority,鈥� Peterson said. 鈥淣ot just in this district, but I think around the nation, kids come in and they sit in rows and take notes, and math is a silent, spectator sport. We need to help teachers shift to focus on student thinking and then facilitate discussions around math.鈥�
Yet leading these discussions is one of the most challenging changes for teachers, Henderson said. Math teachers may have less experience than those of science or social studies in wrangling student debates, particularly if they are grappling with real-life data and problems.
While such conversations can arise in any math class, statistics and geometry lend themselves more frequently to interdisciplinary projects and problems situated in live data. For example, California鈥檚 revisions to its math standards dragged on for four years, in part due to the heated debates over how to discuss social issues, particularly in data-driven math classes.
In Utah, Henderson said professional development will be crucial to getting teachers comfortable with both integrating more statistics content and having more in-depth, organic conversations about math.
鈥淣ot teachers talking at kids, but kids talking to each other mathematically鈥攖hat was something that was really unique and scary to me as a teacher because I was like, what if they talked about the mathematics wrong?鈥� Henderson said. 鈥淎nd it turns out, that鈥檚 important. Being wrong, having ideas, and having a safe space to try to make connections with your peers is superimportant in the learning of mathematics.鈥�
In a June teacher training in Pleasant Grove, Utah, Henderson watched as teachers divided up on either side of the room based on their definition of a trapezoid鈥攄oes it have at least two or exactly two parallel sides?鈥攁nd debate their reasoning.
鈥淲e want our students to be good citizens in their real life. Maybe if we get practice debating about trapezoids, then when we get to the political discussions, it could be a little more civil,鈥� said Anand Bernard, an 8th grade math teacher at Sunset Junior High in the Davis school district, another one of the school systems participating in the Utah pilot, who led the debate exercise.
鈥淗istorically, that鈥檚 how math is developed: through talking with each other, sharing ideas, writing letters back and forth,鈥� Bernard said. 鈥淪ometimes, we鈥檒l be doing a task, and I see like six different methods and then two of them I鈥檝e never even seen before. I can just kind of get blown away.鈥�
Geometry and statistics concepts provide good foundations for exercises like that, Henderson said. 鈥淚f you鈥檙e teaching algebra and geometry, algebra and statistics together, it鈥檚 like double bang for your buck. You鈥檙e teaching both standards and you鈥檙e creating those rich connections between the two strands for students so that they can see that you don鈥檛 just do algebra by itself.鈥�
This story is part of Miscalculating Math, a deep examination of math instruction.
Overview and key data: Advocates say reforms in math teaching are pushing out statistics and geometry and driving a drop in students鈥� math scores. Here鈥檚 what you need to know.
Q&As: Hear three professionals talk about how they use statistics and geometry in their careers.
Handy guide: Find tips, lesson ideas, and free resources for beefing up instruction in statistics and geometry.
Quiz: Test your knowledge of math concepts, and then see how U.S. students fared.
Complete Coverage: There鈥檚 even more to explore on this topic. Check out the complete collection, Miscalculating Math.
