The typical ambitious high school student takes advanced algebra, trigonometry, pre-calculus and calculus. None of that math may be necessary for the vast majority of undergraduates who don’t intend to major in science or another STEM field.
But those same students don’t have many of the math skills that professors think they actually do need. In a survey, humanities, arts and social science professors say they really want their students to be able to analyze data, create charts and spreadsheets and reason mathematically – skills that high school math courses often skip or rush through.
“We still need the traditional algebra-to-calculus curriculum for students who are intending a STEM major,” said Gary Martin, a professor of mathematics education at Auburn University in Alabama who led the team that conducted this survey of college professors. “But that’s maybe 20 percent. The other 80 percent, what about them?”
Martin said that the survey showed that high schools should stress “reasoning and critical thinking skills, decrease the emphasis on specific mathematical topics, and increase the focus on data analysis and statistics.”
This damning assessment of the content of high school math comes from a survey of about 300 Alabama college professors who oversee majors and undergraduate degree programs at both two-year and four-year public colleges in the humanities, arts, social sciences and some natural sciences. Majors that require calculus were excluded.
The 2021 survey prompted Alabama’s public colleges and universities to allow more students to meet their math requirements by taking a statistics course instead of a traditional math class, such as college algebra or calculus.
Martin and his colleagues later realized that the survey had implications for high school math too, and presented these results at an Oct. 26, 2023 session of the National Council of Teachers of Mathematics annual conference in Washington D.C. Full survey results are slated to be published in the winter 2024 issue of the MathAMATYC Educator, a peer-reviewed journal of the American Mathematical Association of Two-Year Colleges.
In the survey, professors were asked detailed questions about which mathematical concepts and skills students need in their programs. Many high school math topics were unimportant to college professors. For example, most professors said they wanted students to understand functions, particularly linear and exponential functions, which are used to model trends, population changes or compound interest. But Martin said that non-STEM students didn’t really need to learn trigonometric functions, which are used in satellite navigation or mechanical engineering.
College professors were more keen on an assortment of what was described as mathematical “practices,” including the ability to “interpret quantitative information,” “strategically infer, evaluate and reason,” “apply the mathematics they know to solve everyday life, society and the workplace,” and to “look for patterns and relationships and make generalizations.”
“Teachers are so focused on covering all the topics that they don’t have time to do the practices when the practices are what really matters,” said Martin.
Understanding statistics was high on the list. An overwhelming majority of college professors said students in their programs needed to be familiar with statistics and data analysis, including concepts like correlation, causation and the importance of sample size. They wanted students to be able to “interpret displays of data and statistical analyses to understand the reasonableness of the claims being presented.” Professors say students need to be able to produce bar charts, histograms and line charts. Facility with spreadsheets, such as Excel, is useful too.
“Statistics is what you need,” said Martin. “Yet, in many K-12 classrooms, statistics is the proverbial end-of-the-year unit that you may or may not get to. And if you do, you rush through it, just to say you did it. But there’s not this sense of urgency to get through the statistics, as there is to get through the math topics.”
Though the survey took place only in Alabama and professors in other states might have different thoughts on the math that students need, Martin suspects that there are more similarities than differences.
The mismatch between what students learn in high school and what they need in college isn’t easy to fix. Teachers generally don’t have time for longer statistics units, or the ability to go deeper into math concepts so that students can develop their reasoning skills, because high school math courses have become bloated with too many topics. However, there is no consensus on which algebra topics to jettison.
Encouraging high school students to take statistics classes during their junior and senior years is also fraught. College admissions officers value calculus, almost as a proxy for intelligence. And college admissions tests tend to emphasize math skills that students will practice more on the algebra-to-calculus track. A diversion to data analysis risks putting students at a disadvantage.
The thorniest problem is that revamping high school math could force students to make big choices in school before they know what they want to study in college. Students who want to enter STEM fields still need calculus and the country needs more people to pursue STEM careers. Taking more students off of the calculus track could close doors to many students and ultimately weaken the U.S. economy.
Martin said it’s also important to remember that vocational training is not the only purpose of math education. “We don’t have students read Shakespeare because they need it to be effective in whatever they’re going to do later,” he said. “It adds something to your life. I felt that it really gave me breadth as a human being.” He wants high school students to study some math concepts they will never need because there’s a beauty to them. “Appreciating mathematics is a really intriguing way of looking at the world,” he said.
Martin and his colleagues don’t have any definitive solutions, but their survey is a helpful data point in demonstrating how too few students are getting the mathematical foundations they need for the future.
This story about high school math was written by Jill Barshay and produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for the Hechinger newsletter.
This article is “right on.” There are far more jobs that use statistics, than use calculus. The number of people who have told me that they took calculus and never use it is pretty considerable. Whenever I hear another math teacher say that they covered all the standards (as opposed to taught them), I know the kids didn’t learn it. Jobs analysis says that the math, of the workplace for 80% of Americans is arithmetic, ration, proportion, percent, and beginning statistics. Forcing most kids onto the calculus track may make math teachers feel good/importrant, but it does not meet the needs of students.
Excellent article. You present the arguments for including more statistical knowledge and the obstacles against instituting more statistics.
Please ask your readers to respond to these questions,
“When was the last time you used calculus at your job or daily life?”
“Worked with any differential equations lately?”
Learning correlation without understanding inner product? Without knowing cosine function?
The real problem is that we teach kids Algebra too late, thus we can only give them all these fancy formulas for the “application” of mathematics. But now, we have ChatGPT, do we still need to teach our students these formulas for data analysis?
I will also say that Teachers in high school would expect students coming from middle school to have a solid foundation in essential mathematical skills. Proficiency in the times tables, basic operations like addition, subtraction, multiplication, and division, as well as understanding fractions, long division, negative numbers, and other fundamental math concepts are indeed crucial for success in higher-level math courses.
Less math is not good math and the standard high school statistics course avoids the mathematics almost completely. Real statistics courses are based on calculus and require calculus as a prerequisite for any statistics that is anything but “baby stat”. Don’t buy it. Some will argue that they never used calculus or, on occasion, ever used algebra, as an excuse to avoid requiring it. Avoiding it limits students’ opportunities and, furthermore, the argument is spurious. When was the last time you used ancient history or most of the stuff you learned in college or even just in high school?
PROOF POINTS by Jill Barshay makes several points about data and interpretation. These skills are not math skills at all and are not an appropriate alternative to math. The skills of reading information, summarizing data, interpreting published information, and summarizing and reporting quantitative information in numbers, graphs, and figures, in oral or written form generally requires arithmetic skills that are taught by fifth grade. These skills are part of reading and writing, usually included in language arts. Many school math teachers could teach this; math teachers have no special training or skill in this knowledge. These skills are taught in college in numerous disciplines to students who usually have standard high school preparation. The teaching of these skills belongs across the curriculum, not as an alternative to high school math.
I worked with a very wise high school math department chair years ago who explained why the algebra through precal/calc track was important. It isn’t that we expect every student to use differential equations and integrals in their adult life, but we do expect them to be able to follow a logical set of steps to get from a problem to a conclusion. Reinforcing problem solving strategies through math classes taught across a student’s high school career helps them internalize the process. I have taught statistics at the high school and college level for almost 25 years. They need to become good/discerning consumers of information – especially sources that involve data description and analysis. Focusing a stats course on how the content is used in the real world engages students at all levels.
I am a junior high and high school math teacher her, and overall I agree. The problem I face is that far too many7th graders come to me not knowing how to add or subtract with decimals. They also don’t know their multiplication tables. This makes it very difficult to make sure they can master integers, ratios, proportions, and percent before they finish 8th grade. If my students came to me with a solid foundation from elementary school instead of being passed because they attended school, I could teach them I troductory calculus and statistics by graduation. But all too often I’m teaching students how to borrow across a zero and do long division rather than explaining the difference between mean, median, and mode or how to solve an equation.
The conversation about whether or not we should focus more on statistics instead of calculus misses the elephant in the room, which is that we’re not very successful at teaching students math in general. The people (like me) who defend calculus, do so because if algebra-through-calculus were taught successfully—if people actually understood that mathematical statements are trying to convey meaning and aren’t just symbols to push around—then it would be really easy for them to learn data science. But the problem is that we’re failing at that. I’d also like to add that I learned a lot of data science skills in science class when I was in school: making charts and tables, analyzing datasets to draw conclusions, etc. So stronger science education would also help with the skills deficit in question. We shouldn’t remove half the math curriculum just because we’re failing to teach it. We should encourage people to take statistics, just as a complement to the other math classes and not as a replacement.
The real fundamental issue, is that the majority of elementary school teachers are lacking basic fundamental knowledge and application of math themselves.
All student teachers should be required to demonstrate competency in fundamental math skills through algebra 2 as well as statistics. They should also be required to demonstrate competency in teaching these math skills to others. If they are incapable of either, they should be denied a teachers license. Why are schools sticking our students with incompetent teachers is beyond me? But we should sue the schools and the teachers for failing our kids.