Larry Gordon/EdSource
Cal State Los Angeles instructor Jennica Melendez leads her Calculus 1 class through a problem about movement and velocity.
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At 8 a.m. in a Salazar Hall classroom, Cal State Los Angeles instructor Jennica Melendez was leading her Calculus 1 class through a lively group discussion about the virtual distance a stationary bicycle rider would cover while changing speed over an hour’s workout. From a projection screen, students studied a graphic showing the curve of the accelerating and slowing pace supposedly set by an aerobics trainer.

The calculation was part of an important lesson in Calculus 1, which itself is extremely important to many students. The course is usually required for anyone pursuing careers in science, engineering and medicine, but it has one of the highest rates of failure and withdrawal across California State University campuses statewide.

With active student participation rather than just lectures, Melendez and other Cal State LA calculus professors are trying to get more students to pass Calculus 1 and qualify for majors in the so-called STEM areas of science, technology, engineering and math. The Los Angeles campus and some others are seeing some success with that new teaching approach. But big challenges remain in teaching calculus — the branch of math that studies rates of change.

At 21 of the CSU’s 23 campuses, at least 20% of students on average in Calculus 1 received D or F grades or withdrew over the past three years, according to an EdSource analysis of data from the schools. Administrators consider “DFW” rates of 20% or higher a matter of great concern. At 10 of those campuses, including Los Angeles, the DFW rates have been 30% or higher in Calculus 1.

Trying to break that pattern, Cal State Los Angeles faculty have changed textbooks and teaching methods, emphasizing “active learning” and class camaraderie over lectures. They have added extra review hours for students and are coordinating material and tests. The aim is for students to “discover things rather than being told things,” Melendez explained.

Since Calculus 1 is among the courses with the highest rates of failure/withdrawal across the CSU, these efforts can have significant consequences, both for students and the entire CSU system.

Failure can mean extra semesters to graduate if frustrated students then switch their majors out of science or engineering. That’s why Calculus 1 is a hurdle for the CSU initiative seeking to improve statewide graduation rates and shorten time to degrees. As EdSource reported, CSU has focused on reducing failure rates in required courses enrolling large numbers of students systemwide.

The failures thwart too many potentially promising scientists and engineers, according to Pamela Burdman, co-author of a new statewide report,  which urges reforms in teaching of college calculus.  California is “missing a huge opportunity to bring in a huge pool of talent to the STEM field – which we can’t afford to do,” said Burdman, who is executive director of Just Equations, a Berkeley-based nonprofit that advocates for improved and more equitable math education.

Calculus success, especially for Black, Latino and other underrepresented students, is “central to ensuring equitable opportunities for the next generation of Californians as well as a thriving economy,” said the report titled “Charting a New Course: Investigating Barriers on the Calculus Pathway to STEM.” It was created by Just Equations and by the California Education Learning Lab, a state-funded grant-making organization charged with improving learning outcomes.

One of the biggest problems is how to build up weak math skills from high school without watering down calculus material or inflating grades, faculty say. Those concerns were heightened given significant declines in recent standardized math test scores for K-12 California students, most of whom spent 2020-21 in distance learning.

CSU Bakersfield reports that 35.5% of students on average have been failing or withdrawing from Calculus 1 since 2018. That is among the worst such outcomes in the CSU system. To help students get over the bumps, the campus now offers more specialized tutoring and recorded online lectures with more class time devoted to problem-solving; class sizes have been reduced for pre-calculus courses, often a prerequisite students must pass.

However, even with extra help, too many students lack basic algebra and arithmetic skills, according to math professor Yangsuk Ko, coordinator of calculus courses at CSU Bakersfield. Some students grasp calculus concepts but then “mess up” in working out equations. “Their mastery of basic algebraic skills is very, very low,” Ko said.

Ko said he hopes future reforms, such as more active learning, will build students’ skills. Campus faculty and administrators “realize that calculus is a bottleneck course, especially for engineering majors,” he added.

One potential issue is the controversial proposal to change the state’s framework for K-12 so that all students take the same math classes through sophomore year of high school, rather than placing some into advanced courses early. Some experts warn that rushing students into high school calculus could be harmful because they need more foundational math. Others object, saying putting all students on the same path means holding back advanced students.

Another problem is the unequal offerings of calculus and Advanced Placement math courses among California high schools, the new state study co-sponsored by Just Equations found. That can result in difficult splits in college classrooms between the ill-prepared and those already familiar with calculus.

At the college level, the report suggests smaller calculus classes; more co-requisite classes, which add an hour or two a week for extra review and homework help; and more active group learning rather than just lectures and tests. It advocates tailoring calculus for majors such as biology, engineering or economics and using more relevant real-world problems.

At Cal State Los Angeles, the 28 students in Melendez’s class were mainly engineering majors who had finished a summer pre-calculus course. The fall course entailed four hours of regular class a week and an extra two hours a week for review. Trios of students stood at the board to present solutions to assignments and, like contestants on a quiz show, received applause. For example, one question involved the changing rates of water levels as a cylinder-shaped swimming pool was being filled up.

Before these course changes, Calculus 1 failure rates at CSU Los Angeles were above 40% in 2018 and then improved in 2020, falling to 17% last summer. The reported drop may not be a reliable indicator, faculty say, because it came during the pandemic when many fewer students tackled the courses. And the switch to online learning might have allowed cheating by sharing answers or looking up answers online.

Still, professor José Mijares-Palacios, campus coordinator for calculus, said he is optimistic.

“I believe if you teach calculus like you would teach a lecture class in a law school, then you will fail,” he said. “Calculus is more like sports, something you learn by practicing little by little, with continuing coaching and working with peers. That is how you learn baseball and how to play the violin.”

Freshman electrical engineering major Alejandro Duran said he was worried at first about Melendez’s calculus class because his athletics schedule too often took him out of high school senior year pre-calculus class. Calculus “is a little scary. It is actually hard and difficult to learn even with all the resources,” Duran said.

Duran, first in his family to attend college, felt the university’s summer pre-calculus course “got me more prepared.” He “struggled a bit” at the start of fall semester but now expects to receive a good grade.

Larry Gordon/EdSource

Cal State Los Angeles calculus instructor Jennica Melendez shows how to estimate areas under curves.

His classmate and fellow electrical engineering major Sergio Arredondo agreed that the summer class bolstered algebra skills and “took my fear away.” Arredondo also praised the vibe of classmates working together for calculus success. “We came in here not knowing one another, and now we all know each other. We know our strengths and our weaknesses,” he said.

At CSU East Bay, calculus failure and withdrawal rates have been cut to 19% last spring from 33% three years before.

East Bay used grants from the National Science Foundation and the CSU Chancellor’s Office to re-envision calculus, emphasizing active learning and faculty collaboration. For problem-solving, examples are pulled from other STEM disciplines as well as “real life.” Professor Jesús Oliver, who is co-leader of a team of calculus faculty, uses rising housing and rental prices as one example of changing rates and acceleration.

Without watering down material, CSU East Bay seeks to create a less threatening atmosphere for students who might be anxious about calculus, Oliver said: “It is possible to increase student success and engagement in a pretty dramatic way.” However, he emphasizes that there is no single “magic bullet.”

Many new Cal State East Bay students “struggle with foundational and essential algebraic skills,” according to CSU East Bay Math Department chair Julie Glass. But rather than shut them out altogether, the reformed calculus classes try to strengthen those basic math skills while teaching the more advanced calculus topics, she said.

For example, an assignment might give separate credit for showing understanding of a calculus concept, setting up and explaining a problem, rather than awarding credit only for the final answer. This allows students to learn from the problem-solving process, she said. “It is not the case that students don’t need to use algebra. Rather, it is not the main purpose of the assessment,” Glass said.  Then students are shown the algebra calculations and how “to rebuild these skills in the context of their calculus class.”

Data journalist Daniel J. Willis contributed to this story.

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  1. Allie Gil 3 months ago3 months ago

    Calculus teachers need to be our heroes, and many of them are already! It’s all about how you present the topic and allow students to try it for themselves one step at a time. However, I do agree that it’s not just all on our calculus teacher but also on all the math teachers leading up to calculus who work to keep students interested in math.

  2. navigio 4 months ago4 months ago

    What happened at the other 2 campuses? Why?

    “Others object, saying putting all students on the same path means holding back advanced students.”

    This would only be an issue if you prioritize time over learning.

  3. Patricia Ramirez 4 months ago4 months ago

    As a high school math teacher, I can see this! We are made by administrators to water down material so we reduce the amount of Ds and Fs. If I taught real Algebra 2 or Integrated Math 3, most of my kids would fail. Same with Pre-Calculus. The kids are coming from years of intermittent math teachers: some middle schools have had positions open for years at a time. So substitutes teach the classes. They … Read More

    As a high school math teacher, I can see this! We are made by administrators to water down material so we reduce the amount of Ds and Fs. If I taught real Algebra 2 or Integrated Math 3, most of my kids would fail. Same with Pre-Calculus. The kids are coming from years of intermittent math teachers: some middle schools have had positions open for years at a time. So substitutes teach the classes. They come to high school with barely enough math sense to solve an equation.

    There is also an attitude of entitlement. They believe they should just get an A rather than work for it. Or, as administrators make us do, allow retakes from the whole semester. This practice makes them think that they don’t have to actively learn mathematics. Homework is not included in their grade so they think “why do it!”

    My colleagues and I are constantly aghast at the practices that are forced upon us. We can’t fail them, make them do homework/practice, then have to allow any retakes at any time. While most believe kids should have a second chance immediately after failing an exam, it has created an apathetic work ethic. We try – but it’s almost as if the rules now are making the kids way less competent. The phrase “It’s what is best for kids “ is so far from the truth.

  4. John Seaman 4 months ago4 months ago

    I’m a retired HS principal who taught math prior to my administrative career. When asked to tutor a grandchild in AP BC Calculus, I needed to relearn the subject. Online “Professor Leonard” of Merced CC is heads and shoulders the best math instructor I’ve ever seen. He is a California resource and should be used. An often repeated statement of his, “Calculus is where students go to fail algebra.”

  5. Eric Ornelas 4 months ago4 months ago

    A problem that I frequently notice, everyone wants to study higher math but don’t want to go through the homework and notes which causes them to fail the curriculum. If you dont practice, you will fail!

  6. Robert L Crawford 4 months ago4 months ago

    Bring back a reasonable amount of remediation and use the summers more as they did here….precalc in the Summer is easier to remember than precalculus in the Spring.

  7. Bernardo Vasquez 4 months ago4 months ago

    My son just graduated from UC Irvine with a double major in Applied Math and Computer Engineering and works at a tutoring firm in Newport Beach tutoring Calculus, Statistics and Physics. His observations are similar as those in the article. Too many students don’t understand basic concepts of algebra, and distance learning due to the pandemic has put many kids even further behind. Maybe we need to ramp up middle school teaching of algebra, so … Read More

    My son just graduated from UC Irvine with a double major in Applied Math and Computer Engineering and works at a tutoring firm in Newport Beach tutoring Calculus, Statistics and Physics. His observations are similar as those in the article. Too many students don’t understand basic concepts of algebra, and distance learning due to the pandemic has put many kids even further behind.

    Maybe we need to ramp up middle school teaching of algebra, so kids are better prepared in high school and beyond for advanced math.

  8. Erik Kengaard 4 months ago4 months ago

    There is a progression, with some overlap and retracing, in math: geometry > algebra > trigonometry > (solid geometry in my day) > differential calculus > integral calculus > differential equations > complex variables > transformations . . . then there are probability, linear algebra, vector analysis, . . . how a student progresses depends on a number of factors, including innate talent. Better identification, understanding and accounting for these factors seems beyond the capability of educators.

  9. John Morris 4 months ago4 months ago

    STEM-turned-business student here. Give examples that look like the homework problems. For instance, if the homework problems all involve cotangents, don’t just give an example that involves sines and expect the student to remember how to make the conversion on top of all the new stuff that’s been thrown at them. Teachers, don’t skip steps in your lectures; it’s sloppy and makes your students’ notes useless when they have to refer to them and can’t remember … Read More

    STEM-turned-business student here. Give examples that look like the homework problems. For instance, if the homework problems all involve cotangents, don’t just give an example that involves sines and expect the student to remember how to make the conversion on top of all the new stuff that’s been thrown at them.

    Teachers, don’t skip steps in your lectures; it’s sloppy and makes your students’ notes useless when they have to refer to them and can’t remember what that stupid trick was. Also, don’t work most of the sample problem in your lecture and then skip the algebraic portion because you think your students should know it already. Review is never a bad thing, especially when new concepts are being thrown out hard and fast.

    Calculus is tricky enough without making it harder than it needs to be. More group work is definitely not the answer; that’s just the blind leading the blind and it adds the complication of chivvying your team members and looking stupid in front of your peers to an already complicated subject.

    Refer to Cengage for the right way to teach a class.

  10. Chris Stampolis 4 months ago4 months ago

    Thank you Larry Gordon for this well-researched article about Calculus 1. Please follow up with the deeper STEM-preparation issue of Calculus 2, 3 and beyond. Engineering majors need math skills way beyond Calculus 1. Science majors need Physics and multiple courses in Chemistry and Biology. There is no way to earn an Engineering degree without advanced math and science course success. Few elementary and middle school teachers have advanced math training, whether … Read More

    Thank you Larry Gordon for this well-researched article about Calculus 1. Please follow up with the deeper STEM-preparation issue of Calculus 2, 3 and beyond. Engineering majors need math skills way beyond Calculus 1. Science majors need Physics and multiple courses in Chemistry and Biology. There is no way to earn an Engineering degree without advanced math and science course success.

    Few elementary and middle school teachers have advanced math training, whether at private or public schools, thus many kids who are highly-prepared in math and science received training from their parents or educational coursework outside of the regular school day.

    Non-STEM degrees have different graduation requirements than STEM degrees. Expanding the numbers of STEM-trained students should be a high priority for the next decades of Californians.

  11. Maya K 4 months ago4 months ago

    I am glad this is being addressed but this is extremely concerning. We *need* more underrepresented students in STEM fields. There was an article a few months from the UK about “racial bias” in medical devices. In particular? ‘Dr Michael Sjoding, from the University of Michigan, who led a study looking at the potential racial bias in pulse oximeters, described the “significant discrepancy” in the device’s accuracy when used on patients with a darker skin … Read More

    I am glad this is being addressed but this is extremely concerning. We *need* more underrepresented students in STEM fields. There was an article a few months from the UK about “racial bias” in medical devices. In particular?

    ‘Dr Michael Sjoding, from the University of Michigan, who led a study looking at the potential racial bias in pulse oximeters, described the “significant discrepancy” in the device’s accuracy when used on patients with a darker skin tone as “a small difference but clinically meaningful”.

    https://www.bbc.com/news/uk-59363544

    This is a matter of life and death.

    Some months ago the transportation secretary was explaining why underpasses were so low in certain areas. To keep minorities out.

    https://www.yahoo.com/now/pete-buttigieg-just-defined-infrastructural-173537746.html

    The NFL for the longest time defined cognitive decline differently between Black and white players making it so harder for Black players to collect damages:

    https://www.nbcnews.com/news/sports/nfl-halt-race-norming-which-assumed-black-players-had-lower-n1269435

    The list goes on (facial recognition technology, etc)

    We need Black, Latinx and under represented voices in STEM to mitigate these issues. Our collective lives depend on all interested in careers in these pathways to have equitable access.

    7 years ago SFUSD being the only district in CA (at least at the time they did this) in removing access to 8th grade Algebra created a “compression” class that they incorrectly call “Precalculus & Algebra 2”

    UC A-G does not recognize it as either advanced math or precalculus : https://hs-articulation.ucop.edu/agcourselist/institution/2035

    It is missing a lot of foundational content, yet this class was created to offer a pathway to 12th grade AP calculus.

    A local group called Families for San Francisco through CPRA (California Public Records Act) requests analyzed the data and found the underserved communities who can’t afford to pay for outside classes or the high school doesn’t have capacity for students to take two math classes in one year are disproportionally reliant on this compression class.

    Full report linked here: https://static1.squarespace.com/static/60412a3a51d4863950d1bdf2/t/616e2f823696906267609f3f/1634611077888/Report-+Inequity+in+Numbers.pdf

    Some schools only offer this compression class and not a full year of precalculus. This article is exhibit A in what happens when students take a class like this in high school thinking they have learned precalculus and will be prepared for Calculus in collage if they decide not to take in high school. They are not.

    I am glad to see CSU is stepping up. K-12 needs to do the same.

  12. Zeev Wurman 4 months ago4 months ago

    Excellent reporting, but seems that a couple of relevant element were, ahem ..., forgotten. 1) The elimination of CSU remedial courses for Freshmen in mathematics and English against academic faculty recommendations some three years back, claimed to show "positive results." https://www.calstate.edu/csu-system/news/Pages/CSU-Remedial-Education-Reforms-Show-Positive-Results.aspx 2) Elimination of SAT/ACT testing for applicants in 2021, to be extended into the future. Against the recommendation of the faculty but, again, CSU Chancellor and administrative leadership knows better than the academic faculty, don't they? https://www.ocregister.com/2021/01/25/csu-extends-elimination-of-test-score-requirement-through-2023/ Perhaps the … Read More

    Excellent reporting, but seems that a couple of relevant element were, ahem …, forgotten.

    1) The elimination of CSU remedial courses for Freshmen in mathematics and English against academic faculty recommendations some three years back, claimed to show “positive results.”
    https://www.calstate.edu/csu-system/news/Pages/CSU-Remedial-Education-Reforms-Show-Positive-Results.aspx

    2) Elimination of SAT/ACT testing for applicants in 2021, to be extended into the future. Against the recommendation of the faculty but, again, CSU Chancellor and administrative leadership knows better than the academic faculty, don’t they?
    https://www.ocregister.com/2021/01/25/csu-extends-elimination-of-test-score-requirement-through-2023/

    Perhaps the floundering of students in calculus are those “promising results” CSU was touting, although I somehow doubt it.

    Replies

    • Beverly Young 4 months ago4 months ago

      You are entirely correct. The Chancellor eliminated remediation for students who needed it as a way to push graduation rates and decrease time to degree. This story is about just one of the many negative results.

  13. Beverly Young 4 months ago4 months ago

    This discussion is incomplete without analysis of CSU’s abandonment of placement exams for rising freshmen. Entry level math skills, no longer assessed or remediated, are critical for success in college level math. That move, from 5+years ago, has an impact on college success, not only in math fields, but in all coursework dependent on academic reading abilities.

    Replies

    • Maya K 4 months ago4 months ago

      I agree. My two children went to the same STEM college in Massachusetts. One is now an electrical engineer and the other is a biotech sophomore. All incoming freshman have to take a math placement test to assess their calculus skills to see which class is the best fit. It doesn't matter if they have Calculus BC, they ask every student to take it. I don't think it's said enough how important it is for all … Read More

      I agree.

      My two children went to the same STEM college in Massachusetts. One is now an electrical engineer and the other is a biotech sophomore. All incoming freshman have to take a math placement test to assess their calculus skills to see which class is the best fit. It doesn’t matter if they have Calculus BC, they ask every student to take it.

      I don’t think it’s said enough how important it is for all of us to understand what we *don’t* know so we can then learn. I worry we’ve become so focused on the finish line we aren’t paying attention to the critical steps along the way.