How do you feel about how math is taught at Michigan?
December 2021
Michigan Math as Perceived by a Math-inclined Student
By: Tuhin Chakraborty and Kristen Boudreau
At first glance, the University of Michigan’s mathematics curriculum, especially the introductory coursework, seems daunting. According to CourseProfile (Atlas), only 9% of students get an A in MATH 115, 14% get an A-, and the grade distribution looks more like a normal distribution than the left-skewed distributions that students are used to. However, after speaking to Robert Buckley—a student in the College of Engineering who is pursuing a minor in mathematics—Consider learned that the reality of U of M math is more complex. In Robert’s view, lower-level math courses are largely in line with the higher levels of rigidity and difficulty described above, while upper-level mathematics and resources for those exceptionally interested in studying math present a much more open-ended environment.
The structure of introductory math classes is what causes students in these classes to struggle. More specifically, the sheer number of students taking them. During the Fall 2021 semester, 1906 students were enrolled in MATH 115, with a cap of 18 students in each section. Such a high number of students taking the same class, albeit across different sections, does not bode well with regard to professor attention. If a professor is teaching even just one section, with 180 minutes of office hours a week, that leaves less than 20 minutes of one-on-one teaching for each student each week. Robert believes that this is not enough time for most students at this level; when he took introductory math classes, he felt it was hard “to really feel like you have your individual needs attended to.” Less time with a professor equals more time spent trying to teach yourself the concepts, which adds to the difficulty of the class. If you are mathematically inclined or had previously taken the course at some other time in your academic career, this would not be much of a barrier considering you’d be more likely to grasp concepts faster and with more accuracy.
However, if you are not mathematically gifted or have not been previously introduced to these concepts, this would prove to be another real obstacle. According to Robert, the professors jump headfirst into the material—there is little to no review of previous concepts. There is “no hand holding” taking place, Robert described, meaning you are expected to rely mostly on yourself and your peers—who are often as lost as you are—if you’re stuck on a problem or a concept. This only makes it more challenging for less naturally gifted math students to do well. However, it is important to note that the individual professors are not to blame. They are “very friendly,” Robert says, and willing to help. But with all these factors working against students in introductory courses, he adds that it is not abnormal for one to feel “intimidated.” Such intimidation could “for sure” be considered a technique to weed out students not math-inclined.
This starkly contrasts the way upper-level classes are taught. When Robert discusses his experiences with these courses, he mentions that students are “working a lot more directly one-on-one with the professor.” This is because upper-level classes are taught using “inquiry-based learning,” also known as the flipped classroom model. In this model, students are expected to watch lectures and complete readings before attending class. Then, in class, students work in groups to complete problems related to the concepts they learned at home. By structuring classes this way, professors are able to provide one-on-one help or smaller-group help in class as students are applying what they’ve learned. It allows professors in upper-level math courses to create a more supportive environment by catering to students’ individual needs, quite the opposite from the “intimidation” lower-level classes induce.
Additionally, in Robert’s view, the University of Michigan supplements its more engaging upper-level mathematics curriculum with really interesting resources to explore research in the field. Robert is a member of LogM, a university program that allows him to do inquiry-based learning beyond class, work with faculty on their research projects, and actually produce written literature as part of such projects. Robert believes that the University could do more to make extracurricular opportunities such as these, inquiry-based learning, and discussion-focused classes available to more students at the lower course levels. Despite this, he considers his work so far very rewarding and is satisfied with his experience studying mathematics at the University of Michigan.
Why does it feel like Rocket Science?: Learning Math as a Non-math Major
By: Aratrika Ganguli and Kailyn Simmons
A senior majoring in political science and minoring in PitE (that stands for Program in the Environment, for anyone wondering), Sam Burnstein would probably not be the first person to talk to about questions about math courses here at Michigan. But, even if math is not his main area of study, he does have some experience with the University of Michigan’s math program, an experience that many non-stem majors share. As an aspiring economics major and eventual political science major, he only had to complete two math courses during his four years of college: Calculus 1 and STATS 250. The reputations of the courses, resources available to students, and these courses being degree requirements all heavily influenced Burnstein’s experiences with these two classes.
In high school, Burnstein completed the rigorous International Baccalaureate (IB) program. At the end of his high school studies, he took the standard IB mathematics test, which did not grant him credit through the University of Michigan. As an aspiring economics major, he knew he needed to complete Calculus 1 as a prerequisite for the major, but he had heard about how challenging the mathematics curriculum was at U of M from other students. He decided instead to take another route: taking Calculus 1 at a local community college. Many UM students choose to take Calculus 1 and 2 at community colleges because of the conversations they’ve had with friends who have already struggled with the courses and the fear of how their grades might be negatively affected once enrolled. His other experience with math came from STATS 250, a popular required class for many majors at the university. Burnstein viewed this course much more positively than Calculus 1, citing STATS 250’s coursepacks, office hours, and numerous other educational resources as reasons he favored the class.
Students differ in their excitement for introductory mathematics courses often because of their majors. Burnstein mentioned that mathematics has a very different connotation to STEM majors versus non-STEM majors, especially at the University of Michigan. For many of the non-STEM students, taking introductory Calculus 1 and Calculus 2 is “something you simply have to do because it is a requirement for your degree.” Many of these students are simply focused on passing their classes, rather than passionately pursuing the particular subject. On the contrary, he mentioned that he was aware of students who are deeply interested in mathematics as a field of study and have a natural desire to exercise their analytical and computational skills. For these students, Calculus 1 and 2 at the University of Michigan might be a completely different experience. Based on Burnstein’s experiences in the Residential College, he also believes that smaller classroom formats and interactive instructor-student relationships positively impact educational satisfaction in the long run.
With more emphasis on smaller classrooms and an engaging, interactive learning environment, Calculus 1 and Calculus 2 at the University of Michigan may not be as difficult as it really seems. Burnstein emphasized that he enjoyed the STATS 250 course he took on campus because of how structured and established the course was. There was a plethora of resources available, including a coursepack that made the lectures much more smooth for both the students and instructor. Burnstein stated that it may be useful if instructors in the calculus courses established a course structure that is similar to that of STATS 250. Students, especially the non-STEM majors, may find it easier to maneuver through this course when there is continuous assistance from GSIs, instructors, and other peers. With some of these changes implemented within the curriculum, calculus courses at the university can create a more positive, meaningful impact on students, whether they are majoring in mathematics or not. Perhaps had this environment been more present at UM, Sam would have stayed to take Calculus 1 here.
Math classes are something most Michigan students will have to take at one point or another. Challenging students is one thing, but making classes needlessly difficult when simple adjustments could be made to foster more learning is another. Peer input; accessibility to resources; a smaller, more engaging environment––these factors could potentially have big impacts on our math department and transform students’ experiences of math at Michigan from a needlessly difficult program that sets students up to fail into yet another manageable, educational challenge for the leaders and best here at the University of Michigan.
Reflections on the Freshman Math Experience: the Truth about Calc I
By: Alexandra Scheib
When you first arrive at the University of Michigan, a school you likely worked really hard to get into, you expect a tightly run ship, however the math curriculum that awaits is far from smooth seas. Math 115, Calculus I, is one of the most commonly taken classes by freshmen. In the midst of what is already a hard transition from high school to college, freshmen from across the country are tossed into the rocky curriculum of Calc I. For a freshman Biochemistry major from New Jersey (who wishes to remain anonymous) the lack of unanimity from one Graduate Student Instructor (GSI) to the next was apparent and the different levels of difficulty, manners of teaching, and preparedness from high school might affect students later on in their University of Michigan experience.
The term “Michigan Math” is something that freshmen learn really quickly. Whether you’re taking a math class or not, you know who’s taking Math 115, because they are stressed. This freshman observed in conversation with her peers two main things. First, everybody has a different level of math understanding. For her, she had taken Standard Calculus her senior year of High School. Having some basic rudimentary knowledge of calculus, she believes, gave her an advantage over peers that hadn’t had any previous knowledge. On the other hand, she knows students who tested out of calculus by receiving high enough scores on their AP and IB exams.. In this case, they were merely taking the class for a refresher or because it was the easiest way to fulfill their quantitative reasoning credit at an otherwise challenging university. All in all, everybody has really different experiences coming into the class, so can they all be held to the same standards when it comes time to grade the class? Is it an accurate representation of how much you learn in the class if students who have a lot of knowledge do really well and students with no knowledge struggle?
The second observation that she made was that the classes themselves all teach at a different level based on the GSI. Each student taking the class has a different GSI that teaches them the material. The only unanimous method of teaching is the textbook, which costs $50. Each GSI writes their own quizzes and prepares each group of students separately for the final exams, which are uniform across sections. While quizzes are only worth 8% of the final grade, each quiz is different. If you ask a student how they did on a quiz, one might say they got a 60% the other might say they got a 100%. Now, this doesn’t necessarily mean the student who got a 100% is smarter than the former, or that they studied harder. Instead, they took a completely different quiz altogether. Each GSI gives students their own quizzes; some provide extra credit opportunities, some are on basic concepts, and some are really hard on purpose in order to challenge the student, but to factor the 60% and the 100% into the grade as the equal weight even though one was much easier than the other is not equitable.
When everybody is being taught at a different level, it’s hard to use the resources that are provided. There are supplementary lectures, but you have to watch them on your own time outside of class. There are GSIs whom you can reach out to, but these GSIs have their own classes that they’re taking and are often busy. So, it’s hard to establish any good relationships because you might be meeting with a different one every time you’re having trouble. This makes the transition to college hard. In high school, you were taught the material, whereas in college, you have to teach yourself with the provided materials. Additionally, in high school, you knew people who were in class with you already so you could work with your peers. As a freshman at a huge school like the University of Michigan, you might not know the other people taking the class. Even if you do know anyone, it is unlikely that they are in the same discussion section because these are the people who have the same GSI and are following the same curriculum as you. All in all, the lack of unanimity between GSIs has led to unfair practices for students who are adapting to one of the biggest transitions of their lives. Different levels of preparedness from high school and teaching difficulties are having large impacts on how well students do in Calc I, which could potentially harm new students’ futures in math.
-
Special thanks to editor Jing He for facilitating the interview with the freshman
Analyzing the Shortcomings of the U of M Math Curriculum
By: Anonymous sophomore
The University of Michigan’s math department strives not to educate students in the most effective way possible, but instead to prevent unfit students from pursuing degrees in STEM. This image of “weeding” students out may not be apparent from the course descriptions on Michigan’s LSA website. However, using evidence and personal experience, I’ll explain how Michigan excludes certain students from pursuing their desired paths. As a student currently enrolled in Math 215 (Calculus III), I have experienced the rigor of Michigan Calculus firsthand. The majority of people, like me, spend hours each day completing homework assignments and preparing for exams. And while select prepared students may be able to breeze through the Michigan calculus program (Math 115, Math 116, Math 215), these students are likely exceptions to the norm.
Students’ preference to transfer calculus credits from universities other than Michigan exemplifies this notion. Although there are no public statistics or figures available to support this claim, through discussion with other calculus students, it is exceedingly evident that this happens far more in the math department than any other field. And it makes complete sense too. Take a freshman who is interested in pursuing a computer science major and just finished their first semester at Michigan. This student recently finished the rigorous curriculum of Math 115–and now must prepare for Math 116 (Calculus II), a class that is expected to be marginally more time-consuming, and far more difficult. The stress of having to take a more difficult version of a demanding class leads them to look at other options. If you haven’t guessed, this student is me, and spoiler alert, I decided to take Math 116 at a community college. And as far as I’m concerned, the only potential downside to doing so would be a lack of preparation for Calculus III; however, this is far from the reality. Every Calc II “review” concept my professor skips has been extremely clear, and as far as I’m concerned, I’m at no less of a disadvantage than a student who took Calc II at Michigan.
Yet if students can receive the same basic math education necessary to continue their studies from other universities or colleges, why does Michigan choose to make these classes so difficult? The most probable and intuitive justification for creating classes so difficult is to “weed out” incapable students rather than letting them find out they are unfit for a STEM education after declaring a major. While this may appear benevolent, the pitfalls of this strategy far outweigh the rewards. First, passionate students with more specialized skills are far less likely to follow a path in STEM, purely by virtue of the Michigan math department. A physics devotee who may not be well versed in finding complex derivatives could easily forfeit their academic aspirations in favor of classes more beneficial to their workload and GPA. Next, many of the concepts taught in calculus classes are non-essential to the fields some of the students might be pursuing. While a chemistry major might need a basic understanding of some of the problem-solving techniques taught in calculus, I see no reason for them to have to endure a course like Math 116, where most topics become obsolete in their following chemistry classes. Students majoring in a field as diverse as STEM should not be confined to take the same introductory classes . Rather, math should be specialized. Sure, a math major should be expected to succeed in Math 115, 116, 215, and beyond, but should a student interested in Computer Science be subjected to the same strain? Of course not. That’s why Michigan should either refine its math requirements or ease the demands of its existing courses.
Since changing dozens of majors’ prerequisites might be too radical, I contend Michigan should make an effort to raise the average grade of their calculus courses. This can be done through simplifying exams, curving classes more generously, or offering students more extra credit opportunities. However, my ideal solution would involve the redistribution of percentages across course requirement categories. Specifically, rather than exams counting for 75% of a students’ grade– the percentage in Math 116 during the fall 2021 semester–homework, attendance, lab work, and projects should make up at least 50% of their final grade. This solution rewards hard work and incentivizes students to take advantage of more resources–skills that are far more important in the rest of their studies than the actual math. Additionally, students who aren’t inherently talented in calculus can still achieve success in the course despite performing subpar on one or more exams. Finally, students may still be “weeded out,” but only students who are not willing to put in the amount of effort required to continue pursuing a STEM degree. STEM major. Overall, Michigan would greatly benefit from this solution, as they would produce a more dedicated and capable group of students ready to continue their STEM education. In addition to being better suited toward success, Michigan students would also be far less intimidated by calculus courses, and rather than feeling apprehensive, students will enter these classes eagerly and confidently.