More than a decade ago, when Adrian Mims was working on his dissertation, he uncovered a confusing pattern in Black students鈥� math trajectories in the suburban district he was studying.
While many Black students enrolled in honors geometry in 9th grade鈥攁n on-ramp to higher-level math courses later in high school鈥�60 to 70 percent of them dropped down to regular courses by the middle of the school year.
Understanding why this happened, and how to support Black and Latino students in advanced high school math classes, has guided Mims鈥� work ever since.
Mims is the founder and CEO of the Calculus Project, a national nonprofit based in Massachusetts that aims to increase the number of Black, Hispanic, and low-income students in advanced math courses that lead to calculus.
In its partner districts, the program offers a summer academy for students, tutoring support available through a school-based academic center, and opportunities for students of color to work together in groups and with peer teachers.
澳门跑狗论坛 spoke with Mims about the Calculus Project, how high school math pathways shape students鈥� postsecondary opportunities, and whether alternative advanced courses鈥攕uch as data science鈥攃ould replace calculus鈥� place as the pinnacle of high school math. These have been among the most debated questions in K-12 math education circles.
This interview has been edited for length and clarity.
Tell me about the Calculus Project program.
The [first component] is preteaching students the math, before they go into the class, really accelerating their learning, starting with rising 7th and/or 8th grade, and building the program from middle school all the way to high school. For students to be on a trajectory to taking calculus their senior year, they need to be in algebra in 8th grade.
What a lot of schools do, if students are taking algebra in 9th grade, they end up doubling students up in math courses, which is something we鈥檙e totally against, because it really doesn鈥檛 work. It鈥檚 a deterrent for a lot of kids, because now on top of all of the other courses, now you鈥檙e thrown in an additional math course. We know that there鈥檚 a better way of doing that, so that鈥檚 one of the reasons why we do this work.
We teach students how to work collaboratively in groups鈥攈ow to support one another, give them challenging problems to solve. It鈥檚 not just seat work, where the students are learning the math ahead of time. It鈥檚 really changing their hearts and minds about math.
We do that also with our second component, which is the Pride Curriculum, where the students learn about the contributions and achievements of STEM professionals of color. They can learn about them through documentaries that we share with the students, through literature, and sometimes by bringing in actual STEM professionals of color in person to speak to the students and answer their questions.
In addition to the Pride Curriculum, we put students in cohorts. That鈥檚 one of the reasons why we teach them to work collaboratively in groups, so that when the school year starts, we populate them in the same sections of honors and advanced-level courses, so that they can support one another.
This is really huge in suburban districts, where you might have 20 percent of the school population that identify as Black or African American or Hispanic. But then when you look at the honors and advanced-level courses, you barely see 1 percent of them represented in those courses. One of the reasons why a lot of students don鈥檛 like to take those academic risks is they don鈥檛 want to be the only one. That sense of belonging is very powerful.
One researcher, Dr. Signithia Fordham, coined the phrase 鈥渞acelessness,鈥� where students would sometimes deliberately underachieve to drop down from a higher-level course to a lower-level course to satisfy their social needs to be with students who look like them. In [the Brookline schools in Massachusetts], it was so powerful, we would lose 60-70 percent of students who are identified as Black or African American.
When we taught them the theorems and the postulates that they needed to know to be successful, to write the two-column proofs in geometry honors, and had them working in groups, and then populated them in the same sections, literally not one student withdrew. It dropped down to 0 percent. So we knew that we were really on to something.
Can you explain why creating a community is so important?
It鈥檚 personal for me鈥攎y own personal experience, as well as the research supports it. I鈥檓 first generation in my family to go to college, and I worked two jobs while I was in college. One of the things that I wish I had known before I鈥檇 gone off to college was the importance of developing study groups.
If you go on college campuses, and you go to the engineering buildings, you go to the health science buildings, you go to the libraries, you see students studying in groups. And too often, in particular, students of color would study in isolation. Uri Triesman at the University of California, Berkeley, one of the people that I included in my dissertation research, [he found] that Asian students were outperforming all other groups鈥攂ut , and they had built community, and they had built teams.
Imagine if we can instill that mindset with students as early as middle school, the importance of working in teams and collaboration. When they go off to college, they鈥檙e not going to only have the requisite knowledge and the skill set within mathematics, they鈥檙e also going to have the survival skills to boot.
Sometimes when you are the only one in a course, whether you might be the only girl in a course, or the only student of color, you don鈥檛 want to ask too many questions, because you don鈥檛 want people to think that you don鈥檛 belong there, that you鈥檙e asking a stupid question, right? But if you鈥檙e there in an environment with people you know, and people who are your friends and people who are part of your study team, then it gives you a little bit more confidence and allows you to be a little bit more vulnerable and ask those questions that you need to ask.
I want to ask about the idea that the math courses students take early on can really affect what they鈥檙e able to do later in high school. How do those trajectories shape our school system?
Schools are really set up to sort students based off of perceived ability. How well did they perform on these state tests? What is it that I believe that they鈥檙e capable of doing based off of my interactions with them?
When course recommendations are made for students, they are made halfway through the school year, so that whoever鈥檚 in charge of creating the master schedule can set up the sections and the scheduling. Often, what teachers do, they鈥檒l say, 鈥淥kay, in order for this student to be recommended to stay in the honors track, they need to get at least a B+ in my class.鈥�
Let鈥檚 say halfway during the year, the student has a C+. The teacher may say, 鈥淲ell, the student didn鈥檛 reach my B+ threshold. I鈥檓 not going to recommend them to stay in this honors level.鈥� If the student at the end of the school year ends up with an A-, how many teachers go back and change the course recommendation? Even if they do change the course recommendation, how flexible is the master schedule, to allow those students to be added to another section? It really becomes an issue of supply and demand as well, because you may not have enough teachers who can teach an honors level course. You might not have enough seats in there.
When we work with schools, we work with them to come up with creative solutions to avoid these types of things. One of the reasons why we do the preteaching during the summer is to prepare students and to provide the evidence and to let the teachers know: If you鈥檙e having doubts as to whether a student should move up a level into an honors level course, we want you to err on the side of moving them up a level, knowing that they鈥檙e going to work with us during the summer, instead of err on the side of putting them in a lower level course.
If you鈥檙e a student who doesn鈥檛 take algebra in 8th grade, then you enter into a time crunch. You can鈥檛 get to calculus at the end of high school unless there鈥檚 some change to course progressions. What are some solutions?
It鈥檚 interesting, because some people think that teaching algebra in the 8th grade is acceleration. But they don鈥檛 recognize that doubling up on kids in math, that鈥檚 also a form of acceleration too.
There has to be a stronger vertical alignment of what is taught and when it is taught starting as early as kindergarten鈥攎aking sure that when students don鈥檛 understand some of the basic fundamentals and skills in math, that those skills, those deficits are immediately addressed, right then and there.
To give you an example: When I was teaching math full time, I taught a senior math class. These were not the strongest students, but they were going to go off to college, and probably ended up taking a College Algebra course as their first course. I鈥檓 dealing with seniors who can鈥檛 even perform operations with fractions. How is it they got from elementary school all the way to 12th grade and they still can鈥檛 divide fractions or multiply fractions?
These are some of the things that I鈥檓 talking about that we have to make sure that we address. It makes it easier to teach students algebra in 8th grade. When you just all of a sudden just say, 鈥淲e鈥檙e going to go into this district, where students have been struggling from kindergarten all the way to 12th grade, and we鈥檙e just going to teach algebra in 8th grade,鈥� it鈥檚 understandable why there鈥檚 a lot of pushback. You can鈥檛 just implement that course in the 8th grade in a district where students have been struggling significantly. You have to build up to that, because math is very comprehensive.
We need to make sure that we鈥檙e spending the right amount of time, resources, and support to make sure that these students have the fundamentals down in the earlier grades. When they do, it鈥檚 a lot easier to incorporate prealgebra in the 7th grade and algebra in 8th grade.
There鈥檚 an idea in math education that subjects like data science can be an alternative to calculus depending on what students want to do after high school. Some states have reorganized math pathways this way. In this landscape, why is calculus still so important?
One of the things I鈥檓 always curious about is when people say data science, what is a data science course? When I look at it, I鈥檓 looking at probability and statistics. And in schools that I see doing a really good job educating the majority of their students, they鈥檙e integrating a lot of the same topics into some of the traditional math courses, so that students get that experience.
I think the language needs to be tighter, and it needs to be very clear. What is it that you mean when you say data science? Because if you鈥檙e saying that students who take these data science courses are going to become data scientists, I want people to rethink that. You don鈥檛 become a data scientist without taking at least one Calculus course when you鈥檙e in high school.
It鈥檚 almost as if we say that we want to have more physicians, and we鈥檙e going to teach a premed course in high school. That sounds really exciting. Wow, kids in high school can take a premed course. But then you walk in and you see kids using ace bandages and Band-Aids, taking someone鈥檚 temperature. That鈥檚 not premed.
There are a lot of school districts who are really struggling trying to figure out how to raise math achievement. Throwing them the notion that the reason their kids aren鈥檛 doing well is because they鈥檙e not teaching them data science, I really have a problem with that. Because the students that I鈥檓 seeing who are thriving and doing really well, the students who are at the top of the achievement gap, they鈥檙e not taking data science courses. Why are we creating a pathway for kids at the bottom of the gap that鈥檚 drastically different from the students who are achieving at a higher level?
The other concern that I have is that K-12 doesn鈥檛 dictate higher ed. Higher ed. dictates what happens in K-12. College admissions folks are still looking at students who have taken the most challenging courses, which is one of the reasons why when they see AP Calculus, AP Statistics, and high school calculus on a student鈥檚 transcript, to a lot of admissions folks, that translates into a student graduating within four to six years. That means a student can handle rigor.
I鈥檝e been doing this work since 2009. I鈥檓 looking at my students who鈥檝e gone through calculus, some of whom are first generation. I鈥檓 looking at all of the scholarships and opportunities that they are receiving because they have calculus. I鈥檓 looking at all of the doors that are opening for them. And I know that that system still exists. So why should we change our approach at the Calculus Project?
The system that I went through is still in existence today, even though some colleges and universities are trying to change their language. I鈥檇 love to see colleges and universities be a lot more transparent, and share acceptance data. Even though they say, 鈥淎 student does not have to take calculus,鈥� it doesn鈥檛 mean that they don鈥檛 prefer that a student does. If you say that you don鈥檛 necessarily require students to take calculus, okay, well, can we see some of the data of the students that you selected? What percentage of students that you selected to your school didn鈥檛 take calculus?
It鈥檚 that lack of transparency that doesn鈥檛 give me a whole lot of confidence in some of the things that people are saying around data science. The system that we have right now is really designed to sort students, not to be very inclusive. Lowering expectations, for me, that doesn鈥檛 equate to equity.
