In this interview, Yifan Guo, a second-year graduate student studying and teaching mathematics at Brown University, shares her thoughts on California’s push to make their math curriculum more “equitable.” Recently, California ended a years-long debate on reforming the math curriculum to be more equitable in three ways. First, the California Department of Education (CDE) wanted to ban the division between regular and honors tracks in math until ninth grade, at which time students would take a test to be placed into higher level math courses or stay on the current trajectory of their curriculum. Second, they included more diverse names from different backgrounds in word problems to ensure that all students see representation in the math classroom. Finally, the CDE tried to make the state’s math curriculum more applicable to the real world by introducing problems related to issues like climate change and data science into the math curriculum.
Raghav Ramgopal: What are your opinions on traditional math instruction and the traditional math curriculum?
Yifan Guo: In an ideal world, all students would have access to both the advanced and regular math tracks. The goal is to have all students do their best and achieve to the best of their abilities. But if we put all of the students in the same class and maximize the amount of knowledge taught in that class, the end result may not actually benefit all the students since some students may be naturally more inclined to history or other classes. I do like the traditional curriculum in an ideal world where all students have access to them. But it seems like the major con of the traditional model is that there are students who are restricted by their socioeconomic background. I agree that this is a problem, now the question is how do we resolve this issue: take away opportunities from other students so that no one has access to the advanced track? Or is the solution to do more for the lower-income students to enable them to have more access?
RR: I think you kind of answered this question already, but do you think that math can become more equitable?
YG: As someone who grew up in Australia, we have private versus public high schools and middle schools. As someone who grew up in the public school system but who is clearly passionate about math, I do feel like sometimes I wanted to learn more about maths beyond the classroom. My school was unable to offer those resources to me. In comparison, there are private schools—very wealthy schools—in the same city where I’m from. They hire people who have done their PhD or are well-trained in mathematics to be their teachers, so these schools have a lot more resources. Whereas most of my maths teachers probably did a teaching course at university, so very few of them actually were maths majors. From my personal experience, I do think maths can be more equitable. Somehow, if I was able to get the resources that wealthier students were getting in high school, then that would be a wonderful thing.
RR: Do you believe that students should be taught advanced math like trigonometry and calculus in high school? And should this advanced track be introduced early on?
YG: In an ideal world where all students have access to them, I don’t think introducing the advanced track early on can hurt anybody since students who don’t want to pursue the advanced track still have the option of doing the regular track. Those who are more interested in mathematics and those who are considering math as a serious career option can also have the opportunity to learn more math to be better prepared for a future career or for college.
Also, from my experience of tutoring high school students, year seven or year eight is a division line. Before year seven and year eight, everyone feels pretty similar about math. But after year nine, if I ask a student, do you like math? They can pretty much just tell me. It’s almost a black and white answer whether yes, they love it, or no, they hate it. So middle school seems like a crucial period where students form their opinion and attitude towards mathematics. And after year nine, it seems like that attitude becomes quite rigid, and it’s really hard to change students’ opinions from then onwards.
For example, if I talk to an adult and tell them, “Oh, I’m studying mathematics at college,” their response is often, “Oh, why would you do that?” or, “Oh, I was never good at math.” So from adults, we can see many of them view themselves as not good at maths, and they don’t think they’re able to change that—or perhaps they are unwilling to change that. This phenomenon is also happening to the year nine and year ten students that I’m tutoring. It’s almost like after year nine, it’s hard to convince someone who already decided they’re not good at math to change their mindset about math.
So, I think it is very important to have this advanced stream available early on, because it’s early on when you can inspire young students and you can get someone to be interested in mathematics. And for some students who can benefit from the advanced stream, they might find the average stream to be boring and not challenging to them. We really don’t want talented students losing their interest in mathematics because the system is boring them with math that they find not challenging. So yes, I think introducing the advanced stream early on is a good thing.
RR: Do you think that by creating more equity in the math track system, and by introducing new types of problems to the classrooms—with diverse names and about real world topics like social justice and environmental science—that the California math curriculum is becoming too politicized? If so, should math should stay apolitical?
YG: You mentioned a few changes. First, you mentioned that questions are going to use a wider range of names that represent different genders and different cultures. I think that’s a very good thing. That is not political, people’s identity is not a political thing—it is just everyday life. I think it is important for students to see their own identity being recognized in a math textbook. As a woman in mathematics, it is a fact that most of the math textbooks and references that I’m studying right now are written by male mathematicians because, as of right now, there are more of them. I’m not saying it’s a bad thing to have male mathematicians. I’m just saying it’s a better thing to have more female mathematicians as well. So, whenever I see a female author, I do feel a particular connection to that book. And, I believe in myself more when I see these female mathematicians’ works because more people that look like me are out there doing math. So, I think with names it’s such an easy change. You don’t even need to change any curriculum. You just switch, maybe, Bob to Alice, and that will fix the problem. I feel like it’s a very small thing that can make a huge impact, and it’s not about politics, politics, politics. It’s more about people and students having their identity seen in the math world.
About real world applications… I don’t think that’s a political thing either. It’s a lot of work to convince someone to put so much effort into learning something. So introducing these motivations and topics that students can relate to more, I think is great. Maybe the only thing that sounds political is introducing social issues into the setup of questions. I’m not too sure what it will end up looking like. One example I have seen before was about global warming. The temperature is changing at certain rates, and you might want to compute this change given a function of temperature as time goes by. I think that if they’re just stating facts about the world, like just stating the fact that rising temperatures exist, then it’s okay because they’re not offering an opinion—they’re just offering a fact. Having more knowledge does not hurt the student. But if the question includes very subjective sentences that are not really relevant to mathematics itself but is a personal opinion, then I will be hesitant to introduce that into the curriculum. The goal of the math classroom is for students to learn math. But if we want to share our views with students about the world and about politics, it’s important to do so outside of the math classroom.
RR: I see your perspective, thank you for sharing. My next question is: Should California have changed its math curriculum at all to include these new policies, or should they have just left it as it was?
YG: There are parts of this policy that I really like and there are parts that I’m a bit hesitant on. I like changing the names in problems and having more identities represented in the textbook. I also really like including more real world applications and even linking math to data science. About introducing social issues in math problems, I’m going to withhold my opinion until I see how that has been implemented. You also mentioned a shift to emphasize more understanding than memorization. I think that is a good thing, as long as we’re still not neglecting memorization because memorization and understanding come hand in hand. Learning comes in a pyramid, and the pyramid has certain steps. Step one of learning is memorization: You can regurgitate whatever is written as it is. The next step is to really understand the topic. Then you should be able to use this to create answers of your own. It is like using your understanding to come up with something new. There’s more steps to this system, but the fact that this has been phrased as a pyramid tells us it’s hard to get to the next step without the previous step. So, while I think understanding is very important, it is hard for students to understand maths without the foundation of memorization.
Finally, coming back to the first part of the policy change, where we remove the advanced track for students in middle school—I’m not sure if that’s a good idea. This is almost like punishing certain students because of inequality in the society caused by adults. As I mentioned before, in an ideal world, it would be great if all students can have all the opportunities. But we also need to do a reality check: That is not happening right now. So the question is, what is the best thing we can do about it? Well, perhaps we can introduce more outreach programs. Maybe this is something the state government can help the school with.
As we mentioned before, the students that the current program—the traditional program—is hurting are the advanced students in less wealthy schools. Regular students in poorer schools, they have their regular program. Advanced students in wealthy schools have access to advanced programs. I can understand that it would be difficult to force less wealthy schools to hire more math teachers, right? Because, if we force them to hire more math teachers for these students, it might mean that we’re taking resources away from other parts of the school. Keeping students warm is more important. So, on one hand, it’s unreasonable to ask every school to hire more math teachers to teach those advanced courses. You have this socioeconomic inequality—this socioeconomic discrepancy—between districts that are geographically very close. Maybe schools or the state government can roll out programs to give students from less wealthy schools an opportunity to attend some classes in adjacent, more wealthy schools. This way, we’re not putting a burden on less wealthy schools, but, at the same time, we’re giving students the option if they really want to learn more math. The solution is not to take opportunities away from students, but to offer additional opportunities to students who are currently at a disadvantage.
RR: As an educator, what do you believe should be the role of policy and policymaking in creating and crafting a curriculum?
YG: I think it’s so important because every math teacher wants their student to excel. But as I’m teaching mathematics, very often, I’m restricted by the syllabus. I’m not allowed to teach these students what I think the best syllabus is. On the other hand, maybe there are teachers who are not sure how to set up the best syllabus for their students. So, whatever syllabus the experts make is a great resource for them to rely on. Either way, what type of policy the state government is going to come up with will trickle down to and affect the day-to-day learning of a student. So, policymaking is very important in math education.
RR: Do you have any other thoughts on the topic, or anything else you’d like to share?
YG: This tiered system where you have a regular stream and an advanced stream seems like it’s a very common thing, not just in California, but all around the US and all around the world. I know this exists for sure in Australia. I know this exists in the International Baccalaureate (IB) system, and this also exists in the UK. I also know that China has a slightly different system. Having a tiered system is not an uncommon thing in the world. So to help California solve the inequality issue, maybe another thing they could do is to look at what other countries have been doing—how they are teaching and tackling these issues.
*This interview has been edited for length and clarity.