Comment due on the OpenLab Sunday, November 1
“I’m bad at math.”
Everyone on earth, probably
Contents
Background
“I’m bad at math.” This is something I’ve heard from a handful of students (in both of my classes) over the last few weeks. It’s devastating to me to hear anyone say this about themselves…let alone my own students…let alone the students who said it…let alone the time at which they said it (in the middle of actually solving a math problem).
Here’s a big secret: I’ve said this about myself. I have a Ph.D. in math. I write math research papers and get invited to give fancy math research presentations. I’ve taught hundreds (maybe thousands?) of students math in my career. And I have said this about myself tons of times over the years.
Here’s another (not-so-big) secret: I’m bad at pushups. I don’t have a Ph.D. in pushups! I can barely do one pushup! I’m, like, definitely, objectively really really bad at pushups! But it doesn’t make me feel bad when I can’t do a pushup. I really don’t care. So what’s different about math?
There is something unique about math: it can make all of us feel bad about ourselves sometimes. The wife of my good friend (who got his Ph.D. in math the same week I got mine) says this: “You mathematicians…if you do understand something, you think it’s because it’s obvious and easy…if you don’t understand something, you think it’s because it’s impossible and you’re too dumb. When do you ever get to feel good about yourselves?” Doing math can be very humbling. (If you’ve never been challenged doing math, let me know and I’ll find a challenge for you.)
There are lots of intersecting reasons that so many people think they’re bad at math, even when they’re not…especially when they’re not. For example, do this right now: do a Google image search for “mathematician.” Scroll until you see someone who looks like you. Can you find anyone? I haven’t seen all of your faces on Zoom, but I’m willing to bet none of you look like this bro:
Assignment
Choose one of the following prompts. Then write a response of at least 5 sentences and drop it in the comments below.
- Read an article on “math anxiety” (for example this one). Math anxiety is a real thing and there have been tons of articles written on it! Summarize the article. What parts of it resonated the most with you? What is a situation during which you remember experiencing math anxiety in your life? Were you able to overcome it? How? Have your feelings about math changed as you’ve gotten older?
- Go back to the results of your Google image search for “mathematician.” Find a picture of a mathematician who looks like you. What is their name? Research this person’s biography and summarize it for us. What did you find most interesting about their life? What is a question you would ask this person about their life if you could?
- Okay, let’s get personal! Have you ever thought, “I’m bad at math,” yourself? Have you ever said it out loud? How often does this thought come into your head? In what circumstances? What do you do when it happens? Have any of your friends or classmates ever said this about themselves to you? What would you tell your friend if they said “I’m bad at math” to you? What do you think makes people think they’re bad at math? What do you do to challenge these thoughts? How can we support people when they feel like this? (Bonus: respond to someone else’s comment on this prompt; be nice.)
As usual, if your response is too long for a comment or if you want to include pictures (especially for prompt #2), feel free to submit your own new post. Use the category Bad at math.
You will earn participation credit for your comment.
Back to pushups
I’ve never been one to enjoy working out. But over the summer, I started doing these “quick workouts” that appeared in a meditation app I use. These workouts are pretty short and not very advanced, but they’re challenging enough for me to do consistently. And guess what…I still can’t do a pushup! Hahahahaha, but I am getting a lot better at the kind of half-pushup where you keep your knees on the floor! At some point, as long as I keep up the workouts, I’ll be ready to graduate to the full-pushup.
So here is one more question for you: why do you think am I talking so much to you about pushups in a math class???
Response to Prompt #3:
I never thought, “I’m bad at math” to myself as I have a growth mindset. Instead, I thought “I couldn’t understand substitution… yet”, “I need help in Trig Substitution”, or even “I’m a little bit behind at math”. However, there is a time where I almost put myself into this situation during Week 1 of Calculus II. Integration by Substitution is an easy topic, but I didn’t understand it completely until Week 5 where we learn about Improper Integrals. I initially thought “Oh no! Integration by Substitution!”, but I was able to relearn this integration technique and I will able to master it. After all, I’m not bad at math at all, but sometimes, it takes a while to master some concepts.
I haven’t heard one of my classmates actually say, “I’m bad at math”. However, if they either say “I’m bad at math”, I would say “Oh no! What topic(s) are you struggling at?”. If they struggle at math in general, I would help them relearn the concepts taught at class, and make them practice problems from the textbook. I really don’t want them to think that they are bad at math. Instead, I will find ways to make them understand math in some way, even if it takes a while. To alleviate the negative thinking of math, tutoring or study groups would definitely help.
Anthony, you hit the nail on the head with your first sentence! Having a growth mindset is so important when you’re facing something difficult. It’s not natural or easy for everyone to think in this way, so it’s really great when we can help each other move away from a fixed mindset and toward a growth mindset. Some of your points were echoed several times by your classmates too: (1) we don’t want anyone to feel like they’re bad at math and (2) sometimes it takes a while to understand. Study groups are great because even if nobody understands something, having the opportunity to bounce some ideas around can help spark an idea that might not have been sparked otherwise AND it can help people feel like they are making progress and not just stuck. Thank you for your thoughts!
Prompt #3
It has never crossed my mind to question myself if I was bad at math. When people asked me if I’m good at math, I always told them that I’m okay at math not good at it. I said that I’m okay, and not good because there are certain concepts about math that I don’t understand. I thought to myself that I will never understand series because there are just so many series tests out there that I have to find to solve a specific problem. When we started learning about series in class two weeks ago, I kind of lost interest because I wasn’t understanding, it and that causes me to be behind with some of my homework. As time goes by and we started learning more series tests, I started to feel more comfortable with series, and solving them didn’t cause me headaches like the first time I tried. I was able to relearn the series technique that I didn’t understand before and become great at it. I can say that I’m not bad at math, but sometimes it just takes a little longer for me to understand certain concepts.
My classmates never said anything about being bad in math. They said that they struggle with it but not bad at it, which is understandable because math can get pretty complicated sometimes. When they say that they’re struggling I take the time to ask them which part of the question they’re struggling with and help them out. We would solve the problem together again and write down every equation that can help solve the problem. Having a group study works well if you’re struggling with math because some members of the group can point out some mistakes that you made without realizing it. I don’t want my classmates to say that they’re bad at math, so I do everything possible to help them solve the problem and to clarify any misconceptions that they might have about math. We are all good at math it just takes some time and effort.
Aaaahhhh Ines I love this: “We are all good at math it just takes some time and effort.” You brought up some of the same points as Yanzu and Aram which I really appreciate. Sometimes (usually) understanding something take a little longer than you think it will and that’s okay. And showing empathy to others when they are struggling or frustrated can really help them focus on what’s important. So well put, Ines. Thank you!
Hello! I googled mathematician and it was just as expected- a lot of portraits you might see in museums or zany looking older men professors. However, a young(er) woman in modern clothing popped up! It was Moon Duchin and though we only look alike as we are both modern living woman with dark hair that was enough for me. After clicking on her photo I was directed to an article about how she was appointed by the Governor of Pennsylvania to help in dividing congressional district maps to prevent gerrymandering.
Moon had been drawn to math from a young age and knew by high school she wanted to be a mathematician. She finished her high school math curriculum by her sophomore year and after that started independant study. Throughout her academic and professional career she has always fought for social justice, for example, by advocating for gender neutral bathrooms and teaching gender studies- while a math major!
Moon has a PHD in math and is currently the director of Tufts College of Science, Technology and Society program. Since 2016 she has dedicated her knowledge of geometry and topology to understand the math of gerrymandering. She developed a program to train mathematicians to become key experts in court cases on the topic, working towards finding an agreed upon standard in order to calculate and better regulate it. She founded the Metric Geometry and Gerrymandering Group (MGGG), whose mission, according to their website, is to “research data science interventions for civil rights.”
Her commitment to social justice and math is inspiring! It is really exciting that she has found a way to apply her interests to solving real world problems that are seemingly more political than math related. If I could ask her anything it would be how (or if) she would change math/stem education in order to help better relate it to its real world consequences.
And lastly, as for why so much talk about push ups- practice! practice! practice! Practice and you will improve.
Katie, I know we talked about this already, but let me say again how thrilled I am that you found Moon Duchin!!! Her work is so awesome. Her gerrymandering work in particular has been really exciting for a lot of my mathematician friends, who’ve taken workshops to become expert witnesses in redistricting trials. A lot of pure mathematicians don’t really expect their work to have relevance in the outside world, so we couldn’t believe it when we suddenly found out that it could be used for such a noble cause. It really energized a bunch of people!
I was saying to Jaquawn, whose research turned up another badass mathematician, Edray Goins, how interesting it is that you and he both found mathematicians who are involved in fights against injustice. I’m so happy you both now know about these remarkable people!
Prompt 1: Math Anxiety
https://www.sciencedaily.com/releases/2019/03/190314075758.htm
The article above discusses the findings of a research into how four out of five adults in the UK during 2014 weren’t math efficient. It was researched that this stemmed from the increased pressure and difficulty in math subjects when transitioning from primary to secondary school (elementary to middle school). I can attest to this hypothesis as I remember the mass difficulty of the subjects as well as the overwhelming work and standardized tests. The study also contributes to this claim of tribulation by claiming that standardized tests and difficult assignments were what made children anxious and uncomfortable with math to the point where they don’t even want to address it in adulthood. I’m certainly one of the poor souls who suffered under math and wish the worse upon it and its creators, however my desire to become an computer engineer gives me the motivation to persevere and seek help instead of whining as I did in middle school. As of right now, math is just a difficult obstacle I need to overcome in order to graduate and get a job.
Aaron, I think you brought up a really important point about standardized tests! During a presentation I went to this week, the speaker brought up how little kids get to play with math and mathematicians get to play with math, but most students do not really get to play. Little kids just *love* counting and discovering new patterns around them. Mathematicians are much the same way, playing around with stuff that they know in order to push themselves to discover something new (this can be frustrating, sure, but it still counts as play). But in between, students have all these high stakes tests and don’t really get a chance to play or explore or wonder. Our class has a pretty strict syllabus and some traditional exams, but what I like about the material is that there is a bit of a chance to play…though I probably didn’t feel like this when I was a student! The integration techniques and convergence tests might seem daunting at first, but as you play around with them and explore what they can do for you, *hopefully* you can find *some* enjoyment in this.
Response to Prompt #3:
To be honest, I would not say, ” I am bad at math to myself “. Perhaps I confuse or puzzle about the new topics. Such as determining if the infinite serious converges absolutely & converges conditionally. Or the elementary matrix in the Linear Algebra. There are general concepts with a few examples so that I didn’t quite understand. In the beginning, I was struggling to catch the main idea. Trying to follow the step which is demonstrated. Sometimes it takes a little longer for me to understand certain concepts. I have to research more detail and example to summarize. There are many videos which are showing specific steps. It helps me clearly understand the concept. I believe that just put more attention and practices will make effort and great in math. otherwise. tutoring or study groups are another choice.
Yanzu, it’s so great that you’ve figured out techniques to help you succeed! You said, “Sometimes it takes a little longer for me to understand certain concepts” and I think that’s true for almost anybody. At some point when I was a student, I realized, “Oh I’m not stupid, I’m just slow. Dang, that means I don’t have an excuse not to do the work!” I think your idea for summarizing concepts can be really helpful so thank you for sharing!
Prompt #3:
Yes, I’ve definitely thought, “I’m bad at math” multiple times in my life and saying it out loud was a must for me, especially when I used to learn about a concept for the first time. I started taking advanced math courses in grade 9, I went to an all private school, thus the severity of competition of who got the right answers was very high. I used to get stressed and start thinking, I’m not meant for all this math stuff, its just too much. At the end I would say, “I’m just bad at it, I’m going to give up.” But then that thought of what am I missing to not reach the end of this question would make try again and again with different approaches. I can say most of my friends have said that they are bad at math. Exam season used to make them think I was a curse they weren’t getting it. I would always tell my friends that it’s not that you’re bad at math, your just bad at knowing where your going wrong. And it’s a fact, half the time we think we can’t do something, all the brain cells we can using to figure something out, we use them to convince ourselves we can’t do it.
When I started off tutoring in math, I realized some people really do struggle to understand stuff we find simple, but its mainly due to the fact that they haven’t either studied the material or they just don’t want to put some effort to learn it. Nothing is impossible so saying I can never do it, is not the way out of it. Putting yourself up to a challenge will help your mind grow, I used to do the same sometimes, so I know how it feels.
Schear, omg I love it: “half the time we think we can’t do something, all the brain cells we can using to figure something out, we use them to convince ourselves we can’t do it.” I wish we didn’t do this to ourselves!!! You mentioned a few instances when there’s a lot of pressure to succeed, like “I need to pass this exam or my life is over,” which I think makes things a lot worse. There are lots of high-stakes challenges that we have to put ourselves through over our lifetimes and we’ll succeed at some and we’ll fail at others, but like you said: “Putting yourself up to a challenge will help your mind grow.”
Prompt #2
Hello my name is Jaquawn and some days I believe I am bad at math. This frustrates me because I am an engineer student and aspiring inventor. Now, I find this prompt specifically interesting because there are a limited amount of mathematicians who look like me. Atleast until I discovered Edray Herber Goins; A mathematician who gave up his position, at such prominent research facilities such as, Stanford University, Harvard, and caltech. He was aware of the lack of diversity in these higher learning math programs and took a job at Pormona community college , to help balance the scales.
Edray Goins achieved his Bsc in Mathematics and Physics at the California institute of technology and His doctorate at Stanford University in the field of “Elliptic Curves and Icosahedral Galois Representations”. He has worked at many prodigious universities.
If I had one question to ask the Doctor , I would ask him if he recalled the day in which he realized he could pursue a future in mathematics.
Ah Jaquawn, if you’re an engineer and an inventor, then you’re *already* good at math. Sometimes you’re doing something mathematical that might not even look like math…like solving a problem by thinking logically…that’s math, even if you’re not using numbers! One time I was talking with a colleague who was worried about her son because she thought he could be good at math but he was too interested in video games. I was just like, “Eh…he’s figuring out how to think logically in order to pass his game, and that’s mathematical too.”
I know we talked about this before, but I want to say again how happy I am that you discovered Edray Goins! He’s such a badass and we’re lucky to have someone like him in the mathematical community. It’s really interesting that you and Katie both discovered mathematicians who are involved in justice work. They’re out there and they’re working hard!
Prompt #3
I believe myself to be pretty good at doing the kind of math you can attach to real-world objects like addition, subtraction, division, multiplication, and I would even include algebra. Now when it comes to more abstract mathematics like Calculus, I consider myself sub-par. The reason for this is that besides dealing with numbers, you also have to work with concepts like infinity, integrals, derivates, or things you can not attach to a physical object to get a better understanding of the subject. I think everyone is at least decent at basic math, but once they reach more complex mathematics they have to also learn new concepts that need to be used with precision and are either not curious/interested enough to learn why and when to use them or are not able to relate them with other things to help them understand. The only advice I can give is to try your best to prevent and avoid distractions while you study and if possible ask someone else for help since they might have a different approach you might be more comfortable with.
Push-Ups
To be able to do consistent proper push-ups you must practice with other easier exercises until you are able to tackle the push-up and once you reach them keep practicing to perfect your form. This is exactly the same thing you must do to learn math so it makes sense you’re talking about push-ups. Exercise your brain like a muscle even though it is not actually a muscle.
Pablo, you’re totally right about the push-ups and exercising your brain! And it’s a good point that some people learn abstract math better when they can how it’s actually used. We don’t have a lot of real-world applications in this class, but I’m working on sneaking more in for the future 😉
There are countless moments where I did say, “I am terrible at math.” It happened a lot in high school where it started to get more difficult with polynomials, expressions, and trigonometry. It just got worse when I took calculus when I began learning derivatives, anti-derivatives, trigonometry substitution, integrations, taylor polynomials, series, etc. I always brainwashed myself that I was terrible at math and easily gave up on problems I had a hard time trying to solve. Especially in college. What I did was give up, take a moment, and then try again by looking at course hubs and other videos that would help me understand math more. I am now convinced that I just have to keep trying and understand that I just need more time and practice to finally get it. Friends and past classmates telling me they’re bad at math themselves is something I hear so frequently, especially during exam seasons. I tried to go over some problems with them to help them understand and help them to pass. I think the reason why people convince themselves they’re bad at math is because they look at a problem that seems complicating and immediately give up. Even when they try to learn, they just don’t understand it at first because everyone’s learning progress and mindset are different. They don’t get it for more than a minute or two and they’ll just give up, and persuade themselves they’re bad at math. I understand them because I’ve been in their shoes countless times before. Even now, there were times where I wanted to give up because calculus was too advanced and difficult for me to get. When I have these thoughts, I challenge myself by keep trying, keep going over review videos, and going over sample problems. People who are going through this situation, I believe we can help them by showing empathy and showing them a way that anyone can understand math. It just requires more time, practice, and more perseverance.
There are countless moments where I did say, “I am terrible at math.” It happened a lot in high school where it started to get more difficult with polynomials, expressions, and trigonometry. It just got worse when I took calculus when I began learning derivatives, anti-derivatives, trigonometry substitution, integrations, taylor polynomials, series, etc. I always brainwashed myself that I was terrible at math and easily gave up on problems I had a hard time trying to solve. Especially in college. What I did was give up, take a moment, and then try again by looking at course hubs and other videos that would help me understand math more. I am now convinced that I just have to keep trying and understand that I just need more time and practice to finally get it. Friends and past classmates telling me they’re bad at math themselves is something I hear so frequently, especially during exam seasons. I tried to go over some problems with them to help them understand and help them to pass. I think the reason why people convince themselves they’re bad at math is because they look at a problem that seems complicating and immediately give up. Even when they try to learn, they just don’t understand it at first because everyone’s learning progress and mindset are different. They don’t get it for more than a minute or two and they’ll just give up, and persuade themselves they’re bad at math. I understand them because I’ve been in their shoes countless times before. Even now, there were times where I wanted to give up because calculus was too advanced and difficult for me to get. When I have these thoughts, I challenge myself by keep trying, keep going over review videos, and going over sample problems. People who are going through this situation, I believe we can help them by showing empathy and showing them a way that anyone can understand math. It just requires more time, practice, and more perseverance.
I feel like taking a step back, even taking a walk, changing your mind and then get back at whatever problem you are trying to solve is helpful. I do that whenever I encounter something I struggle with. I would take a walk, take a deep breath and then try again.
Yessss!! Taking a walk is great when you’re mad and trying to cool off and when you’re frustrated and trying to get a fresh perspective. Excellent suggestion, Imane!
Aram, I love your approach. Showing empathy is important in so many situations where we might not imagine it is at first, like in a math class. Math can feel impossible sometimes, but we’re all humans and a lot of us can understand the frustration because we’ve felt it ourselves. That means that we can also support each other and try to offer help where we can, like your suggestion to try again and again.
During High School I didn’t think I was bad at math, not until I got into college is when I said that I was bad in math. My time during college is where I had the most struggle in math, and I didn’t think I would have that much of a struggle. This doesn’t really come often to my head only when I feel like I can’t understand a topic. I have had one of my friends also say that as well because we both failed a math class before in our time in college. If my friend told me he was bad in math, I would agree with saying that I as well was bad at math, and we would speak on what we are currently having problems with. I think what makes people think they are bad at math is that, they are struggling with a certain topic or problem in math. They can’t figure out a method or solution to work out the problem, so it frustrates the person and makes them believe that they are bad in math. To challenge these thoughts I would just do some research on the topic and try to understand on how to solve the problem.
Kevin, I love your idea for challenging the negative thoughts. It does take perseverance and that can be difficult if you’re trying to understand a math topic *and* juggle negative thoughts at the same time. It hurts to fail, especially if it’s at something you’ve put a big effort into. But failure at some level happens to everyone and it is just part of the process of growing. A lot of my friends are mathematicians and everyone has some failure story. In fact, everyone has *multiple* failure stories that have just become part of their journeys. I think the transition from high school to college is tough partly because you must be a lot more independent in your learning (especially in this class) and it can take some time to figure out what works for you. That’s just another part of the growing process!
Prompt #3:
Til this I know I am bad at math! I have said it out loud, in my head, told my friends and my family like I know I am genuinely bad at it. I repeat to myself everytime I do homework, learn in class, and while I take my test. I understand math in the beginning and out of nowhere it just gets harder. Honest to God, I just want to cry and not think about math at all. When people talk about how bad they are at math, I just agree with them. I would not know how to support them when I can not help myself.
Prompt #3:
Til this I know I am bad at math! I have said it out loud, in my head, told my friends and my family like I know I am genuinely bad at it. I repeat to myself everytime I do homework, learn in class, and while I take my test. I understand math in the beginning and out of nowhere it just gets harder. Honest to God, I just want to cry and not think about math at all. When people talk about how bad they are at math, I just agree with them. I would not know how to support them when I can not help myself.
Joseph, I totally get wanting to cry and not think about math! To be honest, though, struggling means that you’re doing it right and pushing yourself to grow. Anyway, I love your HOT topic presentations, and they just keep getting better and better, so keep up the good work!
As of late I feel like I’ve been getting progressively worse at math. Back in middle school and most of high school I had consistent high grades in my math classes. I feel like by senior year of high school I didn’t have enough time to focus on all of my classes, so it affected my math performance. it only got worse when I started college where I had even less time to focus on specific subjects. So I had to cut corners and only study bits and pieces of key topics and just hope I’d pass. I feel like if I had more time to work on math topics, I would do better in math.
Rafael, yes, anyone would benefit from spending more time to work on math topics. You do have a solid foundation, but cutting corners is tricky because so much of our material is interconnected; one needs to understand all of the bits and pieces at a deep level. Eventually, all of the bits and pieces come together and it’s like a switch flips in your brain and then suddenly everything becomes clear. But it does require time and focus and struggling when you feel like you don’t have those things is definitely frustrating.
Hi everyone! Thank you so much for your incredibly thoughtful responses for this assignment. You all brought up some really good points. I might not get a chance to comment individually on what you wrote, but I *think* I was able to discuss everyone’s response one-on-one with them during the HOT topic presentations. I really appreciate these discussions and I hope I was able to convince you even just a *little* bit that you’re not bad at math! Literally none of you are. (And I should know; I have to listen to each of you talk about math every single week!) You might like to know that some people in this thread who have said they are bad at math already have 8 or 9 H grades; which hopefully helps to show all of you that these negative thoughts are not based in reality, no matter how common they are. There is some helpful advice in these comments about how to deal with these thoughts. I’m thrilled that you were all willing to be so honest and open with us.
So. I would like to share this post and your amazing comments with some of my colleagues. (Basically, I’m just really proud of you all for sharing and I want to brag about you.) Right now, this post is publicly available on the internet to people with the link. I hope you’re okay with keeping your comments public, because I think they’re helpful for everyone! But if you feel like your comment is too personal, you are welcome to make it private; then only you and I can see it. To set your comment to private, click “edit” and then scroll down to “Privacy” and click the box that says, “Make this comment private.”