[00:00:00] Vanessa Vakharia: We have the power to redefine these words in a way that is more empowering. We have the power to say, hey, this is what success means when it comes to math class, and we can enable all students to feel successful.

Hi, I'm Vanessa Vakharia, aka The Math Guru, and you're listening to Math Therapy, a podcast that explores the root causes of math trauma, and the empowering ways we can heal from it.

Whether you think you're a math person or not, you're about to find out that math people don't actually exist. But the scars that math class left on many of us definitely do. Oh, and don't worry, no calculators or actual math were involved in the making of this podcast.

Success and failure

[00:00:41] Vanessa Vakharia: Okay. Hello, welcome to today's episode of Math Therapy. So today what we're gonna talk about is actually something that should seem really obvious, but I feel like it doesn't, and that is how we define success in math class. 

I've been thinking a lot about this lately, and math trauma is often the result of someone being made to feel bad at math, in class. Which usually, by the way, translates into being, and I'm using air quotes, unsuccessful in math class. 

But the crazy thing is if we took a look at how we're defining success in the first place, we might just discover that the definition we've been using has been the root of the problem all along. And we have the power to prevent re-traumatizing students by simply changing the definition of success. 

Let me explain. Okay, so the other day I was having dinner with a long lost friend of mine. We actually haven't spoken in no joke, 15 years. And we were talking, and I, I don't know, at some point I was kind of like, so are you happy? Like, what's going on? 

And she said well, you know, like, yeah, like I'm really, really successful and you know, my parents are happy that I'm successful and blah, blah, blah. She kept saying like, blah, blah, blah, successful, successful la la la. And I was like, wait. What do you mean though? Like when you're saying you're successful, what do you mean? Does it mean you make a lot of money, does it mean like you feel like you're doing a good job every day, does it mean that you're doing meaningful work? 

And she was sort of like, what the fuck are you talking about? She was like, "well, successful". She just kind of kept saying it as though we should just automatically have the same definition of it. And I actually think that's what most of us do. I think that whenever we're talking about being successful later in life or about kids being successful later in life, or about kids being successful in math class, we just kind of assume that we're all talking about the same thing.

But if we've learned one thing in math class, even if you like hated math and blocked it all out of your memory, do you remember learning that it's super important to define your terms? Like it's super important to be like, just before I start the question, I just want you to know, let X equal blah blah blah. Like let X equal the number of tomatoes, or like let X equal the person's age or let X equal whatever. And I think that's what we have to stop and actually do: let success equal fill in the blank. Honestly, so much of math anxiety and trauma has to do with the fact that we were made to feel unsuccessful at a young age.

So what do we even mean when we're talking about success? Like when our teachers or our parents say things like, I just want my students or kids to be successful, what do they mean? And when we say we feel unsuccessful in math class, what do we mean?

So I obviously dug into this a bit because I was like, oh my God, I'm stuck in a word wormhole, like what is going on right now? And I went right to the dictionary and I have to tell you, I was fucking pissed. So first of all, in any dictionary, failure and success are defined as antonyms. Let me back up and say something here. I think that actually right now, if you look anywhere in educational discourse or like on Instagram or on TikTok, people love talking about failure. We're always like fail forward, fail fast, fail furious. I don't know if anyone says that, but I was just like, oh, the fast and the furious, whatever.

We're like, fail, fail, fail. Like la, la, la, la. But what's so crazy is, I know this is gonna sound super existential, but seriously, guys, the word failure can only be defined in relation to the word success. When we say we've failed at something, it implies that we had a definition of what success would look like in the first place. But we never talk about that. Like do you guys not notice that? We're hardly ever talking about success. We're always talking about failure. 

So back to my dictionary thing. Success and failure are listed as antonyms, they're defined in relationship to one another, and they are listed in the dictionary as opposites, which really pisses me off. I think we all know or should be learning, or at least have some inkling of the fact that failure and success are not opposites. They're often actually a part of the same process. But get this, so in Miriam Webster dictionary, success is defined as this: 

"The accomplishment of an aim or a purpose."

Okay? So just like take that in. Success is defined as the accomplishment of an aim or a purpose. And failure, do you wanna know what the definition of failure is? 

"Lack of success". 

That's the entire definition. Lack of success. 

First of all, like, ew. I hate that failure is defined as like, a not, or a less than, when we all know that failure can be so instrumental to our eventual success. But also I have to pause and say like, how many times have you set out to be quote unquote successful, so you've set out to accomplish an aim or a purpose, you have not met that goal, and something way better happened? So you wouldn't even consider it a failure or like, I guess like you failed, you didn't accomplish that aim or purpose, but something way better happened.

For example, how many times, okay, when you set out to be in a relationship with someone, your goal, your aim or purpose is not to break up with them, right? But obviously we've all been through breakups. And down the line, how many of you have looked back and been like, holy fucking shit, why did I ever date that loser, I am so much better off without them. Is that really a failure just because you didn't accomplish your initial aim or purpose? No!

And the same thing happens in math class. You fail a test, you get everything wrong, you look at the test after and you're like, oh my God. The reason I failed this test is because I didn't actually know how to study. You can't actually learn math by osmosis, I now know that I need to actually do questions in order to learn. Or you like, I don't know, you got an entire test wrong, and it's because you made one little mistake, you thought a negative times a negative was a negative when really it's a positive and that's, you made that mistake throughout the entire test, and now you've learned, oh my God, I'm not gonna do that on my higher stakes exam. And you had the pleasure of learning that lesson in a lower stakes way. 

All of these are technically failures. You didn't succeed, you didn't, you know, accomplish the aim or mission that you set out to accomplish, but it's not like the exact opposite happened either. It's not like you're a failure flat out, everything sucks. Something else happened instead. 

Anyways, whatever. This is kind of rambly. The point is I really think that what we need to do is pause and actually redefine failure and success for ourselves and for our students. Because we have the power to redefine these words in a way that is more empowering. We have the power to say, hey, this is what success means when it comes to math, when it comes to math class, and we can enable all students to feel successful.

Redefining success

[00:07:02] Vanessa Vakharia: Let's talk about what success means. What does success mean for you as a teacher? When you're in the front of your math classroom and you're like, I want my students to be successful, what do you mean? And have you actually really thought about that? What would they say if you asked them, what does it mean to be successful in my class? 

How do you show students that they're successful? So you have your own definition of success, how do you show your students that they are successful? Is it by giving them grades? Is it by giving them compliments? Is there something else you do? And at the end of the day, when we're looking at all of these definitions, and by the way, this completely applies to parents too, right? Like if you're a parent and you're like, I just want my kid to be successful in school, like I just want them to be successful in math, do you think that your definition as the adult in the room matches the definition of the child in the room? So do you think your definition of success is aligned with your kids or with your students?

And I ask that because I think there's often a big, there's a lack of alignment between the two definitions, that leads to a lot of math anxiety. So for example, let's say you're a teacher and you're like, honestly, success in my classroom is just that my students are trying their best. But your students think success in this class means that I get an A, it means that I get an 80%. There's a misalignment there. And because there's a misalignment, you might be really, really frustrated as a teacher thinking, I don't know why my kids have math anxiety, I don't know why they feel shitty, I'm here telling them that their progress makes them successful, just the fact that they're trying makes them successful, but they're not internalizing that and they cry every time they don't get an 80. I don't understand what the big deal is. 

And that's called a lack of alignment in definitions of success. What this usually means is that we just haven't, like I said at the beginning, we haven't defined our terms. It's very rare for us to actually talk to kids and say, Hey, listen, this is what it means for me, what success means for me and for me to feel like you're being successful in my class, this is how I'm evaluating it. But let me hear you out, what does being successful mean to you? 

The thing is in school, we've kind of fucked up, because we have taught students that being successful actually means that an adult thinks they're successful. Like I wanna phrase this the right way, but like, it's kind of like we have taught students to only be externally motivated when it comes to success. This is something that we've been taught from a very, very young age, that being successful comes from external validation and external motivation. And that's where we've really messed up. 

Because even as an adult now, it is very hard for me to feel internally successful, or you know, happy with my accomplishments unless I'm getting externally validated. I mean, you see this on social media all the time, we're posting something, we think something like, yeah, what I posted was really good or really meaningful. But we don't internalize that as something good or successful or positive that we've done unless we get a certain amount of likes or comments. 

The same thing happens in a classroom, right? We teach students, we can say to them all we want, yep, I really care how much work you put in, I really care if you're progressing, that kind of thing. But students are taught from a young age that what really matters in school is marks. Everyone knows that, right? The motivator to do homework is so you get marks. The motivation to study for a test is to get marks. The motivation to review those tests and to keep studying further is to get marks on your exam, right? The motivation to hand in that assignment, to collaborate with your team, to participate and raise your hand in class, it's always tied to marks.

We have taught students that being successful in math class is a linear relationship between them and the marks they got. Right? Success for students in math class is entirely measured by marks. So I bet you if you ask any of your students, what does it mean for you to be successful In my class, they would say things like, it means getting the right answer, it means getting good marks. I've heard a lot of students say those things and at the root of all of them, I'll be like, well, what does doing a good job mean? It means to get good marks. What does getting the right answer mean? It means that I get a high mark.

So we have a lot to undo here because you can imagine that if that's how students are defining success in our classrooms, a lot of them are going to feel unsuccessful. Now that's because all of us have a different benchmark of what grade or mark is equivalent to success. So you might have one student who thinks a ni, you know, a 75% means success. You might have another student who thinks they need a 95 to be successful, and either way, these are really unhealthy definitions of success. Because at the end of the day, that is just an outcome. It's an outcome of every single thing they're doing in your classroom. And if they're only evaluating their success by an eventual outcome, there's going to be a lot of pain and anxiety along the way.

So I invite you guys to actually think about how you can redefine success in your classroom. In conjunction with your students. So with your students, how you can start a conversation with your students in which you come up with definitions of success that embrace the empowering role of failure, mistake making, curiosity, and problem solving that is inherent in mathematics.

A tool for validating success

[00:12:08] Vanessa Vakharia: I also have to qualify, I think that both external and internal motivations and validations are really important. They're both important. And the truth is we can't ignore the rule of grades and marks in school. We all know that. Maybe we wanna completely change the structure of education, I know I do, but for now, that's the way it is. Part of the role of school is to allow kids to move through this ladder system where they get grades and they potentially go to post-secondary and then they go to post, post, you know, whatever, whatever. 

So it's not that that isn't important, but I think it's really important to realize that if that is the only way we define success, okay, so if students are taught, the second they enter the classroom, that the only way that they can achieve success is to reach a certain grade or mark, we are leaving a lot of students out that might eventually reach those benchmarks, but simply aren't reaching them as fast as they might like to, or we might expect them to. 

And I, you know what, from personal experience, I can say this, I failed grade 11 math as most of you know. You know, I barely passed grade 11 math for the third time. And when I went into grade 12 math, it's not that I suddenly got the grades I wanted, but the teacher I had made me feel successful for other reasons. 

So, for example, she made me feel successful for asking questions. You know, she'd be like, that's a really good question, that's a very thoughtful question. She made me feel successful for doing things like putting in effort and coming up with interesting ways to solve problems, even though I didn't get the right answer right away. Those things made me feel successful, which made me feel confident, which made me feel empowered enough to actually put in the work, seek the resources, and do all of the other things required for me to eventually get that 98 in grade 12 math.

Not all learning is linear and success certainly isn't linear either. So by redefining success, I think what we're trying to do is broaden the scope of success so that more kids can feel included and more kids have the opportunity and access to do what they need to do and access what they need to access in order to eventually maybe hit those external benchmarks.

One thing I really, really love doing is if you're a teacher, and even if you're a parent, and actually even if you're a student, okay guys, I have this table that I make in which I redefine success to include internal and external validation and to break it down more. 

And you know what? I don't know if by this point you're kind of like, oh my God, but success is like, it's just success, like I just get it. I have to tell you guys that there are words like this. Another word by the way is the word love, the L O V E word. Okay? I have to say I watch a lot of reality tv and you see this every single time. Two people will like match and whatever. They'll both be like I love you, blah, blah, blah. The show will end. Later, you'll like read something on Instagram or whatever about how inevitably the couple broke up, and it'll always go the same way. It'll be something like, well, like when they said they loved me, I thought they meant like they wouldn't cheat on me and that I was the only person and they wanted to start a family with me and la la la and the other person will be like, well, I said I loved them, but like, I still want an open relationship and I never even want kids and I don't believe in marriage.

Okay. That's like a very specific situation. And if you watch Perfect Match, you know exactly who I'm talking about. But the point is, it is a word we throw around assuming somebody else consumes it the exact same way that we intend it to be consumed. Success is another word like that. And again, we have the power to redefine it and get on the same page. 

So in my chart, I make three columns. The first column is "success is". The second column is "success feels like". And the third column is "signs of success". And the goal with this exercise is to literally get on the same page. 

"Success is ..."

[00:15:44] Vanessa Vakharia: So we start with "success is". Okay, so you're doing this with your students or with your kids or with yourself, whatever. 

Some examples are: 

Success is knowing you did your best.

Success is meeting your goal.

Success is progressing and growing.

Success is getting an 85%. 

Whatever kind of benchmarky things you wanna put in there. And by the way, the "success is", that's kind of like the external validation part of it, or the, or more like the external benchmarks. Objective, concrete ways we can see success or define success.

"Success feels like ..." 

[00:16:17] Vanessa Vakharia: The "success feels like" column is kind of a harder one to fill in. But this is where we wanna put in that internal, that intrinsic motivation and validation. So for example:

Success feels like satisfaction. 

Success feels like pride. 

Success feels like the knowledge that you did your best.

Success feels like relief. 

Success feels like excitement.

Like, whatever. You wanna put in those internal things you feel when you feel successful. When you feel personally successful. And this is a really important part to do with kids, because they aren't taught how to do this. 

Again, remember this, think about it. Kids are taught to evaluate success by the way the adults in their lives react. We want them to be able to be internally motivated by their own feelings of what success feels like to them. 

"Signs of success ..."

[00:17:05] Vanessa Vakharia: Okay. And then the third column is "signs of success". So signs of success can be things like:

A good mark.

My teacher or parent compliments me.

I feel one of the success feelings in column two.

I get a sticker on my test. 

The class applauds for me.

One of my peers or friends tells me I did a good job.

So these three columns, success is, success feels like, signs of success, starts fleshing out this, this more like rich, like nuanced version of what success might be for any person.

And you can do this in a classroom setting. You can do a little bit of a show and tell with it. And what I love doing is coming up with a classroom agreement of what success looks like in your math classroom, if you're a teacher. And if you're a parent, you can do something like what success at school or what success at math looks like in this house. Put that up on the wall so your kids can see it all the time. 

And okay, hello, if you're an adult, a math anxious adult, do this for yourself! Because, and I'm, I'm speaking from personal experience, currently recording this episode with severe imposter syndrome, I often, um, I will do this. I will give a presentation or I'll record an episode or I'll do an Instagram post and I will ignore everything on my personal success chart and I will do something like this, let's just say it's a presentation, I'll do a presentation in front of an audience of a hundred people, I'll do the entire presentation. I'll leave, and this is what I'll do. I will focus on one thing, like one little thing, like nobody laughed at the third joke I told. Or like, you know, not enough people reached out to me to tell me I did a great job. Or like, I didn't get enough followers on Instagram. 

Like, I'll just focus on some nitpicky thing that will render me feeling unsuccessful. But I won't look at all of the things that are my signs of success on my board. For example, I felt really satisfied. A ton of people laughed at most of my other jokes. Three people reached out to tell me I did a good job. I got invited to speak at another conference after. I felt proud of myself. Like all of those things I will ignore if they're not right in front of me, and I will focus on some other little check boxes that weren't filled out.

So I actually think this is a really, really important exercise, whether you're doing this for yourself or for someone else. Because remember, we throw around words like success and failure and love all the time without stopping to think of not only what they mean to us, but how much we are defining ourselves and our self worth by those words. So if you are constantly defining your math ability, or if a student in your class is constantly defining their math ability against this large, like vague, nebulous, umbrella term "success", without knowing what it actually is, it's impossible to ever feel successful. So actually quantifying it, qualifying it, and sticking it on a wall somewhere, allows people to feel successful every single day when it comes to math, when it comes to math class, in at least one way or another.

You know, we often talk about a student-centered approach to teaching and to learning, and that's kind of what I'm advocating for here, is a student-centered approach to success. And remember that doesn't mean that like you and all of your students get to team up together and kids can just say, I think success should have nothing to do with marks anymore. No, that is a part of success, but it's just a part of it. So I really think the idea of crowdsourcing, getting input from your students, getting their views on what success might feel like. 

And like, there's so much cool stuff you can do with this. Like you could even have a thing every single day, you know, everybody gets maybe this chart with a list of check boxes, and every single day allow your students to check off where and how they felt successful throughout the day and talk about it.

And I really want us to start thinking about how this changes the conversation around not only math ability, but around math trauma and math anxiety. I'd be really, really curious to see, how much better, you know, how much of a better relationship kids can build with math once they start feeling successful in math class. 

Assessment 

[00:21:06] Vanessa Vakharia: Now we cannot talk about success and failure without talking about assessment, my favorite, least favorite topic, I can't remember who said this and maybe I've said this in another episode, but kids learn what to value based on what you assign value to. It is impossible to untie the word success from grades and marks. Ultimately, when we're talking about a classroom setting, when we're talking about school, it is so deeply woven and embedded. 

So I really suggest, there's two things I suggest. The first is that you find ways to incorporate differing versions of success into your assessments. Now, it doesn't all have to be summative. You can do this in a formative way, but I think it's very important to show kids that they are being assessed not only on things that equate to high marks.

So let's say something on your chart is, success means progressing and growing. Or, here's another one, success means that you did your best, you know you did your best. Let's use those two. You have to find a way to show students that they are being assessed on that. And that might mean something like, okay, I'm assessing "progressing and growing" because I value that as a teacher, you value that as a student, we've decided that that's what success, you know, it's part of what success entails.

So something you can do, for example, is you can allow students to rewrite tests, or to rewrite different versions of tests, you can take away one shot assessment. So maybe some of your assessments are one shot, but maybe some of them actually give students the chance to show you that they're progressing and growing, show you that they know they did their best, and they can get grades for that.

Another thing is, and I know that every teacher is dealing with different circumstances, but there are a lot of boards that are starting to become more accepting of the "most consistent, most recent" method. So again, if on your list is progressing and growing is a sign of success, it's a part of success in my math classroom and me and my students believe that, you can use the most consistent, most recent method, and that just basically means that throughout the year, you are willing to look over grades and marks that don't necessarily reflect your students. 

So, for example, like your student walks in on week two and they take a test and they get a 40% and three months down the line they get an 80% on a test. We know math is cumulative, if that test is incorporating some of that stuff that in week two they didn't get, you can overlook that 40, right? Like you can, you can veto that with that 80 because your student has shown you that they have progressed and grown. They might not have known the material in week two, but they now know the material, they've incorporated it into a much higher concept in math, math is cumulative, and you're like, yep, cool, progressing and growing is a part of success, we're gonna get rid of that 40. 

So again, a lot of boards and schools do this completely differently, but that is something you can really think about, maybe talk to your team about and be like, hey, maybe if progressing and growing is something we're really trying to teach students as a part of success, is there a way that we can assess that way? Is there a way we can incorporate that into our summative assessments? 

And then finally, I love this one, I've heard of a lot of teachers doing this, is involving students in the creation of rubrics. So often when a student gets a rubric, a lot of studies have shown that they don't really look at the rubric, right? They scan it over, but they kind of know what each level is for, and all they really care about is reaching that level. But rubrics can be really, really instrumental in helping kids define success. So for example, if a kid gets a low level mark on an assignment, instead of just being like, ugh, that's a low level mark, I know that that kind of sucks, I'm not even gonna look at what the rubric said about it. Using your definitions of success to inform the rubric can really, really help. 

So, for example, like maybe a kid gets a one in a certain section, but when you look at what the rubric says, the rubric says something like a one means that you're demonstrating some basic understanding of the concepts, but you haven't mastered how to apply them to unusual or unique situations you haven't seen before.

This is something I really recommend talking about with students before you hand out an assignment or a test, right? Helping kids inform that rubric. So that, you know, they come out of it being like, yeah, that's actually really, really fair, like that actually makes me feel successful. If I actually know the description for a one isn't like whatever, I'm completely fucked and I have no hope of getting any better, but the definition is, yeah, you're actually showing some seedlings of understanding, but you need a little more practice before you apply them to concepts you haven't seen before. 

That helps kids realize that every single level on that rubric and every single thing they're doing has some seeds of success within those sections, and they're on a path to even more success. They're on a path to progressing in a way that they want to, and that progress isn't like the opposite of success. It's not like, failure, it's just a part of success. Because again, remember on your chart progressing and growing is a part of success. Okay. I've really like driven this point home now, I think.

Conclusion

[00:26:12] Vanessa Vakharia: Okay, so I have laid it all out for you guys. These are my thoughts on why we need to redefine success in math class and also my thoughts on like what success might look like if we stop using the definition of success equals marks in math class, and that's the end all and be all.

But I'm really, really curious what you guys think. For me, it's been a big theme of my life that language defines reality and that through our own language we can change how we feel and how students feel about themselves as successes, failures, or a little bit of both in our classrooms. And I really believe that allowing all students to feel successful reduces the likelihood of trauma, and is the pathway to overcoming math trauma, mitigating math trauma, preventing math trauma, and just allowing students to open themselves up to the idea that they really, truly belong in our classrooms.

So if you guys have thoughts on success, what it means, how we use it, how we don't use it, its role in math class, I wanna hear from you. Find the Twitter or Instagram post about this episode and comment away.

Cheers to a successful or unsuccessful episode. 

Episode outro

[00:27:18] Vanessa Vakharia: If something in this episode inspired you, please tweet us @maththerapy, and you can also follow me personally @themathguru on Instagram, Twitter, and TikTok. 

Math Therapy is hosted by me, Vanessa Vakharia, it was created by me and Sabina Wex, and it's produced and edited by David Kochberg. Our theme music is by Goodnight Sunrise.

And guys, if you know someone who needs math therapy or just needs to hear someone else getting math therapy, please, please, please share this podcast, and rate or review it on whatever podcast app you use. Those things actually make such a big difference for us. I'm determined to change the culture surrounding math and I need your help, so spread the word. Until next time, peace, love, and pi.