You Might Also Like...
Episode Show Notes
Anxiety in engineering education sometimes comes from doing math. What does math anxiety feel like? What are its causes and effects? How do you deal with it, as a student and as a teacher? Guest cohost Rachel joins again to talk about these questions and possible answers.
Our closing music is from "Late for School" by Bleeptor, used under a Creative Commons Attribution License.
Subscribe and leave episode reviews wherever you get your podcasts. Support Pios Labs with regular donations on Patreon or by buying a copy of the reference book Engineer's Guide to Improv and Art Games by Pius Wong. You'll also be supporting educational tools and projects like Chordinates! or The Calculator Gator. Thanks to our donors and listeners for making the show possible. The K12 Engineering Education Podcast is a production of Pios Labs.
Pius Wong 0:00
This is The K12 Engineering Education Podcast, season three.
Pius Wong 0:10
Welcome back to another installment of the show, a podcast that features discussions and stories about how to teach and learn engineering throughout kindergarten all the way up through high school and beyond. Thanks for tuning in. I'm your host and resident engineer Pius Wong. Today educational consultant Rachel Fahrig is joining me again to cohost as we talk about math anxiety.
Pius Wong 0:36
What's up Rachel?
Rachel Fahrig 0:37
Pius Wong 0:38
Welcome to 2018. This is season three.
Rachel Fahrig 0:41
Woohoo, Happy New Year.
Pius Wong 0:42
Happy New Year. It's also Chinese New Year.
Rachel Fahrig 0:44
I know. I just got an email from my son's teacher. She gave them little gifts.
Pius Wong 0:49
What did he get?
Rachel Fahrig 0:50
The whole school.
Pius Wong 0:51
Little lucky red envelopes or something?
Rachel Fahrig 0:53
It's a red envelope with a little bit of money in it.
Pius Wong 0:58
We Chinese people appreciate money, I guess.
Rachel Fahrig 1:00
Well, we white people appreciate money, too. [laughs]
Pius Wong 1:03
Promoting stereo -- Yeah, we all appreciate money.
Rachel Fahrig 1:05
Pius Wong 1:05
Money that this podcast does not make.
Rachel Fahrig 1:07
But it was unexpected.
Pius Wong 1:09
Rachel Fahrig 1:10
It was very kind and very lucky. We're lucky to have her in our lives.
Pius Wong 1:14
Rachel Fahrig 1:15
The year of the dog.
Pius Wong 1:17
Yes, the year of the dog. Because they're hard-working.
Rachel Fahrig 1:20
Right. So Kobe and Bo will both be happy.
Pius Wong 1:23
Yes, our dogs can be happy this year.
Rachel Fahrig 1:26
It's all about them.
Pius Wong 1:28
Yes. All right. Well, we are starting out a new season. Thank you for joining me on this.
Rachel Fahrig 1:34
Pius Wong 1:35
Season three. A lot of stuff has happened, I think, since our last year of stuff. I took a little break since the wintertime, and now we're back. And I wanted to start off this season broaching kind of a big topic that we might be able to narrow down.
Rachel Fahrig 1:50
We can have some follow ups.
Pius Wong 1:51
Rachel Fahrig 1:52
Pius Wong 1:54
I want to talk about anxiety.
Rachel Fahrig 1:56
Pius Wong 1:56
Specifically anxiety in engineering education, which may manifest as math anxiety, I feel like, most often. And I'm thinking about this, Rachel, because I am teaching math right now to bunch of students.
Pius Wong 2:10
And it's, it's cool because, like any group of students -- You've taught lots of students yourself. So you know this. There's like wide range of attitudes towards math and problem-solving. Sometimes there are people who just jump right in, and they don't care about making mistakes. And then there's others who might know stuff, and they freeze up during tests. And there's others who just feel lots of anxiety.
Rachel Fahrig 2:10
Rachel Fahrig 2:37
You just walk in, and you see the problem, and you're over it already.
Pius Wong 2:42
Yeah. Which I imagine is not very helpful if you're going to be studying engineering.
Rachel Fahrig 2:47
It's not. So beyond teaching students with math anxiety, I have math anxiety.
Pius Wong 2:55
"Have." You say that in present tense.
Rachel Fahrig 2:57
Present, because it doesn't ever go away.
Pius Wong 3:00
Rachel Fahrig 3:01
So there are accommodations that you can get in your learning, either self-found, I guess, accommodations, things that you discover that help you muddle through a math problem. Or sometimes they're prescribed by, you know, a state or a learning plan or whatever it happens to be. Sometimes you just have a really, really excellent teacher who gets you, and they know how to teach things multiple ways. But essentially the root cause of that anxiety doesn't ever fully get eliminated.
Pius Wong 3:45
You say that you have math anxiety. What does that feel like, for someone who doesn't know what that is?
Rachel Fahrig 3:51
Well, imagine that you have to accomplish a small problem, let's say loading the dishwasher. So you have a sink full of dishes, and they have to go in the dishwasher and get washed. That's that's pretty much it, right? Now, we all know that there are multiple ways to make that happen. How many marriages argue over the right way to load a dishwasher? Or parents who argue with their kids or whatever.
Pius Wong 4:28
I get it. I grew up not having -- Chinese people don't use a dishwasher. So speaking of Chinese New Year. So yeah, I would probably have disagreements about that.
Rachel Fahrig 4:36
Yeah. And even if you -- Sometimes, too, this piece has to be hand-washed. Why? Because it has to be. Why? Because I said so. There's nothing wrong with putting it in the dishwasher. Whatever. It turns into an argument. And so because there are so many different methods of solving problems, and depending on what class you're in -- So I think about the difference between solving some problems algebraically versus solving them geometrically, versus solving them trigonometrically, which -- That's telling you my age, because those were the math that I studied in high school. You can take a problem and solve it any of those three different ways, but only one is "right," in air quotes, for that specific course. So there's a sense of memorizing the rules and the processes and the the theory behind it. But I can tell you when my math anxiety started.
Pius Wong 5:42
Rachel Fahrig 5:43
Multiplication tables in third grade.
Pius Wong 5:46
Rachel Fahrig 5:48
I was paralyzed with fear that I could not get the right answer in the allotted time. Multiplication tables and recall actions are often timed activities. Even now for simple single-digit addition and subtraction problems, students will get worksheets of somewhere between 15 and 50 addition or subtraction problems, and they have to complete it in a certain amount of time. Now, I get that there is some argument for expediency and the need for immediate recall, especially once you get into higher-level mathematics. It is incredibly difficult, if not near-impossible, to teach someone advanced calculus if they're still doing out three-by-three or twenty-seven divided by nine on their fingers or with a calculator. I get that. But when we are drilling so hard that it's making kids unable to function at those higher levels, I don't know. I don't know what to say. I don't know what the balance is. I don't know what the solution is. What I do know is: Doing those kinds of things made math so hard for me to accomplish. Even though I took advanced mathematics in high school, I had to have extra help, extra tutoring. I went back to former math teachers and said, Can you teach me this new concept in the old way that you used to teach me? Because I can't get it from this new teacher. Now granted, I had a lot of agency. I was also very outspoken. I had no concept that students shouldn't approach teachers to ask for extra help. I just did what I needed to do. I'm pretty bold. I was then, and I am now. But it definitely affected me all through my childhood. I would spend hours, literally hours, like two, three, sometimes four hours a night, on my 15 math problems. Yeah, because I just couldn't get through the process. I couldn't wrap my head around it. I couldn't understand it, and then I would become so overwhelmed by my own frustration that it essentially sucks all the knowledge from your brain. You forget what you just learned, because all you can do is try to cope.
Pius Wong 8:32
So there's like a feeling of stress, deer-in-headlights kind of thing, where you lose the knowledge that you had.
Rachel Fahrig 8:39
Drowning. I would say drowning.
Pius Wong 8:40
And when you're drowning, you aren't thinking about, what is three plus seven?
Rachel Fahrig 8:43
No, I'm not thinking about, swim perpendicularly to the riptide. No, I don't even know what this symbol means.
Pius Wong 8:49
Rachel Fahrig 8:50
So yeah, it's a real thing, and it's really difficult. So for example, when I first started college, I had an environmental engineering major, but because I struggled so much with math, and I started college at a time when we still did this, I wasn't given support. I was weeded out.
Pius Wong 9:15
Rachel Fahrig 9:15
And that does still bug me.
Pius Wong 9:23
Hey, in the short break, I want to say thank you to the spectacular listeners who helped fund this podcast ever since season one, season two, and now season three. If you like what I'm doing with my independent studio Pios Labs, and with this show, keep on listening. Keep on tweeting me. And if you'd like to donate to Pios Labs on Patreon, as well, go on to your browser and type in patreon.com/pioslabs to donate. That's patreon.com/pioslabs. It's also in the show notes. Thanks.
Pius Wong 10:07
Rachel, I heard you say three things there, which stood out to me. First of all, I noticed that you are an example of someone who could experience strong anxiety about one particular thing. And yet you're not anxious about going out and speaking to the professor, to the teacher, which would have been the opposite for me, probably.
Rachel Fahrig 10:28
Pius Wong 10:28
Yeah. Because I was a shy kid. I don't want to go to my professor and argue about my grade or, like, get into a special class or anything, back then.
Rachel Fahrig 10:36
But if you don't learn -- If you're not learning, and you know that you want to do well, wouldn't you?
Pius Wong 10:43
Sure. That's the logical decision.
Rachel Fahrig 10:46
Pius Wong 10:46
But that anxiety would make me throw logic out the window.
Rachel Fahrig 10:49
I see what you're saying.
Pius Wong 10:51
So that's just an interesting observation, that someone can have anxiety in kind of specific domains. You also talked about how two things seem to be sources of stress for you, or sources of anxiety. One was the different choices that you can make in solving a math problem, because when you open that can of worms of solving a math problem, you could solve it a whole bunch of ways. And I've noticed that, by the way, in teaching some of my classes, some of my students might be a little overwhelmed or anxious about having all these different ways to solve the problem, and you have to help whittle down the choices. It's kind of like -- What's that called? Not anxiety of choice.
Rachel Fahrig 11:37
Pius Wong 11:38
Well, you know how -- You've heard of those sociological studies where you go to a supermarket, and you have like a million choices for potato chips. It makes you not want to buy any of them.
Rachel Fahrig 11:46
Yeah. No, I am going to leave this behind them. I'm so overwhelmed that I am going to ignore it.
Pius Wong 11:50
What if I choose the wrong potato chip? But really, any of them are fine, probably. So it's kind of like this grab-bag of math solution strategies, like, what if I choose that wrong one?
Rachel Fahrig 12:00
I don't think that I was given good solution strategies. I went to school in a time and a place where, this way was the way. That's it.
Pius Wong 12:12
They were giving you one way to solve this problem.
Rachel Fahrig 12:15
Yup. But if any of the teachers -- and teachers are human. If they accidentally missed a step, or if they didn't explain a step in a way that I could latch on to, oh well, that's tough for me. That's the explanation you have, and you only get two examples.
Pius Wong 12:35
Wow. Math builds on itself, so that would be horrible.
Rachel Fahrig 12:42
So another problem that I have is fluidity and context. Typically, we teach algebra first, because it does have a lot of those foundational skills. Manipulating variables, for example. Understanding the relationship between a numerical sentence and what it looks like on a graph. So when we're looking at graphical information, we can understand the mathematical function behind it. I didn't put that together, honestly, until I was in my early 30s. And I took algebra -- The last time I took algebra, I was not yet 20. So it took a long time and a lot of space and sort of different contexts for me to understand, oh, this is a function, and this is how we represent it. And that's what that means. I'm assuming that things have changed significantly. Again, this isn't a "back in the day" story. I'm all about, you know, innovation and change in education. But I know that sort of conceptual understanding is not occurring with regularity and with high fidelity.
Pius Wong 14:17
Not every school across the country.
Rachel Fahrig 14:19
Exactly. Some educators that are still relying on: Here is a problem, here's how to solve it, period. Now go practice 50 of these. Without any sort of context or relevance or, you know, why would I use this? And certainly -- I taught science. I heard plenty of: When am I ever going to use this? You have to be very, very explicit, I would say, in mathematics instruction. And I think that would have helped my anxiety a lot.
Pius Wong 14:56
Connecting it to the real world?
Rachel Fahrig 14:57
Yes. Even going back again, to that third grade multiplication tables. First of all, yeah, there probably should have been some flexibility in the timing. But understanding the bigger picture of how all these pieces sort of fit together and why three times four is twelve, and why nine times whatever is whatever it is.
Pius Wong 15:23
Do you do you think that giving students more ways to visualize or abstract or think about these math concepts -- Do you think that gives them more choices to freak out over? For example, we're teaching negative numbers right now. And you could think about negative numbers in many ways, with money, with directions, with Othello pieces that are black and white. I like doing that. But like, I noticed that, yeah, one method that may work for someone may not work for someone else. And if you show all of these methods, maybe that's overwhelming. I don't know.
Rachel Fahrig 15:55
It could be, but I think it's more likely that showing more options will include and engage and reach more people than not. You're likely to turn on more people than you are to turn off.
Pius Wong 16:13
Okay, because you don't need to know every single method, but maybe you find that one that works for you.
Rachel Fahrig 16:17
And if you don't show me -- Let's say there are five methods to solving a specific problem, and you only show me two. But for some reason I latch on to -- Let's say, another teacher years later shows me methods three, four, and five. And it was method number four that not only made sense for that specific context, but also made it possible for me to see the links between that particular concept and other related concepts, well then you've expanded my learning just by showing me one additional method.
Pius Wong 16:54
Alright, well, I want to go to the third thing you had mentioned, that we mentioned several times: the timing issue. I know that feeling.
Rachel Fahrig 17:03
I get it.
Pius Wong 17:04
It's related to test anxiety.
Pius Wong 17:07
We taught an engineering class at the college here in Texas where you had to do circuits and do math all within this hour. And it was like defusing a bomb, with all the wires and everything. And if you didn't do it in time, you would get a metaphorical explosion of getting a C or D on the lab. And that's really anxiety-inducing. And so I assume that the way we ran that class -- I didn't choose to run that, but that's just how the department ran it. There was a decision to do that. I guess they decided that there was a value in teaching people to do some kind of mathematical work, or scientific work, in a time limit, just like how we have time limits for the SAT, for midterms.
Rachel Fahrig 17:07
Rachel Fahrig 17:54
Pius Wong 17:55
How do you balance that? Like, giving people a time limit and teaching people to work under pressure, with teaching them to have math anxiety for the rest of their lives. What's that balance?
Rachel Fahrig 18:05
I don't know, to be honest.
Pius Wong 18:08
Maybe it's different for different people.
Rachel Fahrig 18:10
it for sure is, and for me -- So for example, I learned how to do most of my multiplication tables. And we did up through 12 times 12. In other schools, they did up through 15 times 15. It just depended. So even now, if you asked me to do 11 times whatever, I don't know, because it wasn't on my -- or 13 times, whatever I guess I should say, because it wasn't on my learning radar. But what I had to learn how to do -- and again, this is an accommodation. There were some sets of numbers that I just didn't learn as well, and even now, I still kind of have to count them out on my fingers. So sevens and nines were exceptionally hard for me. I don't know why. But if the problem comes up, what is seven times six? I don't know, I really have to think about it. I know now that it's 42. But I had to have some extra think time. I hope it's 42.
Pius Wong 19:14
What's really interesting is that you might have had trouble with that, but you knew that you had trouble with that, which was the key, or most important feature, I feel. Sometimes some people don't know things, and they don't know they don't know things. That's the most dangerous thing for engineers.
Rachel Fahrig 19:30
I don't know that I'm always a good comparison. I was always pretty self-aware and self-reflective, as a learner, as a student, even as a small child. Not every child is, and maybe the answer, or maybe one of the possible solutions, is allowing children to recognize their own strengths and their own challenges, and then asking them: What might help you with those challenges? Or, can we work around those challenges? Or, do we just have to accept that challenge as it is and build up other areas to compensate? So I can do other groups of multiplication just fine. I just take longer with sevens and nines. But I mean, it worked out okay. I ended up with multiple college degrees, and I can balance a checkbook and do some algebra here and there, you know, calculate how many bags of roof tiles I need for replacing my roof or whatever. So I got there, I made it, okay. But I also recognize that I'm going to need more time here, or I don't do this part well, or I have to do this part out on paper. And so maybe walking students through their own accommodations and their own methods of making up for those weaker areas, maybe that's a way to not only improve their learning process, but also help ease that anxiety. I don't have to be perfect at every single part of this. Because I can make it up over here. And I'm still going to get good grades. I'm still going to get the right amount of learning. I'm going to understand this concept, and I'm going to be able to apply it later.
Pius Wong 21:34
Thank you, Rachel. I think we are almost done. I just want to talk about what's upcoming for this year. What topics do you think we should cover?
Rachel Fahrig 21:43
Teaching in alternative environments.
Pius Wong 21:46
Oh, all right. Alternative environments including prisons. All right, we're going to do that. So stay tuned. We have some viewpoints about that. And especially how you teach STEM classes in prison.
Rachel Fahrig 21:58
Pius Wong 21:59
I know that school choices a big old buzzword for this year and last year and probably for the next couple of years.
Rachel Fahrig 22:05
In the long past, and in the long future, I'm sure.
Pius Wong 22:08
Yeah. Now I know that some of us on this podcast are in real-life professional positions where they cannot just talk about every single thing that they want to talk about. But I am not in one of those positions. And I can say whatever I want. So that's what we're going to do. I am going to work with Sadhan, our other special guest cohost, to do kind of an introduction to engineering in general. We're going to pilot some of the episodes here. And then if you want to learn about mechanical engineering, and not go to college for it, well, you can get a preview of it on this podcast. So stay tuned for that as well.
Rachel Fahrig 22:43
Pius Wong 22:44
Rachel Fahrig 22:44
Why don't you tell them the good stuff though? The other thing. The big thing.
Pius Wong 22:47
Well, then they have to listen to after the credits. I think the music will be playing by now.
Rachel Fahrig 22:52
Well, then stay tuned. Everybody knows you're supposed to sit through the credits.
Pius Wong 23:01
Did you want to look up more about anything that Rachel or I have mentioned today? Well, just check the show notes for this episode, and I'll have some links and other info up. Don't miss out on new episodes coming out, subscribe on your favorite podcast player, and leave me some reviews on iTunes or Stitcher to help others find the show, too. Also, I can't say enough how gratifying it is to get little tweets and emails and other messages saying you've enjoyed particular episodes, so keep them coming. Find the show, find Rachel, and find me on Twitter, Facebook, etc. Get all the details at the podcast website k12engineering.net. Our closing music in this episode is from "Late for School" by Bleeptor under a Creative Commons Attribution license. The K12 Engineering Education Podcast is a production of Pios Labs, and you can support Pios Labs at patreon.com/pioslabs.
Rachel Fahrig 24:09
You sit after the credits. This is what you get.
Pius Wong 24:13
It's like the blooper reel.
Rachel Fahrig 24:14
Pius Wong 24:15
You can hear all my uh's and likes all in one take.
Rachel Fahrig 24:18
Gosh, I just realized that I have started saying "like" a lot, again. I got rid of it, and it's back.
Pius Wong 24:24
My brother had said that you have a very good radio voice, the other day.
Rachel Fahrig 24:29
Did he really? Which brother?
Pius Wong 24:31
Linus. I don't know if I can namedrop on here.
Rachel Fahrig 24:34
Thanks, Linus. He's still in Asia.
Pius Wong 24:37
Yes. He's doing the software engineering in Asia type thing.
Rachel Fahrig 24:40
Shoutout to Linus. Be safe, bro.
Pius Wong 24:43
The life of an engineer. Yeah. I agree. Well, we are in the post-show notes.
Rachel Fahrig 24:48
Pius Wong 24:49
The most important thing is that: Whoever's listening should know we are at --
Rachel Fahrig 24:54
Pius Wong 24:56
South by Southwest.
Rachel Fahrig 24:58
South by Edu.
Pius Wong 25:00
Rachel Fahrig 25:01
Where'd that come from?
Pius Wong 25:02
You should do the audio branding for them. Like how NBC has that --
Rachel Fahrig 25:08
I don't think they want me to do that.
Pius Wong 25:09
But no, we're doing a lot of things, actually. We have, first of all, a podcasting meetup.
Rachel Fahrig 25:15
Pius Wong 25:16
Podcasting for education meetup,
Rachel Fahrig 25:18
Networking and learning opportunities.
Pius Wong 25:22
Finding people who you want to learn from.
Rachel Fahrig 25:24
Pius Wong 25:26
Create a podcast with. Or if you want to --
Pius Wong 25:30
Share your ideas.
Pius Wong 25:31
Learn how to teach your students using podcasts. Oh, yeah, have a podcaster in a future episode coming up. So besides that meetup where you will meet us and other people, we also have a workshop.
Rachel Fahrig 25:44
A full-on workshop. Yes.
Pius Wong 25:46
It's a -- What's it called? It's called "Designing lessons using tips from improv" --
Rachel Fahrig 25:51
Pius Wong 25:53
Rachel Fahrig 25:53
So it's fun, and it's smart, and it's useful.
Pius Wong 25:57
It's yours truly, including Rachel and me, as well as a local improv trainer here. Yep. Amar will be helping us out, and it's going to be real fun. And so besides that, I'm doing a book signing.
Rachel Fahrig 26:09
Shameless plug. Couldn't be prouder.
Pius Wong 26:12
Yeah, no, just take a look at my reference guide. It's Engineer's Guide to Improv and Art Games. And I can play some with you.
Rachel Fahrig 26:20
It's available on Amazon.
Pius Wong 26:23
In print, yeah, on Amazon, as well as in an ebook on Amazon.
Rachel Fahrig 26:28
I have both. Get both.
Pius Wong 26:31
It's on sale.
Rachel Fahrig 26:32
It's really, actually -- So I keep it at work. And I work in an educational environment, but not around students. We guide administrators toward improving their schools. But I share that book with all of my colleagues. And they have shared some of those strategies with their administrative teams that they're supporting.
Pius Wong 26:57
Rachel Fahrig 26:57
We get great feedback.
Pius Wong 26:59
Cool. We're going to do one of the methods that are in the book inside our workshop.
Rachel Fahrig 27:04
Pius Wong 27:04
We're going to do empathic lead user analysis, but for educational classrooms. That'll be interesting.
Rachel Fahrig 27:09
Pius Wong 27:10
Yeah. So I think that's it. I'm also going to be poking around with my microphone, trying to find little stories at South by Edu. So if you got any leads that you don't want public, just email me silently, and I'm officially going to be a journalist.
Rachel Fahrig 27:24
Or if you know someone who wants to talk, let us know, or let them know. Have them seek us out, or we'll go find them.
Pius Wong 27:31
We are definitely meeting people for the podcast at South by, so come by.
Rachel Fahrig 27:35
Pius Wong 27:35
We'd love to have you.
Rachel Fahrig 27:36
I can't wait.
Pius Wong 27:37
Rachel Fahrig 27:37