Portland Community College | Portland, Oregon

Edited by: Hannah “Asher” Sham

Introduction to Let’s Talk! Autism

Michelle: You’re listening to Let’s Talk!. Let’s Talk! Is a digital space for students at PCC experiencing disabilities to share their perspectives, ideas, and worldviews in an inclusive and accessible environment. The views and opinions expressed in this program are those of the speakers and do not necessarily reflect the opinions or positions of Portland Community College, PCC Foundation, or our community partners. We broadcast on our home website, pcc.edu/dca, on Spotify and on X Ray 91.1 FM, and 107.1 FM, and KABU Community Radio 90.7 FM.

Amanda: Welcome to today’s Let’s Talk! Autism podcast episode. I’m your host and producer Amanda, and we will be discussing the recent cultural shift around Math 111. Professor Heiko Spoddeck, co chair of the Math Department of Sylvania Campus, joined me today for the discussion. We discussed the thought process behind the shift, what motivated it, along with how math has been traditionally used as a barrier in STEM and higher education as a whole. We additionally discussed how rebranding it may change people’s perception of the course. While listening to this podcast will not automatically solve any math difficulties the audience may have, it may reassure everyone to know that educators want students to succeed in these courses.

Host & Guest Introduction

Amanda: Thank you very much, Professor Heiko Spoddeck for joining me today on Let’s Talk! Autism. I am really looking forward to this conversation. Because, Math 111 has been the bane of many students existence for many, many years. Including when I was in my early 20s, getting my first undergraduate. From what I understand, there has been a cultural shift around Math 111, and I’m very excited to hear your perspective on it, both as a STEM professor and just someone who has had years and years of experience with math.

Professor Heiko: Yeah, thank you. Thank you for inviting me and having me here. So yeah, look forward to discussing more of it.

Amanda: I think it’ll be a great conversation either way. And I think it’ll just be kind of informative and enriching just to see what’s going on in the secret world of math. So to start off, I’m gonna have us introduce ourselves, with names, pronouns, neurodivergence or conditions, if you’re comfortable with that, as well as our profession slash degrees. so, my name is Amanda. I am the host and producer of Let’s Talk! Autism. I use she, her pronouns. I’m finishing up an animal science degree at Oregon State, and I’m applying to vet school this year. I’m also excited to be a research undergraduate with a dog training camp this summer and I’m autistic.

Background and Teaching Journey of Professor Heiko Spoddeck

Professor Heiko: I’m Heiko Spoddeck. I use he, him, his pronouns. I do teach math. I have done math most of my life. But, I actually have a master’s degree in physics. I also have a graduate counseling degree. I do identify as “neurodiverse”, I like the term. Because, I don’t fit any category of any kind. And the main thing that I think I had to learn to live in the world with is that I’m a completely visual thinker and I had to learn to navigate that in the world of talking.

Amanda: Yeah, and before we begin, I just want to say, like, the great Temple Grandin, who is, to me, one of the most prolific autistic advocates and speakers of our time. She is also a visual thinker, very much like you, so I just want you to know you’re among the greats when you say you’re a visual thinker, and to never be ashamed of that.

Professor Heiko: Thank you. I had to learn to figure that out because I always thought I’m stupid because I wasn’t doing what other people were doing. But somehow I got good answers.

Amanda: it’s actually interesting you mention that. Because, I am the opposite of you, I am not a visual thinker at all. When people say, visualize a field of grass or something, or like an ocean side, or, I don’t know, whatever they tell you to visualize. I can’t. I just describe what I know the thing they want me to describe is, and I just nod my head and go along with it. Because, I always felt weird that I couldn’t do that. like, With physics, physics was a real struggle for me in this particular case, especially with graphs and diagrams, which you’re very familiar with, obviously. I’m not saying that’s anyone’s fault, but that contributes to why I hated physics so much. Because, the formulas themselves weren’t that bad. In fact, physics too, I thought was very intuitive because it had a lot to do with fluid volume and capacity of pipes and stuff like that. And that made total sense to me. Your diagrams were just, you go in one direction, then it reflects or refracts off of another angle, and it’s like, I could not keep that straight in my head. So, it’s just interesting how you say you felt stupid in the past. Because, I felt stupid for not being able to do what you did.

Professor Heiko: I actually studied physics. Because, I didn’t have to read much but look at pretty pictures and read the caption.

Amanda: No, that makes total sense to me. So, you talked a little bit about this in your introduction, but what is your background in mathematics, and how long have you been teaching this subject? you mentioned you got your degree in physics, so how did you end up teaching math, and how long have you been teaching it?

Experiences with Math and Physics

Professor Heiko: So I did math throughout my childhood. I grew up in a Society, I had to talk one way at home. Politically, at school another way. And that isn’t my thing. I like to say what I think. So, I struggled with that and math two plus two is four. And if you write five, you don’t get a point. If you write three, you don’t get a point. And if you write four, you get a point. something about that appeal to me. I also had a father who’s also physicist. Although, I always like to point out I studied physics despite him being a physicist. Because, we are very different styles of thinkers. But, whenever I had a question, he sat down and he did his best to help me and answer my questions. So, that’s a big part why I think people struggle in math, that they don’t have somebody to go to and have their questions answered. No matter what gender they are, no matter what race they are, no matter how they think, how they act. That they could just have somebody answer their questions. We would have a lot more people being okay with math, just like they’re okay with reading and writing. And so then I just did a lot of math throughout, went to a special high school for math and physics and chemistry. Did extracurricular stuff and went to university already as a child, in middle school and high school, had lots of opportunities to do extra courses at university. But, then learned through all that, that applied part, like in physics. That math was really I love to do. But, just the math where you had to Cross all your t’s and dot all your i’s. I make too many mistakes for that and that didn’t really interest me. So, I studied physics and I loved astrophysics, that seemed a good match and i’m really happy. I had a good time there. then I tutored during school a lot. Was asked to help other kids. Then learned that, “oh, my god! You can get money for that!”. So, I made money with that. Also throughout my studies, I came here to the U. S., I’m originally from East Germany. Kept tutoring people and then was was hired here at PCC as a tutor 21 years ago. Became, then, the tutoring center coordinator and math teacher eighteen and a half years ago. I’ve been here ever since. And now just teaching math.

Amanda: If you don’t mind me asking as a follow up, Why did you not teach physics instead of math, or have you ever considered teaching physics? I was just kind of curious. Because, you have a strong background and are very comfortable in both subjects.

Professor Heiko: I was actually hired as a tutor for math, physics, and chemistry, specifically, in this student learning center. like my predecessor there, really was trying to get more science tutoring off the ground. And, so he was looking for people who could not just tutor math, but also physics and chemistry. So, that’s how I got in. But, then he left and that position opened up and it was the math center coordinator position. So, half of it was the coordination and the other half was teaching math, especially to students who need more support and stuff, which exactly had I done a lot as a tutor. I tutored so much in my life at that point already that, that was a good fit. And, so that happened to be a math teaching position. So, that’s how I ended up teaching math at PCC. But, because I’ve done math, and I always was also in physics more interested, with some exceptions. But, for the most part, math has been my thing, so also really good fit and I love doing math and teaching math. Yeah, I’m very happy that.

The Importance of Support in Math Education

Amanda: I did want to reply to some of what you said about students not having a lot of help with math and why they struggled with that traditionally. I definitely did experience that at the university level where there just was too many students. Like we’re talking about a class size of like 3 to 500 kids. So, that to me was a major issue. And to me, that was not the university’s fault specifically. But, the reality is the class size was too big, there was only one professor, and there’s only so many spots in the tutoring center, and the tutoring center just does not have time to help every student. Especially if those students don’t have accommodations, and it was just a bad combination and I don’t think PCC is like that as much, especially with the tutoring center, because we naturally have smaller sizes. But, I just really like that comment because I do think that’s a big part of why a lot of students do fail. They get overwhelmed and I just don’t feel like they have the support.

Professor Heiko: I do think it’s maybe not the fault of the university, but the fault of the educational system. Which is set up to be mass producing education, which has opened the gates for a lot of more people on one hand, but then also leaves people who just need more or can’t go home and have a parent who answers their questions. So, it’s been a very unequal opportunity in that regard.

Amanda: in doing the research for this talk, I actually talked to several, university math professors. They didn’t participate in this interview, obviously. But, They said that there was a big cultural shift around math 111 specifically because it’s like what you said; you had two sides of math where it’s like even people who were really good at it they tended to be good at one equations that tend to be like really practical like physics. But, you also have it on the other side like engineering where you have to be as accurate as possible and you do have to dot your i’s and t’s because engineering is all about precision. To me that’s just unavoidable unfortunately with calculus and engineering. So, it’s just interesting you say that, and I definitely agree with your comments. That kind of goes into my next question, actually.

Rebranding Math 111 and Its Implications

For years, Math 111 has been the most failed class in at least one university, in the Pacific Northwest, with at least one study suggesting it was one of the most frequent courses students struggle with and had to repeat. This, again, was true in my 20s when I first attended university. But, some sources say this hasn’t changed in over 10 years. Why do you think this is?

Professor Heiko: It’s interesting. I looked at a couple past rates, that we have now access to at PCC, and actually, for us, it’s 95. At least for the couple of years. I looked at a few terms and math 111 has a passing rate. the fall 2023 is what I wrote down. But, I kind of compared it. Everything’s kind of plus minus 5%. So, there was a 60 percent for 111, and 49 percent for 95. But, yeah, it’s still you could say somewhere there is a bottleneck where people really, really struggle. One of the things was, 111 and 95. Students come nowadays straight from high school. like If you have taken certain classes, you can just take 111, then if it was within the last few years, then a lot of students self select and they’re going, “this is a bit straight into 111. I haven’t taken stuff yet.”. So, then they go into 95. So, that would maybe explain a little bit of that. I don’t know, but one of the things that stands out with math 95 is it’s very, very dry. So, actually in the one of the later questions, I compare math 95 and 111 are completely geared to prepare you for Calculus 1. But, it’s like preparing you to play a basketball game by, in 95 practicing dribbling only and in, 111 passing the ball and free throws. so, if you just do that, it’s annoying. You never play a game, you don’t know why you’re doing it. It’s just like over and over the same thing. I was also thinking a little bit of the movie Karate Kid, right? Like going this way, and going this way, and painting the fence. this way and that way. And that’s all you do. and It’s hard to see the bigger picture. Once you come to calculus, you start seeing, “Oh, wow, this is where you’re using this as what you need functions for.”. “This is where you need the algebra in order to, do those cool things that are so directly applicable to the sciences and engineering, especially physics.”. They straighten them in engineering applications from there. So, that is definitely one thought I have, and there’s a lot of details. You have to remember this and you have to remember that. And again, from like a long time ago. I’ve taught 256, that’s differential equations, kind of one of the last classes you can take math at PCC, and people still struggle with adding and subtracting fractions. Not everybody, but you still have people. there are certain themes that come back over and over. And there are other themes people go like, “oh, yeah! No problem!”. But, it’s usually the algebra. That calculating and remembering this detail and that detail and how to do this and how to do that and why do I have to do that. With that, though, because you’re then going into the cultural shift. So, one of the things we’re really hoping to change, and there’s actually new developments happening right now and I don’t know yet how that all will shake out and when it will happen. But, we’ve already like really done our best to funnel people in the right math class and so 111 should really only be taken by students going into STEM, or then some extra other degrees they also need it for whatever reasons. But, only very specific. There has been a tendency still to say to people, “oh, just take 111. It keeps your options open!”. But, most students, if you ask them, ” are you interested in engineering or science?”, They’re like, “no.”, Or they’re like “yes”. It’s very clear that general question is most students either answer “yes” or “no”, done. So, anybody who answers clearly “no”. Not like, “probably not.”, but really clearly, “absolutely not”, should not take 111. I’m actually also excited to see that, will probably hopefully go through with support that students get a chance to actually don’t even have to take 95 for taking 243 statistics. but, even now they could take 98 instead of 95. It’s much more applied. So, we’ve really created new classes in the 58 / 98 to kind of help funnel people who only need one or five. Like one college class math, that’s it, or who needs statistics or interested in statistics because our world is so data driven. So, those are like developments that we’ve already tried to just free the people who actually need it, can make a huge difference. Because, then it’s not like, “why do I have to take that?”. It’s like, “you need this.”. If you want to be a physicist, you need that. if you don’t know it yet, let’s practice.

Amanda: I actually had several thoughts to what you said. So, this goes into the next question, but one thing I noticed you say about Math 95 versus Math 111 is; Math 111, basically, at least from the catalogs I’ve looked at recently, they don’t even mention college algebra in the catalog at all now. in course description, that definitely wasn’t the case 10 years ago. So, do you think Math 95 is becoming a higher failed class than Math 111 because of the same issue Math 111 had in terms of the college algebra? Or, do you think it’s the material? Do you think it’s the pressure students feel? Do you think they’re just not prepared for the course like you said earlier? to me it’s just very interesting that it’s college algebra that students just universally seem to struggle with, even if they’re really good at math.

Professor Heiko: Well, 95 is actually called intermediate algebra. So, there’s introductory algebra, 60, 65, and the math 95 intermediate algebra, and then a 111 college algebra slash pre calculus. I think for the most part, these are just two different words for the same class. I looked at the CCOG’s, so those are the course content and outcome guides which list everything, and They haven’t changed that dramatically In the last 10 years. So, in 2014, it was still called college algebra. Then we switched sometime after that to pre calculus. And, I think it reflects rather the notion that we want to clearly communicate that this is a class that’s preparing people for calculus. Not the general college algebra for the general population. This is not for the general population it’s for people who are interested in science and engineering, so any STEM field. But, really only the samples that need calculus. So, anybody needs calculus needs 111. Also needs 95 if they need to brush up on stuff. So, everybody else is much better served with, statistics or math for life. ” Math in society”, I think, Math 105, if you only need one class. Or, you could take 105 and statistics. Both are fine to take if you need two math classes.

The Role of Statistics in Modern Education

Amanda: So, when I took math 243, I did manage to test out of math 111 at the time, and math 243 was like what you said, where you have to be really precise. Because, they have you do all the calculations by hand, and these are really long calculations. And, the reason I bring this up is because a lot of four year universities require you to have that background anyway to even enter stats, even if stats doesn’t even use calculus. So, it’s like with that in mind, do you think it’s still a good idea for students to consider math 95 or math 111? Even if they may not want to pursue science, but they may enter a university that might want to have them anyways?

Professor Heiko: that is then a question to the transfer people, right? So, if The transfer university requires math 111, then they will need to take math 111. but, the one other thing with 243. For instance, you mentioned, you have to do all the calculations by hand. That, I think, is a big shift. I don’t think people sit there anymore and they use “GeoDebra”, “Desmos”, “R” is popular…

Amanda: I was forced to use Excel for that. That class actually helped me get this undergrad research position. Because, no other candidate knew how to use Excel. I found that super interesting.

Professor Heiko: that’s why we have made the 58 / 98 classes, for instance, is one big part is that students learn to use Excel in those classes, and effectively these equation. This is why we need that stuff! Like, equations, we need it to know how to put something into excel and have the idea, or this cell times this cell equals this cell. So, that whole “using a excel spreadsheet effectively” can be super helpful and so we teach them 58 / 98, so they are ready for statistics. When I started, you actually said sometimes you use the calculator, but you still did a lot of equation manipulation, that is no longer there. At least as PCC, we no longer teach it that way. So, that opens up a lot more time to actually discuss the data. discuss what they actually mean, interpret them, but then also doesn’t need the requirements by actually sitting there and doing cultural work.

Amanda: Yeah. and I know we’re kind of spending a lot of time on this question, but another thing I would say is other struggle I just thought of with math, at least for me, was the fact that a lot of it was just abstract concept and it was just kind of garbage in my brain, if that makes sense, where the way my autism works in math, it’s like, I have to learn math one specific way, like I have to do one equation one specific way in a specific order. Many times, I call it the, “lather, rinse, repeat cycle”, I have to break it down and do a one process with it in the same steps, probably for half an hour before I get comfortable with it before I move on. It takes a long time, but I do learn in that way. But, that was a huge struggle I had with algebra specifically, and up to a certain point, Math 111. Math 112, interestingly, I actually didn’t struggle as much. In fact, it was kind of a cakewalk after I mastered the unit circle, believe it or not. It’s really funny, because now I understand why people say, you should have calculus when you take physics, because it actually is genuinely easier than algebra. Because, I actually didn’t take general physics with algebra and not calculus, because I didn’t have the classes at the time. So, I hear what you’re saying, where calculus really is only applicable to specific fields. Whereas before it felt like “P- Lord” is telling students to take Math 111. Because, it was just like a “end all be all” requirement, if that makes sense? To no matter what course you were going into.

Professor Heiko: Right. I mean, it’s now become more pre college class, but there’s also a part where you’re like, logarithms. Like once I sent my students out and now with Google and all that. Like, go find out or talk to somebody from your field and find out where they use logarithms. And they’re like, “wow, that really weird concept!”. It’s like earthquakes. You know, we live in a earthquake zone. like you need it for other things like chemistry and, all sorts of things. Like once you start understanding how functions show up in life, you’re like, “yeah, they’re everywhere!”. So, students come up with all these examples of functions and people. However, the calculations are still just calculations that people need to do, but they get a little bit more, ” seeing the meaning” than in 95. I think, that is a little bit more dry in 95 and I’m a big fan of bringing in applications since it’s hard

Amanda: Yeah, and I just don’t know how to avoid that, but I definitely do agree with you. I think that’s in particular where I struggled with earlier math classes, because it really is just abstract concepts where it just doesn’t mean anything by itself. So, on question four, I think I talked about, we already talked about this a little bit, but Math 111 has recently undergone a name change from College Algebra to PreCalculus 1, with Oregon State now calling it Math 11Z, or Math 111Z.

Professor Heiko: All of Oregon.

Amanda: Yeah.

Professor Heiko: So, that was the Oregon CC. And I don’t know what the acronym stand for. I apologize, but, it’s not CNN, but CCN. So, colleges from around the state, at least the representatives. So, there were representatives from the colleges and universities, that sat down and said, “we all agree to at least teach this in these classes, name them, have this many credits. But, then also accept each other’s classes.”. So, if you take 111Z at PCC, it will be accepted at every other, Oregon school, of higher learning. And so that is really exciting. That part of it. And so, yes. They decided on pre calculus. Because of what we just talked about and making very clear this is preparation for calculus. And other areas are better served with 105 and 243.

Amanda: So, we may have talked about this already, but why was the decision made to change the name? was there a cultural shift? Were there complaints? Like, what exactly caused officials to officially change the name of Math 111?

Professor Heiko: So, I mean, at PCC, we had done that already. So, we changed. I didn’t look exactly at the time that it actually changed. But, I know in 2014 we still had college algebra, and then a couple years later we changed to pre calculus because, this is a class meant to prepare you for calculus. It is not the, “oh, I just take the college algebra!”. If you just need a college level math class, take 105. or statistics, or both. But, taking 111 should only be taken for that. Or, if some degrees needed for other reasons, that’s fine too. But, most degrees don’t need it. If you become a psychologist, you don’t need one. You need statistics. So, rather take statistics and put all your interest and knowledge into that and learn.

Amanda: Yeah, so I’m just wondering what caused the change though. Like what made teachers think, “okay, let’s only make students take math 111 if they are going into calculus. Like engineering, or like another stem course.”, versus making it a general requirement across the board like I mentioned earlier. What happened to make that change. Do you know?

Professor Heiko: Well, the funny thing is we actually used to have 111 A, B, and C. And so we used to have 111 C , the one that was the calculus route. And then, 111A is kind of the 105 now. And then, 111B more for business people. So there was always a recognition of, “Certain people don’t really need this. They need something else.”. They need a college level math class and there’s lots of things they should know and learn. But, what we’re really looking for is not being served by taking this class. like in 105, they can talk about voting and, gerrymandering, and how that actually, looking at the percentages and looking at finances. So, you might use the same things. Like you might use exponential functions and all that. But, really in a very strong contextual way. Which a lot of people do much better, when it’s like, “oh, this is what I’m calculating instead of some abstract X.”. Right? Like, “what’s X?”. so, in calculus, you still have a lot of “X”, and you need to, learn how to make sense of something very abstract at first sight. This is how life kind of goes. There’s like this and then this comes. Like, you know, you also try something. I think there was, at some point, the feeling of like, people were mostly taking 111c anyway. So, we created 111. And then that somehow didn’t quite serve the students who didn’t need calculus. So, then we’re like, let’s actually make separate classes. I mean, statistics already existed. We don’t really need 111. Instead, we taught a little bit of functions in 95 for teaching. So, that students have enough understanding of it and statistics. and the rest, they don’t need in the same degree. What would we want if students only take one college level? Math, what would we want them to know and be able to do? Like, determining whether a function is increasing or decreasing? it’s very useful and important for calculus. Extremely important. It’s all what calculus is about. Not for a student who’s, becoming an art major. Also I think the change you’re referring to is like what I’ve seen over the 20 years 15 years, definitely more and more focus on really what is best for students. and so you try something, you think this is better than, you revise it from there. from what i’m seeing We still hope that it’s still getting people in the right classes while we’re still working on that. That, that gets better. But, also we are started by making all these classes available, so that students have a place to go that is best for them.

Amanda: So, we were kind of talking about this.

Inclusivity and Accessibility in Math Education

The cultural shift we were talking about, was it to make math more inclusive and accessible? Basically, by making Math 111 more specified to calculus, and making a lower math class than Math 111, like the standard college math course, is that like an effort to be more inclusive? And do you think this new strategy is going to help?

Professor Heiko: What students in calculus struggle most with is 95. like the whole series 20, 60- maybe not 20. But, definitely 60, 65, 95, And some parts of 20 as well, are all geared towards calculus. So, they give you everything that you need in calculus. so, that’s what we’ve been trying to get people into if they need calculus. And so then we created 58 & 98. 58 is also accepted now for, any associate degree as a math requirement course. Which is awesome because it’s very, very applied, in its approach to mathematics. So, the cultural shift, that I’ve seen is very, very for students. And it’s not that prior there were not people also who were absolutely interested in student success. But, in my experience, there’s more people now. Pretty much most people who are actually at this point teaching at PCC, I would say, doing what they believe is best for the student. So, the focus on the student, we may disagree with what is best for a student. But, we are looking for what is best for the student. So, yes, I do think that rebranding Math 111 as pre calculus hopefully helps to make clear this is for calculus. This is not the general. You know, “hey, just take a college class is 105.” . And if you need statistics or just are interested in statistics, you can do statistics. Or if you need two college level math classes, you can take 105 and statistics.

Amanda: Another thing I would say about statistics is, you might disagree with me a little bit on this, but I actually think statistics is the most valuable math class anyone can ever take. I don’t care what field you’re going into. And the reason why it’s not about the equations, it’s about the fact that you’re learning to interpret data. like, I learned that statistics 2, to me statistics 1 didn’t really teach that very well. Because it was more about the calculations themselves and stats too, we just flat out used geogebra. And it was more important to the professor that we understood what the numbers meant. I really appreciated that because he actually required us to write out the answer in a sentence, if that makes sense? Like we would calculate the answer, or put it in Geogebra, or whatever system we were using, and then he would have us write a couple sentences about what the answer was, what it meant on the bell curve, and just what that means. Like, is it below the average? Is it above the average? does it meet these requirements to be statistically significant? I really appreciated that. Like, I understand how to read studies a lot better because of that class. So, with that in mind, even if students aren’t really gonna go into engineering, or any other kind of math field, or anything like that, do you still feel it’s valuable for students to take it?

Professor Heiko: To take statistics, yes. Absolutely. yeah, no question. and most people, I mean, there’s a lot of degrees that do ask for statistics, and non STEM fields, like many, many non STEM fields, like the social sciences, like they all, need statistics and constantly talk and make statistics. So, yeah. People who don’t need it. I don’t know if they actually get statistics in 105, but they get a very round also, you know, as a person living in this world. This is math that is really helpful to know and you should know. then if they are rather interested in statistics and how this whole data thing works, then they could take that and highly encouraged that. Maybe they’re like, “Oh, just a roundabout, nice.”. Learning one of five is a big class and people are very passionate about teaching a very student focused. Also highly recommend that.

Amanda: So, Math 111 has traditionally been used as a weeding out course. which to me likely contributed to its high failure rate in the past. why was this attitude supported for so many years, and how would you describe the process of weeding out students using this class?

The History of Nursing and Math Requirements

Professor Heiko: I mean, that’s, it’s interesting that question of, why was it supported the questions and also who supported it. Right. so the way it works as each field. Decides what math requirement they want. So that’s not math. So we offer classes. I mean, there’s some, of course, back and forth and also in like 58, 98, so there is collaboration and there’s also like, “okay, these are the classes we have.”. And then the degrees decide that this other math classes, we need our students to know. it’s correct. So, here’s the thing, right? The situation is if you just opened it up, there would be lots and lots of applicants. I wrote down for myself the history of nursing, for instance. So, when I started, the nursing had actually math 20 as a math requirement. So, that means that number of applicants were much more. so, then they had the lottery system of who would get in and then they had people then who did not succeed in nursing. Because, it’s hard in nursing. I don’t know how that historically came. But, at some point, somebody must have said, “well, if they do well in the math classes of a certain level, then they will also succeed with us.”. In order to just have fewer applicants, but then also those who apply have more of a guarantee that they’re actually will be sticking through and succeeding. I cannot speak to whether that works for them.

Challenges Faced by Nursing Students

However, my concern is, first of all, that gives math a bad reputation. So, that’s one of why math is not liked. Because, then it looks like us math people are “the people”, when it’s, we need this class to prepare people for calculus. So then other people put people in there that don’t need calculus. They just need a math class. It’s hard because the class is not designed for nursing students. But, what really is also very sad is I’m sure there are many applicants that would be totally fine going through a nursing degree, That will not be fine going through a math class. We were talking in the beginning about, people not getting their questions answered. If you’re a woman and you have a question, you’ll very likely be told, “hey, you don’t need to ever know this.”. If you’re a person of color, And you have a question, the teacher already looks at you as thinking like, ” oh, you’re not capable of understanding this.”. So then they’re like, whatever that might not actually answer your question. So this field is so stacked. but, these students who are totally capable of going through a hard program. But, already the field and math has been stacked so, so against them from childhood that it’s really hard. To then say, “Oh, it’s not an equitable way to distinguish between people who can make it through the program or not.”. Now, that said, then it still leaves the question. How do you make that determination? Because, there’s so many people wanting it. And so you want to choose the people who are likely to succeed. So, that you maximize the resources that you’re giving to students. And what is an equitable, way to do that? I don’t know. I don’t have the answer for that. But, math is not an equitable tool from my point of view. The way things are at this point.

Amanda: I would agree with that.

Personal Experiences with Math in Education

And this question is a little personal for me in terms of my own experience and how math was used against me to weed me out. I wasn’t diagnosed with my autism until I was 31. So, when I was first in undergrad, I didn’t have paperwork, I didn’t have any accommodations, I couldn’t get any academic support. No one really knew how to work with me, and I didn’t know how my brain worked. And the reason why that’s relevant, is because I want to be a veterinarian so badly. I know this for a fact about vet medicine, unless if I’m going into medical engineering, I’m not going to need calculus. But, it was still required by basically every graduate school I wanted to get into. and it really was just for the sake of weeding out, it really wasn’t for any other practical reason. That is specifically a weeding out class, it just is. I think that’s very unfortunate, because I don’t think math itself has to be evil, like you said, or it doesn’t have to be something painful. To me I kind of have a love hate relationship with math, at this point. Because, I actually did enjoy 112 at the end of it, when I mastered the unit circle, because I’m a pattern thinker. So, when you have the unit circle memorized, you just have to remember the patterns of the unit circle. And if you memorize specific things about the unit circle; like, if you have anything over a fraction of four. You know that the xy coordinates are the square root of two over two, and the square root of two over two. And whether they’re positive or negative, it’s gonna depend on what hemisphere they’re in. But, if I were to answer any questions about the unit circle in January, even of this year. I would be able to tell you what it is, but I wouldn’t be able to tell you that. So, it’s just a shame that students, they’re just really, scared of math basically. They’re just scared that they’re not good enough and, at least this was my experience, they just put all this pressure on themselves. They just don’t feel like they can even ask their professor. And for me, I didn’t ask for help. It wasn’t because I was a woman. Or at least I never got that impression about why I wasn’t helped, it was just, professors did not know how to help me. I didn’t know I was autistic, and my brain just doesn’t work the same as theirs. And, quite frankly, even if I wasn’t autistic, no one’s brain works the same anyways. You shouldn’t assume that a student will understand how to solve a problem the same way you do anyways. I don’t know what your experience was growing up, especially in East Germany.

The Impact of Neurodivergence on Learning

But, when you approach math problems, did you remember kind of having a similar experience where teachers didn’t know how to work with you, or were you just naturally really good at math that they didn’t have to help you? If I may ask?

Professor Heiko: I was in the very fortunate situation that I was always good from the beginning. So, then if you’re good and you have a question, they answered you. And then if the teacher didn’t make sense, I then asked my father, and If he didn’t make sense, I would also get frustrated. But, he was more stubborn. Than he would, try again, and I would get annoyed. Because, It wasn’t quite the right way for me, but in the end, I did end up with enough understanding then to keep going. I remember coming home in fifth grade, like, I hate fractions and my father was like, “come here.”. So, in the kitchen, takes an apple, cuts the apple. One apple, two halves, two halves, like one apple. Well, then cut half one half into two quarters. Two quarters, make a half. Right? And like, well, that’s not difficult at all! So, I had that luxury. But, I think, if I had not gotten right answers, I would have had a much harder time. But, I was fortunate. Also in reading, writing, always just got it, a lot of it, quickly. So, then if I ask questions in class, I would get answers. Because, they were always considered. If I had questions, then of course, everybody else had questions.

Amanda: So, another thing that I encountered with math, including at PCC is, I’ve had great professors at PCC with math. But, there are some comments where it does make students, especially me, reluctant to ask for help. I have to repeat Math 111, because one thing I just kind of forgot how to do in algebra was how to get rid of square roots in an algebra equation. I remember how to do that now, but I just hadn’t done that in a while in Math 112, and when I asked the professor how to do that, he was like, “Yeah, you should have learned how to do that in Math 111.”. And I’m like, “uh, that’s not helpful and I don’t remember everything from Math 111.”. Especially, because you don’t have to do that a lot with square roots. There’s not a lot of situations where you have to get rid of square roots in an algebra problem.

Professor Heiko: two, three problems. That’s it at the most in math 111.

Amanda: I did appreciate his candor about the trig identities, and he just was very honest about how useless he thought they were. oh my god. I’m not gonna lie, I think trig identities, at least most of them, should be eliminated. Unless if you’re going into calculus itself. But, that’s another discussion.

Professor Heiko: Something like that. I like, because it’s like a puzzle. I love trig actually. Cause it’s visual. But, in terms of, usability, it’s…

Amanda: just comments like that to me are really unhelpful especially. And it just makes students like kind of more reluctant. He was a nice person, but I don’t think he realized just how damaging and discouraging that is for students. Because, they’re not going to want to ask you for help if you’re going to question whether or not they deserve to be in this class.

Professor Heiko: right. Yeah, no. I’ve also heard somebody had A’s all throughout and then was told, “oh, you don’t belong in this high level math class.” like, how can you say that to somebody like who has like A’s all throughout math. it’s horrific.

Amanda: In physics too, I remember we had this substitute for one class and I was in office hours with a couple of other students. I forget what concept or chapter this was, but she was kind of starting at a point in the equation where I wasn’t used to it, so I had to ask her, “Hey, can you stop and just start from here? I can’t solve the equation the way you’re doing it.”. And she told me, ” Algebra is a requirement for this course, you should know how to do this.”. I actually talked with her afterwards and said that was very rude, and I’m autistic, and you shouldn’t have said that to me. Especially, in front of other students. Looking back on it, I feel like I should have reported her. But, I did feel bad for her because she didn’t have my disability paperwork. But, even if she didn’t, that’s not okay to say to a student especially on such a public setting like that.

Professor Heiko: Yeah. I mean, how you word it is important. And sometimes in class you have to say, “please see me in office hours.”. Like in office hours, I’m happy to go through every detail of a calculation. in order to get through the material in class, sometimes I just have to keep moving. After class, I stay as long as you need to happy to explain it all. But, in class, I lose the other, half of the class. That’s the other thing. you always try to keep each half interested. The ones who are like slightly bored and the people who are like, what are you doing to me?

Amanda: Yeah, and this was actually in office hours when I asked her this question. This wasn’t in class. But, I was pretty upset by that, actually. Again, I felt kind of bad for her because she was pretty stressed herself. But, I probably should have just reported it. I don’t even remember her name. So, that’s just unfortunate. Because, I feel like incidents like what we just described are common. Where it’s like, they think it’s harmless, but it really is harmful. So, when a student has a question, don’t say they should know this or they learned this in a earlier class. Cause, we just aren’t going to remember everything anyways.

Professor Heiko: sometimes they’re rushing. Especially part time instructor rushing to the next college to teach another class. You know it’s a rough, gig unfortunately for some people. But, that does not excuse that. It just shows also the other side is, as you say, stressed and complex as well.

Amanda: Yeah.

The Role of Math in STEM Education

Do you think the rise of autism, ADHD, and other neurodivergent diagnoses in both students and instructors have contributed to this attitude change in math? or like the cultural change in math that we discussed?

Professor Heiko: I feel like there’s been a shift more even because of the pandemic. That each situation is different. Each student learns differently and so it used to be, you do this and kind of expect people to go, along. That never happened. I mean, it’s kind of funny as a child and ask to help your peers. which means the instructor couldn’t help, couldn’t explain it. And then I’m supposed to explain it, better. it’s interesting that way too. But, the focus on that each person needs something different, and isn’t like, “oh, they’re not interested and they just don’t want to do something.”. But, no. Assuming that everybody wants to learn and we have to provide the opportunity to make that happen. So, I do think that. The other thing is, the accessible education and disability resources has very strong support, trainings, and, just more widespread and also streamlined all the, notices we get as instructors. Knowing what students need in our classroom also has been very helpful. Everybody can learn if you’re just getting the support to learn. And some people always had it. Some people have learned it. As we have done more and more group work; for some people, group work is not the right learning environment. And how can we, navigate that in so that each person has a good experience and gets the support they need.

Amanda: So, I just wanted to say that I feel like, I don’t know if the rise of neurodivergent statistics is causing a shift. But, I have talked to several professors who believe they’re neurodivergent and actually asked my opinion, should they get diagnosed? And first of all, I’m not a professional and I always make sure they know that. But, I just told them, for me, the reason I got diagnosed, especially in adulthood is it really wasn’t about accommodations. Although it definitely does help. It was about closure. It was about getting that explanation for why I was so different as a child compared to my peers, and just why I was treated so different. Why I process things so different. Why I saw the world so differently. So, the reason I bring that up is I think there is a lot of neurodivergence in STEM. And Temple Grandin actually does talk about that in her book, “The Autistic Brain”, as well. Like a lot of autistic people are in Silicon Valley. Because, it’s like that constant stream of stimulation. They always have something to do and I’m definitely like that in the veterinary field. Like my favorite shadowing experience, hands down was “emergency”. Because there’s always something going on. Always.

Professor Heiko: I mean, I think like one of the things I’ve also gravitated to that. It’s like, I’m okay in math. I’m not weird. I’m just like one of many people who are all somehow different and do this different or that different. And. I think, however, that might be part of why students then struggle. Depending on what the neurodiversity is of the instructor, they’re also more good for these students, not so for these students, might not be as flexible. Some people might be really good just this way. But, cannot for the life of them understand this way. So, I think that also comes in why maybe the teaching is not as perfect as it could be. Or, if we knew then we could match the right people with the right people.

Amanda: To me, the most difficult thing about, both, math and other STEM courses is that you’re never going to have a perfect system. You’re never going to be able to accommodate literally everyone in a class. To me, the best thing teachers and students can do is just be empathetic to each other. To me, that can take the form of group work. But, the biggest thing professors especially need to practice in classrooms is just be patient. Like, that’s the biggest thing I ask for from professors every term, regardless of what course I’m taking. I need patience, I need you to understand that I’m autistic and I need you to listen to me about my disability. Do not make any assumptions based on your own experience. Because, I have had professors compare their own autism to mine and just think, I need the same accommodations and learning style they do. Which, by the way, You probably know better than this, but I’m just gonna say it anyways, don’t ever do that. Everyone’s autism, everyone’s neurodivergence, is different. No two people are the same. Or, they have a child or a loved one who’s autistic and they assume. I had a couple of professors like that who are really well intentioned, but they did not understand that my autism was not the same as their child’s. They just kept assuming I needed the same accommodations or assignment format in class as their child, and I had to fight them. not fight them, but repeatedly tell them, “Look, I need more structure.”, or “just give me an example of what you want. This tells me nothing about what you want.”

Professor Heiko: that has definitely changed. Like that is a change with more understanding that an individual person is an individual person. Then how does it look in teaching and when we still have a big class in front of us, how can we make that work as best as we can?

Amanda: This kind of goes into one of the last questions, but I’m gonna reword this a little bit. Because, I think it’s a little more relevant to what we were talking about. how do you think that Math 111 or Math 95 should be taught to make it more accessible and less daunting to students? How can we make math less scary to students, I guess, is my question there.

Professor Heiko: There is this thing that goes, “Oh, if you just take Math 111, you keep all your options open.”. Sometimes I feel like we are closing options. Because, then people are not happy in that class and they go like, ” never again!”, Or they’re failing that class and there’s other implications. So, instead of going that, it’s more like, “Where are your interests, right now?”. And then if a person; like let’s say, takes 105, totally falls in love with math, and then takes one of them. There’s no harm done. There’s absolutely no harm done. We have a more solid foundation, realize how applicable math is in life. Now they’re ready, because now they’re like, “yay! I love math! I want to study math, or science, or engineering!”. It’s totally fine. Rather than, “oh, take this one then you keep all your options open and then don’t have to retake a math class.”. I think that is something I really hope with that rebranding. it is just for math, that’s why it’s math for life, and math for society. Take that set and really following people where they are at right now. Because, we’re not teaching their future self, we’re teaching them where they’re at right now. So, that is my real hope. And then, 111 we’ve made them half lab classes, right? so, people really like having more group work, and class together. Because, there several stages to learning. There’s the passive knowledge, where you’re like just absorbing stuff. Then you are starting to make it active knowledge, by actually being able to apply it. Then you starting to teach it, or you express it verbally and tell somebody else how to do it. Then, it’s yet another way of really understanding it. And so these are different stages. The hardest one, I heard that first from Nolting winning at math, it’s a book. He said, “if you take a government class, we ask you to describe how government works. if you take a math class, we ask you to run for governor.”. We actually ask you to apply what we teach you, not just explain what we do. So, we are more and more, through the lab, making time in the class to start that active learning process. So, then you do some more practice at home when you have some time to digest what happened in class. Or, people give videos first, so you actually have that passive knowledge experience at home. Then you come to class and you work together, you talk to each other. Already getting into that teaching experience in class. So, these are many of the ways, and some of my colleagues, also doing fantastic things.

Amanda: I like your comment on not teaching their future selves. Because, I kind of say something kind of similar in the peer core science group. I tell the students that taking the stem courses isn’t about mastering the material in this class. You don’t have to be a master. This is about building foundation. Because, here’s the thing you’re going to repeat these concepts throughout your education journey. So, don’t worry about being completely perfect in class, it’s about getting comfortable with it. To me, that kind of relates to what you’re saying, and relates to what I said about math in the unit circle. I know I’m never going to use the unit circle as a veterinarian, I know that. But, it’s about the fact that if I do need to take math 251 this summer, and I know I’m going to be in good shape, because I do have that foundational skill, because I got comfortable with it. And even if I have to revisit, that’s fine. To me, the biggest thing; I really wish that math just wasn’t weaponized as a gatekeeping class. If that wasn’t weaponized as a gatekeeping class, I think people would enjoy it a lot more. Cause I really do feel like that’s where a lot of the bad reputations come with math, at least that’s my opinion.

Professor Heiko: Yeah. And then it’s also, unless you can do this your whole career is done. That’s just rough. it’s not, necessarily that relevant. I mean, you should have the option, but again, it’s always been traditionally like, “Oh, you have all these options that you be a veterinary technician and you might need calculus or engineer.”. But, most veterinarians probably will never know that. The other thing in a traditional education is, that having “very broad” was considered good. And I do agree with that, in part and in part, not. You’re having a broad range, yes. not in a gatekeeping way. So, it’s like exciting things. Okay, math is not your thing. Then maybe you take engineering 101 instead. Because, you’re like, “Hey, what do engineers do? I’d like to know.”. just because having options to have a broad range of things that, you could do. So, some of that, I do sometimes worry that we are like narrowing the education field into, “oh, you want this. You only take these classes, and only take these classes.”. yeah. So, that’s one worry. The other worry that’s been on the back of my mind is that math is very good at is learning abstraction. That’s why it’s hard, but it’s a very abstract thing. how can we teach so that, people can zoom out and look at patterns? That’s so needed in society and voting, the way we do politics. I feel a lot of people just in it and have a hard time stepping outside and looking at it from a more abstract viewpoint. But, I don’t think math, right now, is the vehicle to quite accomplish what we would like to do. if that makes any sense.

Amanda: No, it does. But, my brain, just with my autism. That abstract part was just the hardest thing for me, and it just my brain just was like, “this is just useless junk. I don’t need this. Why do I need this?”. Because, I am a pattern thinker, and I do notice patterns kind of in society, like you were saying. But, I would never know how to connect that to math. I think it makes a lot of sense, like, in music and language. My wife, was raised a pianist by her mother and, to me, she’s also really good at math. And I don’t think that’s a coincidence. Like, I have heard that quite a bit, where if you’re good at language and you’re good at music, you’re good at math. I bet it’s based on the same abstract patterns you’re talking about, at least that’s what my guess would be. The unfortunate part about Math 251, at least in my opinion, is that, Veterinary programs really are just purely using it as a gatekeeping tool for the most part. I can’t really think of how it’s practically used, unless if you’re going into medical engineering. Because, even vet techs, any calculations that are done, they usually do them on a machine or they just do them in their head and that’s not pre calc, it’s algebra. Or it’s just counting, or it’s basic multiplication, like if you’re taking a respiration rate, or a heartbeat, for example. So, I think that’s the really sad part, because I do think math could be fun. But, it just isn’t treated that way, and I’m going to use organic chemistry, synthetic transformations, as kind of a comparison a little bit; the way organic chemistry synthetic transformations were taught traditionally, I hated that because they use the flashcards and you cannot learn them with flashcards. I’m sorry, you cannot. Or, if you can, good for you. But, that is very rare. The reason why is because You’re not going to understand what’s happening in the reaction to make it start from 1 reactant to a product. To me, that’s the same thing with algebra. Especially, at the beginning of algebra, where it starts off very simple and it adds up very easily. But, when it becomes really complicated, or the equations start getting nastier, the equations start making less and less sense to me. Because, more and more is added on to the pattern, if that makes sense?

Professor Heiko: Yeah, yeah. Totally.

Final Thoughts and Encouragement

Amanda: So, my final question is, what would you like to tell the audience about Math 111, or any audience members who are thinking of pursuing a STEM career?

Professor Heiko: Like it’s where you practice dribbling and passing the ball and free throws. it’s really just the skills. In German the, finger skills, where you don’t have to think about it. You can just see an equation go like, boop, boop, boop, boop, boop. So, that then you can focus on the big concepts. I’m learning Spanish right now. So, I’m taking a Spanish 101 class. And so they let you go in the first chapter and you learn things and I don’t have a lot of time. I come to the second chapter and you still kind of like managing on the third chapter. I’m like, “Oh, I still have to think about this. I have to think about that. I haven’t practiced it enough. I haven’t spoken enough”. To now have all chapter one and chapter two, like fluently available, so that I don’t have to think about anymore and can think about chapter three. ,So similar in math is, like 95 you can get through it and you do your thing. And then you’re like, “okay, thank goodness I’m done with that.”. And then, you go to 111; you’ll need that. But now you have a new concept to worry about. But, you need this, what you learned in 95. You come to 251 and you’re like. “Oh, there’s all this new stuff!”, which is cool and exciting and not useful. Then you’re like, “how am I supposed to like just do these math simplifications or rational expressions?”. And it’s just like a little sidekick. Oh, and then here, throw in a logarithm, just like, ” and I’m supposed to know the logarithm.”. Well, you’re not, but you’re supposed to know how to apply them. So, it’s like all these things. And so, it’s kind of like delayed gratification. We are living also in the time where it’s like, “oh, I want to see how I apply it now.”. But, if you are interested in science and math and engineering; just knowing calculus, it will be worth your effort to just like practice, practice, practice. Some of my students, they then go, “Oh, I guess I’m in this meditative zone.”. And that’s what I like was like, “Oh, I do this. I do this. And I get an answer. It makes me so happy.”. , So I celebrate the little wins. That is something I would definitely encourage you. keep in mind and kind of see, “when I can do this, I can play the big game.” I used to play violin. You have to also practice your scales over and over. So, you have the fingers move without you thinking. They don’t move fast enough if you have to think. I also want to acknowledge that there’s a lot of scientists and also especially engineers that are like, “I know I need math. But, I want to be an engineer. I don’t want to do all this math!”. All of the math that you have to do will be so much easier if you can just do 95 and 1 alone. probably for engineers, especially, also trig. Especially electrical engineers. So, there’s a lot of trigonometry as well that is very helpful. But as you said, people have an easier time with that. But, you make your life so much easier, going forward, if you can do that well, and just put in the time to practice. Just like I have to practice my conjugation for all the verbs in Spanish in order to be speaking them at some point.

Amanda: Yeah. My final thoughts to this question are similar to what you just said. I definitely encourage people if they especially want to pursue engineering; these are hard classes. If you’re struggling in them, there’s no shame in that. Always go to your professor, if you want help. Or the tutoring center, if you want help. If you’re struggling in these classes, you aren’t stupid. It’s not that you’re not good enough. These are growing pains and You just have to get comfortable with the material; you don’t need to master it. It’s basically just figure out how to make this enjoyable to yourself and just do your best. It’s not the end of the world if you aren’t the best in these classes, or if you’re not getting it right away. If you’re neurodivergent and you’ve never been particularly confident in math, but still want to pursue engineering, medicine, or any other stem field. Give math a try, kind of like, Heiko said, cause you never know, and it’s sometimes it’s about the right teacher and getting the right support and just figuring out how your brain works. Everyone’s brain is different, we all need to be proud, and we all just have to own our brains and own our learning styles. So that brings us to the end of today’s podcast. Thank you so much for joining me, Heiko. I hope to have you on for another talk.

Professor Heiko: Thank you so much for having me. Really enjoyed our conversation.

Conclusion and Podcast Wrap-Up

Amanda: Thank you for listening to today’s episode. I hope you found the conversation engaging and thought provoking around the topic. When discussing STEM, math is often viewed in disdain, having a long held reputation as a gatekeeping tool. But, colleges and universities recognizing the variety and student needs. Math may become more accessible and recognized as a skill building tool like other core requirements. As Heiko and I discussed, students do not need to become perfect in math or other foundational courses. It’s about becoming comfortable with the material and knowing that you are not alone in your struggle. With higher education recognizing that individual students have different strengths and weaknesses, math can hopefully become another skill for advancement rather than forcing students to stall out or quit their major. I hope you enjoyed today’s episode and will listen to the next one.

Asher: Thank you for listening to Let’s Talk!, Portland Community College’s broadcast about disability culture. Find more information and resources concerning this episode and others at pcc.edu/dca. This episode was produced by the “Let’s Talk! Podcast Collective”, as a collaborative effort between students, the Accessible Education and Disability Resource Department, and the PCC Multimedia Department. We air new episodes on our home website, our Spotify channel, X Ray 91.1 FM and 107.1 FM, and KBOO Radio 90.7 FM.