Uncovering the Role of Mathematical Thinking in Today’s Technological Landscape

Kevin
Yeah, it’s a great question. So, I started twenty-six years ago as an eighth-grade math teacher. Never wanted to be an eighth-grade math teacher. I wanted to be a high school math teacher. It got to be middle of August and I needed a job, and I interviewed in a district, and they said if you want the high school job but you’re 1 at 3 finalists. If you want the middle school job, it’s yours. I said I would love to teach middle school and fell in love with them. The eighth-grade group and stick with that eighth grade age for that many years. I first got involved with the Michigan Council of Teachers of Mathematics through some of my graduate school work. We presented a couple more times after that got asked to serve on their board that I volunteered to be the conference coordinator for 6 years so I ran the annual conference for the Michigan version of it and then I was nominated to serve on the National Council of Teachers of Math Board, never in my wildest dreams did I think it ever get nominated for that. Never in my wildest dreams did I think I would be elected to that so I served on that board from 2016 to 2019 and then when the time came around for the next presidential election for it all of a sudden, I started getting emails and texts from a variety of different people saying hey Kevin we think it’s time for you to run for the board. We think it for the presidency. We think it’s time to have a classroom teacher. So, after a lot of thinking, a lot of saying oh everybody else has been a PhD I’m not a PhD I don’t know nearly enough about math education. Finally said sure I’ll run for the presidency and much to my surprise and I’m very very pleased. However, that I was elected to serve in this role, and it’s been a wonderful role. It gives me an opportunity to meet with so many people and to think about so many different things that I normally would in my classroom.

Olivia
That’s a cool story and that’s really interesting to hear about the just first of all I mean taking on those kinds of responsibilities while in the classroom as well and then I love that you know your community at the NCTM felt so passionately about having a teacher in this kind of leadership position I think you know whole point of our podcast is that we know that teachers have so many great insights and so it’s nice to hear that alignment between you know, organizations and I think you know you spoke to your twenty something years 26 years in the classroom and teaching mathematics and I’m curious just in that time how is the landscape of teaching math evolved over the years especially in the context of those digital enhancements and technology that we started to see.

Kevin
Yeah, and I would think you know the technology has changed tremendously from a first-year teacher to now as a first-year teacher the technology was an overhead projector and some of the younger listeners may not even know what an overhead projector is and those of us who are a little more veteran a little more seasoned can remember the day that you walk at the end of the day, and you have colours all down the front of your sleeves, the front of your arm because of all the overhead markers, we progressed then to the document camera, and we thought oh my goodness what a revolutionary thing progressed to the smart boards and like wall this is completely and totally revolutionary. So, the world of technology has changed significantly. As a brand-new teacher Email was not really a thing, I remember in my first district that I worked at the Principal got to choose I don’t know 10 people in the entire building to get email and our team felt so privileged that my group of 4 teachers that shared a common group of students we were the team that got selected to have email and we thought wow what a privilege it is and it was a privilege and when I think about Technology. It’s so increasing and it’s the pace at which new innovations are coming out and it can be difficult at times for teachers to feel like they need to stay on top of all of it and I think our job as educators needs to be to look at what are those emerging technologies, What are those things that our students are using outside of the classroom or inside the classroom but what are they using and how do we best integrate that into our instruction so that we’re keeping education relevant and meaningful for our students.

Olivia
That’s a great point just thinking about you know, kind of coming back to that question when picking new technology is what is the real purpose of it, like at its core, I think about you know my time in the classroom. You know as a student definitely using those overhead projectors and while I didn’t use them in the classroom I think something to think about is for any newer teachers out there who may be feeling overwhelmed by some of the new technology or even just the fact that they’re having new technology brought to them each year or even in the middle of the year you know this is. It’s not nothing new teachers have always been adapting to new technology and so it’s just about figuring out as you said going back to that core question of how does this technology start the students I think that’s some really great advice.

Kevin
Thanks, and think of is so important and you know there’s no way that any of us can be an expert on all of the technologies that are coming out just as no student is the expert on all of the technologies going out. But I think our driver educators we had to stay current. We had to continue to grow professionally. And the way that I taught three years ago should look different than the way I teach now, should look different in the way that I teach three or four years from now. As more and more technology is available as more and more research about how students learn is available. It’s an ever-evolving field and that’s what makes education so exciting for me.

Olivia
That’s what yeah, it’s definitely. It’s important you know I think most teachers I know in this world are very much lifelong Learners. So, I think they can relate to that. Um, and you know getting to you know, speaking at math more specifically you know I had. Opportunity to be a science teacher and taught math both in the science context as well as you know helping out that’s those state tests. But I think that you know math often gets the reputation being very abstract So how do you bring some real-world applications into your math teaching and how can technology perhaps enhance this connection for students.

Kevin
I think that’s our job. It’s difficult to find those real-world applications at times. Although that’s one of the beautiful things about and the generative AI that can really help us with it if we’re utilizing it correctly. But I think it’s our job to find those real-life applications. For many of our students they view math as that subject that you just have to get through for no apparent reason that math has no value and if we’re truly interested in math that’s problem solving as helping them see that math has some value and that we should become math literate. We have to find those applications to the real world otherwise it becomes that subject that the students just don’t see any purpose for learning.

Olivia
No, that’s a great point I think it’s you know math doesn’t exist in a in a vacuum, right? It’s something we use every day both you know we have the calculator on our phones and we’re still using Math. So, I think that that’s a great point about bringing in those real-world applications. I mean I think I wanted to just you know in thinking about future of technology and education at this point I think you and I spoke a little bit about this but what what really is math.

Kevin
Yeah, and I think the way we answer that question to what is math really affects how we teach math and if we think math is just strictly getting a correct answer that has implications for how we teach and if we think math is strictly getting that correct answer for many of our students. They don’t see a reason for learning math because they look at technology tools. They look at generative AI, they look at photo math, they look at other such applications and different tools and they say if I could just take a quick little snapshot of it and have technology find the answer. Why am I trying to learn and memorize the steps. So, I like to take a broader view of math getting the correct answer is important, but I really think about math. It’s that developing, that reasoning that critical thinking. Taking a real-life situation, putting it into math language, doing the calculations, having the technology do the calculations when appropriate and then answering that real life situation. So, I think it’s really a lot more about the modelling, about the reasoning, the sense making rather than just getting that correct answer. I think that really has that motivates the students to want to and to learn then when they see that there is some practical application for what we’re trying to teach our students.

Olivia
Yeah, you mentioned as well. But you know things like photo math and calculators, if these things can solve a student’s math homework I think you’re right, we need to you know help students get invested in that mathematical reasoning piece and I think making sure that teachers are aligned on that as well. So, they can then bring that to their students and help them understand sort of the beauty of math and the purpose behind it all and I think this might be getting, addressing it a little bit but what are some of the key challenges that math educators face today when it comes to adopting integrating technology in the classroom.

Kevin
Yeah, I think when I talk with some of my colleagues when I think about you know why have I not embraced some of the technologies right away. Someone’s fear factor on the educator end is that we feel afraid of what happens if our students know more about this piece of technology than we do and they’ve come to realize. That’s the reality. My students are going to feel more comfortable with new technologies than I am. They don’t have this fear factor that they’re going to break it where someone who maybe is a little bit more seasoned or not so seasoned may have this fear factor and we’re going to break this technology. But if I want to make my math education relevant and you can insert any content area in there. But today we’re talking about mathematics. We have to embrace that technology because our students are using it and if we want to make math relevant, we’ve got to figure out ways to and to incorporate that. So, I had to just remind myself. It’s okay if I don’t have all the answers to how it’s going to going to be used. I need to start to figure out some ways to incorporate some of that technology into my classroom so that students see that math has relevance to them.

Olivia
Yeah, I think you’re so right that we’re kind of bringing it back to the same thing but making the math as you said relevant for students and really the purpose behind it. I think these are some of those questions that hopefully educators are given opportunities to really ask themselves before they dive into actually lesson planning and picking the technology they’re going to use for the year and all those pieces. And you know, I think that you’re kind of already getting to it but you know as you mentioned there’s so much related to fear about technology in the classroom and just in education in general but what opportunities do you see that to technology presenting for creating those really engaging and effective learning experiences in math.

Kevin
Yeah, so what are my biggest aha moments as a brand-new teacher, I quickly realized all of my middle schoolers did not have that same passion and that same appreciation of mathematics as I did. I mean I loved math from kindergarten all the way through my undergraduate degree right? I still love math. But as a learner of mathematics, as a student of mathematics. It was always my favourite subject. I was always so excited to go to the math classroom. As a teacher I need to realize not all of my students have that same passion. So, I look at technology that may be a way that I can get a student who may not have otherwise been passionate about math, may not have seen her reason to and to learn math, may have wanted to sit there in the past and say time out forget it. I don’t want to. I don’t want to participate in this. Maybe I can use in tech now do that. I can utilize technology to literally have my students do a lot of thinking about it. I remember as a high school student, graphing calculators were a brand new thing. My high school had one set of the original graphing calculators that we all shared and we thought well this is remarkable. You can just type in the equation and a line appears. Well now it’s a readily available tool. Now there are multiple different online graphing calculators. There is demals.com which is graphing calculators on steroids with all kinds of other stuff that it can do, and we can change the way.
It used to be, if we want to have our students graph lines by hand you could get 3 or 4 lines grafted per class period. Now with technology you can get 3 or 4 lines within about 2 minutes, so now all your conversations can start to change, now you can start to have the students make explorations, you can say oh what is changing that number in front of the x what does that do to the line. No student wants to graph by hand y equals two x plus one y equal equals three x plus one y equal equals four x plus one gives them a graphing calculator give them an app. They’ll gladly graphles and they can start to look for those patterns. They start to become math becomes reason and sense making rather than just purely rope memorization, purely just regurgitating something and doing those calculations. So, I think technology, when we utilize it correctly, can be that. I also think we need to be cautious. If all we’re doing with our technology is replacing a traditional worksheet and putting the worksheet in some technology thing and saying oh I’m integrating technology. That’s not an integration of technology, that just taking something that we’ve done in the past and putting it on there. We’ve got to look at ways that we can really revolutionize education and using that and again, it’s scary. It’s difficult for some of us to think of how can, how can we do that because for so many of us the way that we did K12 mathematics worked for us. But maybe that’s why we became math educators because it worked for us and if I’m truly interested in meeting the needs of all of my students not just those that see themselves as capable of learning me. I have to be willing to try to do things differently and I have to be willing to utilize the technology that’s out there and continue to look at ways to integrate that technology into my classroom and figure out what are some of those things that I may have historically done, can now be replaced by some of the technology and then what skills do my students need to better be able to use that technology.

Olivia
That’s a great point I think that you know as you mentioned you’re talking about you had a point where every student had in a class had a graphing calculator. But for that one period and those types of things and I think a lot about equity when we think about the changes happening here. There’s so many so much more access for each student to in a classroom or in a different setting to not only have the access to the technology. But then as you’re saying the ability to explore with it in a way that they find what works for them and it is something that some of the best teachers I know hated the subject that they were learning or that the subject that they teach when they were learning it as a student and that was part of what brought them to teaching was that it was so challenging for them and I think that that really that ability to think outside the box has really helped them and so I think that for any teacher I love math as a student I love science that’s where how I got into science teaching but all of us can definitely benefit from really thinking about how can I be creative with all this technology to allow a student to have that 1 on 1 experience with the content that really helps them learn. So, I love a lot of that.

Kevin
Actually, it comes back to that idea of being a lifelong learner. You know, I’ve had people say how in the world you teach the same grade level for 26 years in that classroom and love it. You know what? It’s not like my lesson plans from year one are my lesson plans for year twenty six the way that I taught is an early career teacher to the way I’m teaching now in whatever stage of a career you want to call it looks different. If we’re truly interested in meeting the needs of our students if we’re truly interested in making education more accessible to more and more students to make it more equitable, we have to be looking at what we’re doing. We have to be looking at what new tools are out there, how do we better integrate them in there to meet the needs of every single one of our students not just those that are privileged not just those that have historically done well. But for every single one of our students what can I do. And I see there’s so many potentials with technology. There’s also potentials with technology to really divide and to really grow that divide and to really make it the haves versus the have not so to speak and we had to be cautious that we’re and we’re being equitable with our use of technologies and that we’re affording every single one of our students the opportunities to grow in their skills through technology.

Olivia
Now I think that’s great and just thinking about giving the teachers that space and resources to grow alongside with the technology as it evolves is a really important part here. And I think one thing I wanted to think about just you know we’re kind of talking about what got us into the subjects we taught but for you like what really sparked your passion for mathematics, and I was speaking to my love for science that brought me there but what kind of sparked your passion there and how do you strive to really ignite that enthusiasm your students using some of the tools available.

Kevin
That’s a great question. Mathematics was a set that I always felt confident in it was a sort that I always liked and maybe because it was sort of in my student eyes. It was either right or wrong. Language arts I always felt like but sort of open for interpretation and I didn’t like that. I want to be able to know am I right am I wrong. So, I think because I had that initial passion for math and I felt good at doing mathematics I want to continue to pursue that and I think I knew from an early, I always do, I want to be a teacher. And I think probably already starting in second or third grade I started to verbalize but that I wanted to and to be a teacher and when it got to be middle school and you started to departmentalize at that point in time from that point on I knew without a doubt that I wanted to be and a math teacher because I just appreciated that I like the way that you could see different things and that you could express the math through the numbers and through the problem solving and I would say my knowledge of math I appreciate for math has grown as I started to teach. I know as I as a student I probably thought there was 1 correct way to do something and we may haven’t taught that was just sort of 1 correct way, you just mimicked what the teacher told you to do. But as the longer I’ve taught, the more I’ve realized there’s lots of different ways that a students can arrive at that same answer and that’s what’s what makes math so fascinating for me, that you can give that same problem to 5 different students and they may have 5 different ways of getting there and that excites me. It gives me the opportunity just to look into to see what’s happening How is a student thinking about this problem and to see the look on student spaces when they finally figure something out they’re like oh and I like yes you’ve got it. It’s such a fascinating subject and I love it.

Olivia
I so see that and I think that there is I think that that’s the passion that a student who doesn’t like math definitely needs to see from someone and have a model of someone that can bring that in so you know I think anyone who once you get into your subject as you said many of us are lifelong learners and I think just modelling that for our students is so important and I think thinking about you know we’re part of that is that we have to prepare our students for an everchanging future just like our teachers are now preparing for an ever changing future and us as Ourselves. So what skills in Mathematics do you think are so essential for students to thrive in the new everchanging future and how can technology support in developing those skills.

Kevin
Yeah I really think we need to continue to push math to that and that what do you understand? Can you represent a real life situation and put it into math language that I think historically when we think about math our students just see math as oh it’s a set of procedures that I have to memorize so that I have to mimic and with all the new technologies that exist when I think about AI especially, our students don’t see a need just to memorize how to solve an equation. They don’t see a memoir or reason to and to memorize how to multiply 3 3-digit numbers with decimals. For example. Because the technology can replace that we need to get to that understanding stage with our students. We need to help them look at it at a situation and help them realize oh we can use math as a tool to help us analyse the situation. So, I think it’s really and a crossroads for math education. We need to think deeply about what it is that and that we’re teaching. For so many students, the data and statistics is always that very last little bit of the school year sort of saved for the end, and I would argue we need to have a whole lot more of data and data interpretation throughout the school year throughout our students’ lives because when we look at world outside of the K12 world. There’s so much more data and we want students feel to make sense of that. So, I think it really comes down to that sense making the real life applications modeming representing a situation with mathematics.

Olivia
Yeah, you know I laughed a little when you mentioned like statistics always say for the end because I mean it happens every year and it’s just across you know I remember it as a student and as a teacher and I think that especially just thinking about there’s so much more emphasis now on. Data science because we have to think about where is this all this data coming from that all of these Ai tools are actually using and how is it being categorized gathered all those things and so I think it’s a great point that you know we’re talking about being a little bit overwhelmed by how many tools there are well that in itself is this a space for sense making so I definitely think using the curriculum and using tools that were might as we mentioned earlier instigate a little bit of fear can actually be brought down a little bit by thinking about as you said the data science and sense making piece of it all.

Kevin
Absolutely and it’s so important and that’s what makes education relevant for students. It’ what’s engaging for our students. You know I talk with many educators, and they say oh my students are so disengaged in math and happens in other content areas as well. But often here a lot of times of math oh my students are disengaged. Well let’s make math relevant for them. Let’s find ways to utilize the technology to engage our students so that they start to begin to think more deeply about the mathematics and it’s challenging. It is not an easy thing to do but it is so important if we’re interested in meeting the needs of every single one of our students and developing a math literate society.

Olivia
I think that’s a great point and just thinking about help supporting our students in the ways that they’re in a need for the ever changing future and I think with that I would also love to know from you like what are some of the promising trends in the future of math education just especially that you’re getting the chance to see on a more national level math education, thinking about the integration of technology what promising trends do you see?

Kevin
Yeah, you know I think about promising trends I think it’s figuring out ways to use that technology and there’s a lot of conversation around from a lot of different situations and lot different people throughout the nation that I think about how do I better integrate the technology and I think that’s definitely a promising trend. I also see a promising trend as there’s a refocusing on making math relevant for our students and helping them see that humans develop to mathematics and sharing some of those stories and a focus on making math accessible, equitable for every single student. That it’s not just those that are going into stem careers can get a good math education. Every single student deserves a good math education and I see and an ever increasing as amount of student-to-student discourse in classrooms and that excites me. When it’s the students engaged in sharing their thoughts about the mathematics and having that rich dialogue that’s when good things start happening and that’s when students start to really develop that understanding and start to recognize that there’s lots of different ways, we can solve a problem. But we’re still going to reach that same solution if we’re solving that exact same problem and it’s exciting to see that revitalization and that refocusing on me the needs of every single one of our students.

Olivia
Yeah, you know someone I was recently listening to a podcast about you know interviewing some other educators and former educators and there was this concept of you know, not just asking students what they want to be with it when they grow up but what problems do they want to solve, and I think. As you mentioned just helping students feel confident about their problem-solving skills is really going to be helpful to help them think about how they’re going to engage with the world around them as they grow up.

Kevin
Absolutely and the recognition that we can look at a real-life situation and depending on the parameters we put in place depending on the assumptions that we make we can get a variety of different answers for that and that’s okay, that’s where that communication needs to come in place and that’s where student A can say oh here’s a solution that I derived because I made this assumption because I put this parameter and student beat may have a slightly different final solution because they had different assumptions. And it’s the thinking that goes behind that the ability to communicate your thinking, the ability to communicate your thoughts, your assumptions. That’s what’s so critical and that’s why I think the workforce is looking for people who can articulate what they’re doing, not just those that can sit down and fill out a worksheet of problems done correctly. And unfortunately for too long mathematics is that just do worksheet after worksheet after worksheet and that’s not relevant for our students. They don’t see them as math as capable as a reason to learn and they don’t see any particular value for it.

Olivia
Yeah, really important points and I think just you know as we wrap up today, I just wanted to kind of give you an opportunity to share maybe some advice or insights that you can offer to teachers out there who are now being a landscape you know along with all the advice you’ve already given them but any kind of last thoughts on advice you might give to offer them to make the most use the technology they now have.

Kevin
Yeah, be willing to fail with the technology. It’s okay if you make a mistake with and utilizing the technology, the students will see that you’re trying to grow in your skills that you’re trying to better educate them and they’ll be okay. It’s okay to ask your students hey how do I do this with that because again at least from my perspective my students are much more willing to try and fail with a piece of technology than what I am. I want to make sure I know how to do it before I dive in, they’re willing to dive in, they don’t want to read the step-by-step directions. So okay to utilize their inquisitiveness and to build on their inquisitiveness and I need to keep reminding myself and fellow educators we don’t need to have all of the answers for how to use the technology for it but let’s start to figure out how we can use that technology. Let’s build relationships with others, Let’s build from our students funds of knowledge about that if we’re truly interested in making mathematics accessible for every single student.

Olivia
Yeah that’s great and I think that I definitely hope that teachers out there are feeling a little bit less on. Yeah as you mentioned the fear side of technology and really being able to take those moments and really just kind of sit back and embrace the options and opportunities that all of this amazing technology offers us really to get back to that original point of thinking about what really is the purpose of math and how can our teachers support students as they’re getting into that mathematical reasoning and understanding. Well, Kevin thank you so much. We really appreciate having you on today and to all of our listeners thank you again for tuning in.

Kevin
Absolutely.

Olivia
We trust that this discussion has sparked some maybe fresh perspectives and fuelled your passion for innovative teaching methods. We definitely encourage you to share your thoughts reflections and personal stories on today’s compelling topic across your favourite social media and you can join our conversation with the hashtag #MagicEducatorInsights. We are looking forward to our next podcast but until then catch you later.