In this episode of Room to Grow, Joanie and Curtis talk about an important role of math education: preparing students for the life they want to pursue after high school. Whether it’s college, trade school, the military, or directly into the work force, a student’s goals and desires should drive their learning experiences throughout their PK-12 years, and the course offerings, counseling and advising, and school system overall should, ideally, prepare all students for the outcomes they desire.
They recognize early in the conversation that this isn’t just about high school, isn’t just about courses, and isn’t just about math. They dive into ideas around career choices, advocating for students’ best interests, and the challenges in creating a system with the depth, breadth, and flexibility required to truly prepare all students. There aren’t easy answers to these questions, but we hope the conversation sparks thinking, discussion, and actions in your setting that support more students to be better prepared for their chosen futures.
We encourage you to explore the resources below, referenced in this episode:
Did you enjoy this episode of Room to Grow? Please leave a review and share the episode with others. Share your feedback, comments, and suggestions for future episode topics by emailing email@example.com. Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy.
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Students often don't realize or don't know or aren't able to advocate for themselves. And so where do we as teacher, get the opportunity to advocate for our students?
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In today's episode, Curtis and I take up 30,000 foot view of considering how school prepare students for their lives after school. We discuss the importance of career advising that includes the personality characteristics and work styles required by a career, as well as making explicit connections to the learning that prepare students for that career.
We talk about mathematical pathways in high school and busting the trend of calculus driven sequences of courses. But so much more. So let's get growing.
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All right, Joanie. Well, I am so excited to be sitting here today recording with you. We are at the AP annual conference and really excited about that. It's going to be a great podcast.
We've had some good precession talking about all of this stuff. It's really exciting. But the opening session this morning set us up so great.
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It really did. And I was saying before we started recording, talking with some friends and colleagues that we only get to see at conferences. People are asking about, Well, what's your process for the podcast?
How do you guys plan your conversations? And I said, Well, we don't. We like pick a topic and we'll maybe mention two or three big ideas that we want to be sure come out and then we just have a conversation. And this coming to this conference and listening to this open plenary totally set us up for what we talked about last week that we wanted to be our topic for today.
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So I think we're both just kind of sitting on the edge of our seats with excitement about things we want to say and things that we want to bring up so Curtis, why don't you like give us a little opening framework so our listeners know like what it is we what are we talking about today? Because I feel like we just dive right into the weeds and kind of leave people behind.
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I agree. So I think the general theme of what we're trying to tackle today is really thinking about our students as they process from students in pre-K and early elementary school all the way through their high school careers and what are the steps and the things? I don't want to just call it coursework because it's not just coursework, it's the other things that we do as educators to set them up and to prepare them for their goals.
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And I underline that maybe with my hands or something, I tried to emphasize it. There, but it's their goals. Post-Secondary. Right. And I'll admit freely that my eight year old, my 12 year old doesn't really know what he wants to be when he grows up and shoot. I'm 42 years old right now, and I'm not sure I want to know what I want to be when I grow up, but I'm loving what I'm doing right now.
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So I think there's something to it, though, about getting them and helping them have vision, helping them have dreams and putting things in front of them such that that they see themselves being able to have those right. That's the general theme.
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I love it. And I just want to kind of fill in some gaps a little bit because we started an initial working title for this podcast was about high school math and thinking about, you know, high school math pathways, which is a really important conversation that's happening in a lot of places around the country right now.
But as we thought through and did our own individual research, I think we both realized like, no, this has to start way earlier than high school. This is not a high school conversation. And to your point, it's not just a course offering kinds of conversation either. It's really about I don't know if a broader term that might work better is learning experience is like what kinds of experiences do we need to ensure that students have as they progressed through school so that they are able to have the right opportunities, make the right decisions, and really be able to pursue, know what matters to them and pursue what matters to them so that they can be
successful post-graduation. So I just kind of want to add a little bit of a frame to our conversation as an overarching topic, because one of the things that was most powerful to me in the opening plenary session that we just listen to here at the AP conference was about opportunity and about as adults, especially adults in the field of education.
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We make decisions for kids. We do, and in a lot of times we make decisions for kids that they can't or wouldn't make for themselves. Right. And there's a lot of responsibility that comes with that. And it's not that the student shouldn't be involved. They always should and the parent should. But Trevor Parker, who's the vice president College Board that oversees the AP program, told a really powerful story of his own experience where he would not have chosen to have put himself in an AP course as a sophomore in high school.
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And that decision was chosen for him. Yeah. And then even the decision to take the AP exam at the end of the year was kind of not really his decision either. And yet the outcome of that experience really shifted the trajectory of his whole learning. So I think for me in that moment, I was thinking, Oh, this is such an important point I want to bring up in the podcast, because as an educator, I know when I was in the classroom, I was a department chair for several years, like I was making decisions for kids and not realizing that I might be changing the path of their outcomes in doing that.
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And I am positive that I didn't always change their outcomes for the better. So I'm just thinking of like this awareness that if we have that awareness more at the front of our minds, would you know that great biological quote that when we know better, we do better?
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Right, Right. No, I think you bring up a great example.
I had the same thought when I was listening to that, and I wrote myself this note about we don't often think about the decisions we make as educators. I mean, maybe we do. I know myself personally, I don't think I thought about the gravity of even the smallest things that sometimes we did. And I think back sometimes to the students that I had, particularly the ones that I recruited.
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Right. Right. Yes. I recruited you to continue to take AP statistics class, and I watched them change from I'm not sure I can do this right to I can do this, too. I like doing this. I want to do this like this is awesome. Yeah. And how we set them up, I don't think I thought about that early on, Right.
I don't think I thought about that when I saw them coming in as freshmen or the students that I had in my sophomore pre AP Algebra two class, where I had students in there and in trying to project, I often recruited in that class, but trying to project what they could be when was coming, right? What they could do. Yeah, I don't think I did that quite enough.
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Well, and I think it's easy to think back and I know many of our listeners will relate to this. When I taught juniors and seniors in high school, I remember the back to school time and you get your class list and then you're sitting in your math department meeting and the teacher sitting next to me is like, Oh, well, let me tell you about that kid, right?
So this the preconceived notions that we often bring or and that could be around behavior, that can be around how this person is as a learner or that can be around perceived ability and whether or not a student can be successful. And there are just so many parts of the high school systems that I had been a part of in my classroom days that made those decisions for kids.
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Yeah, based on nothing based in randomness. Right. So really being able to kind of push back on that thinking and think about each and every student being a person who has amazing potential, who could be a Trevor Packer, who could go from being a straight C student to valedictorian and attending an Ivy League college because somebody believed in you, because somebody made a decision.
Right? That shifted the learning opportunity for you. So I think we're kind of going off on the pious conversation here, which is great. But I also want to bring us back to this idea of of schooling, not just being about accumulating credits and getting a diploma, but actually as a preparation for what comes after schooling and thinking about how do we help kids better understand career choices and how school leads to different opportunities for them Outside of that.
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So I was thinking about how we do that. And one of the things that came to my mind I was mentioning this earlier on is that my son's school at the end of every school year, they have sort of a career week. It's actually I think it ends up being two weeks and they bring in parents to the they have morning announcements that they do they do them video wise.
And it's really kind of cool that these kids do that every week and they do this all throughout the school year. But during those two weeks, they bring in they have a special segment and they have parents come in and they talk about their careers and the student gets to introduce their parent the, Hey, this is my dad, this is my mom, my aunt, grandma, whatever.
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And they talk it. They say this is who they are. And then the parent talks about their career and introduces that. And I was thinking about the importance of such an experience because I mentioned that I don't think my eight year old has a clue what he wants to be when he grows up. Right. And my 12 year old definitely doesn't have a clue what he wants to be when he grows up.
And I mentioned it that if you ask those students, typically they're going to talk about whoever it is that's closest to them. That's what I see every day. And I'm going to be just like you. That's right. He just like whatever adult influence that they have right in front of them. That's right. And so the importance of in our school systems, providing opportunities to see careers that are beyond the typical things that people hear about and think about airline pilot is something that some people see and some people get exposure to.
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But not everybody right? Policemen is one that almost every kid usually has some sort of they bring them into the school or the fireman come in. They do safety things. So they have lots of exposure for those kinds of things. But a kid who has an engineer, what what does that even mean? Right. How do we even talk about that?
And so I think just the importance of exposing students to careers and career possibilities well beyond what is normally out there, we don't normally talk to or show students an accountant career, Right? It's true. But just showing them what actually could be or might be done as an accountant gives them an idea that this might be something I want to do.
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That's right. And I would take that even a step further and say another thing we don't do well is help them understand based on what you like to do or what you enjoy or what's kind of baked into your personality. Here's a career that you might be good at, right? So not just like what does an engineer do, but what are the personal traits and the work styles and the things that you get energized by to be a successful engineer like to you love to solve a puzzle.
Do you like to take things apart and figure out how they work and put them back together? Yeah, and I know that's a really like sort of trait example, but how do you help kids understand when you're in this career? This is the kind of thinking you're going to engage in? You know, I think about my own experience.
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I shared this, too, before we started recording. To your point, what I wanted to be when I grew up was the really cool guy that lived next door to us, that worked for a big oil company and said, Oh, you enjoy math and science. Well, you should become a metallurgical engineer and you can come work at my company.
And I walked around from the time I was about 11 years old saying, I'm going to be a metallurgical engineer. And I didn't even really have any idea what that meant. But as I thought about pursuing an engineer path, I ended up in computer science. So it was my major, my freshman year of college and that summer my dad's company had an internship opportunity.
So I went in and did some coding for my dad's company over the summer after my freshman year, and I'm like, Oh my gosh, I'm sitting in this tiny closet of a room with no windows all by myself, with the computer in front of me coding all day. I'm like, I hate this. I need to talk to people.
I need to be up and walking around. I didn't realize until I'm like a quarter of the way into this degree going, wait a second, This doesn't really fit who I am at all. So, so not just the exposure to the career, but helping kids identify how do I know what's a good career for me? Not just the thing that the really cool person who live next door says I should do, but what I know about myself and what I enjoy and what is my skill set and how can I apply that to a meaningful position.
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And then I'm going to take that one step further and then say the other thing we don't do well, I don't think is connect the learning that kids are experiencing in school to those outcomes, to those careers. So what is it about what I'm learning in third grade that I would connect to? I mean, maybe it's because the connecting of the dots is too far, but how do we help kids see?
Like because you're learning this thing right now, it's getting you ready in this way to be able to do that job.
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Yeah. Now I think those are really important things and actually that was a great transition to kind of our next little point, which is what are we doing inside the school? Okay, great. We could do some of these career experiences.
We can even have recognition of the character traits that kind of help you see these things. Maybe there's some career training about here's the things that happen inside of this career. And where do you see yourself in more? Here's where I see you. These are the kinds of things because I think one of the things that we as adults have the ability to do, the responsibility to do is speak truth into these kids lives about the things that we see in who they are.
Right? Right. We mentor them whether we sometimes take responsibility for that or not. We mentor these students and the opportunity to be able to speak truth into them and recognize who they are right is super important and help set them up for their future. So those are important things. All of that is the stuff that we can add in, right?
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But then let's talk about let's actually talk a little bit about the coursework and the things that we're doing to set these students up from an academic sense. Right, Right. We get the personal sense. I think that's a big, big missing chunk. I think we're trying I think there's lots of programs out there that we're trying and we're doing these things, but we can always do better, right?
So now let's turn the page a little bit and start talking about what course offerings and what kinds of advice that we can give to students as they begin to think about what we're doing. So what do you think about some of the course offerings or maybe how we're setting students up for those postsecondary things?
Well, it's interesting because I think this is a really I don't know if controversial is the right word, but it's certainly a loaded conversation.
Absolutely. And again, back to our opening comment that the conversation around mathematics, pathways and opportunities, of course, sequencing for students is is really a hot topic across the country right now and understandably so. And I think finding the balance between not assuming that everybody needs the same thing, but also not closing any doors of opportunity for sure by trying to address the different needs.
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Right. So how do you find that sweet spot? And I can say this in words that make it sound like it's really easy to do, and I am not naive enough to think that a system can do it as easily as I'm going to make it sound. But it's creating course offerings that have enough structure that every student is having a rich mathematical experience challenged, not watered down, sort of dumbed down kinds of experiences.
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But no matter what sequence of courses, there is that mathematical depth and opportunity to learn deeply and at the same time provides enough flexibility to support any outcome that any student wants post-secondary and flexibility for them to be able to change their minds along the way.
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You just said something that caused a visual in my mind to pop up, and it was one of the visuals from the articles that we were looking at the American Progress dot org has an article, Math Pathways that we looked at, and there is a visual in here that as you were talking about, this idea of rich mathematical depth, yet flexible right space, I was seeing the breadth of
these bars that are in here kind of leading from and I know we often end up talking about high school because that's just where our minds are. But the idea of the algebra one and a little bit more breadth to geometry and math, to add a little bit more breadth to algebra to or some kind of advanced algebra course.
And then the more width that those bars have kind of representing the diversity of application in each of those things, but to their post-secondary goals. And I think that's what you were trying to get at. But in my mind, that's what I was having to visualize, because this is a very difficult thing to kind of think about how do we prepare them early enough on such that they can be set up for success in those advanced courses.
And within the time frame that secondary high school happens. Right. And still give them enough flexibility such that they can choose something different at the end of their high school careers.
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Yeah, Yeah, for sure. And I think another interesting point is the counseling part that happens, right? And even course recommendations, I think about the the giant long sheets of paper that kids would have like eight and a half by 17 with every course, different colors for the different grade levels and every course that we offered at our high school.
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And kids would check and get the signatures right and at how are we making those decisions like, oh, you took that, you took this course this year, so here's the course you're taking next year instead of like, what are your goals for yourself? What are your interests? What do you want to pursue? And and again, I'm not saying this like no one ever is doing this.
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We know this is happening for sure. Well, in places, but it's not the experiences of all kids. And it should be. It should be. Yeah. And being able to really counsel students from a good understanding of back to the career conversation, do they have enough exposure to know what careers actually interest them? Do they have a good enough understanding of what does the work style look like for this career, and does that match with my my style?
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Like, is that something I've wanted to pursue for the rest of my life? And then do we actually have the courses to offer them and the ability to give them the experiences that they need and want to have? So the importance of having all of those components lined up is it's a lot to ask of a system. It is it's a lot to ask of a system.
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It is it's a lot to ask of a system.
And it I mean, I hate to say this it sounds so trite, but it does take all of us as we like, think about this and we consider what we're asking of this system. We need to realize we're all participants in it, right? And that fact that we can play a role in developing that, that we don't just leave that up to the counselor or we don't just leave that up to the specific teacher in this specific thing.
And knowing enough about disciplines or no, our students come and talk to us about the other disciplines, right? And so I've had students come and talk to me about their science courses and ask me questions about what should I be trying to do. They know a little bit about my engineering background. And so there's a little bit of that conversation that is good and they come to me for that reference.
But just knowing enough about little things to be able to kind of help boost them along.
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I was really thinking about another piece of this puzzle. So often our students have experiences that they themselves don't have a ton of control over, right? But they have desires and dreams. Maybe they do come to us with desires and dreams. One of the questions that I've been asking and you talked about this quite a bit was the supports that we have to help students be successful in reaching those goals.
Break student has come into a ninth grade, is taking ninth grade Algebra one Calculus AP Calculus is a challenge to get to. Yeah, if I have an algebra one like I have to take algebra one requirement in ninth grade. Ninth grade? Yeah. So what am I going to do? How am I going to set a student up to be ready for and to be successful in that 12th grade calculus course that they have a goal of getting to do I have a pathway for them?
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Yeah. Yeah. It's a great question and it comes down to that like is there enough flexibility within the pathway that a student can decide that calculus during high school is important to them? They can make that decision as a ninth grader or even a 10th grader, rather than having to make that decision as a fifth or sixth grader.
Right, right, right. That's a huge, huge challenge. And I think as we start to uncover this conversation, I want to say something that you said before we started recording that I think is really powerful, Like we're trying to set a new trend. We're talking about taking apart a system that has been how we've done things for such a long, long, long, long time.
And so I think that's super challenging. And at the same time, I think we have to just decide there is a solution to this problem for sure. I think saying to a student like, Oh, well, sorry, you're in algebra one as a ninth grader, bummer for you, but what you want doesn't work within the system that we have.
And, you know, all told, just a quick story. My own personal experience. I went to private school up until 10th grade, and when I was in eighth grade, there was no, you know, seventh and eighth grade. There was no algebra one opportunity for me. Sure. I mean, I was in a small school. There were 50 kids in my class, two classes of eighth graders, and we all just took the same math.
It was pre-algebra. So I didn't have any choice but to get algebra in ninth grade. That was the soonest it was an opportunity for me, right? And I enjoyed math and had success in math. And had I been in a school where I could have taken a more advanced math class, I might have, and yet I still went on to be a math major.
You know, I can't tell you how many parents and kids I shared that story with. Like, I got a degree in mathematics and I started in algebra one in ninth grade. So, you know, just know that that doors aren't closed,
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door isn't closed. And that's the most important thing is realizing that my junior year all of a sudden I decide and I've really found an interest in mathematics, but I've been taking the standard coursework every year.
I'm about to take maybe I, maybe I bombed a little bit and I'm about to do geometry again for the second time, but I'm really now passionate about this. What? Okay, calculus is a goal for me. Yeah, probably not something I'm going to be able to do as a senior in high school. Right? Junior year, I'm taking geometry.
It's just probably not in the timing for me. What do I do as a school? What do I do for that student to help them reach that goal? How do I set you up? Here's what we're going to do inside of the walls of this school, right? That we have control over. We can set you up. We're going to offer these things for you.
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Yeah. It's so interesting that you give that specific example because the response needs to be to the specific example, right? So I think it's having opportunity. I think one of the things that has to be consistent across whatever the situation is, those high expectations and opportunity and thinking outside the box is what needs to happen. Sometimes. So maybe that junior I don't know, we'd have to, we'd have to know a whole lot more about this kid
that's just making a hypothetical, because what I'm really trying to do is get us to have the the thought and to as we develop the systems that we develop, as we develop the way that our courses are writtenin high school, as we develop the counseling sessions that we have with
the students as they choose these courses and as they choose their paths through high school, are we offering both the depth and the breadth that we need to to these students? And I get it. I came from a small school in a rural setting, limited opportunity, not that many teachers to begin with.
Yeah, right. So how are they going to be able to handle this and offer things for me? We as a society need to figure out how we can. That's right. Hope that. That's right. And I don't know what the answers are. I'm not pretending that I know what the answers are. I just know that there's a need. Yeah, it makes me think of my experience.
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Yeah, it makes me think of my experience. I was a district math coordinator when the Common Core came out and helping. I was in a large district, 55,000 students. We had six comprehensive high schools and helping think through those systems and how those systems might adjust and change. And this was one of the things that I tackled with my high school and middle school math coordinators was how do we provide more opportunity for more students to take calculus in high school?
And not that I don't want to set the stage, that calculus is the end all, be all but the calculus sort of driven system is one everyone's familiar with, right? So how do we think about a kid who comes into ninth grade algebra one and says in ninth grade, I really want to get to calculus? How can we think creatively about that sequence of offerings that gets that kid to calculus?
And some of the interesting conversation that might help our listeners that might be wrestling with some of these things are we wanted to be really intentional about having multiple decision making points. Yeah, clearly one of those is going to be starting in middle school in our district. That's when students first had the opportunity to do a kind of honors level, a differentiated math course.
So how do we make those decisions at those decision making points? And so we wanted to think through what are all of the decisions that could happen? What do we do if a kid decides in ninth grade, I want to take calculus. Well, let's be sure we have a path that gets them to calculus. In our case, it meant thinking about condensing Algebra one and geometry concepts together and algebra two and geometry concepts together.
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That could take three years of math into two years for those kids who are highly motivated. And what might that look like? And what if a kid doesn't decide that until the end of ninth grade? Like how do we think about the flexibility within those pathways to get kids to be able to reach that outcome? Now, could a kid go from geometry in 11th grade to calculus in 12th grade?
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Probably not. But if we're having that conversation every single year, we're catching more and more kids and getting them to the outcomes that they want more and more often,
I think you just hit it and just having those conversations, the multiple touchpoints, all of those things are really important in terms of beginnings of a solution, right? Again, I'm very careful to admit that I don't have all the topics are all the solutions or not.
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Joanie / Curtis
This is news to me. Oh, come on. No, it's in the name room to grow.
We want to grow and grow.
We offer the opportunity to grow along with that. Absolutely.
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But no, this. This this idea of the calculus pathway, we've hit on that a ton. And I want to make sure we bring up this idea that for hundreds, even thousands of years, right.
We've had this one goal towards this one type of mathematics. And only recently in the last hundred and 50 years ish, we've kind of began to expand that into data and analysis of just the world from experience, right? Experiential types of things. And we're collecting data now trying to figure out how to analyze it. So we have this whole world of statistics and data analysis.
Yes, we now have this financial world that we also kind of explore and we think about. We also have connections to all of the sciences that would matter in a modeling course like trying to figure out the way that math kind of models, the way the world works. And so there's a ton of different things that we have now begun to recognize as needing the influence of the mathematics.
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Yeah, or even opportunities to apply the mathematics that students learn and know. And so what I'm thinking about what's in my mind, I'll eventually get there, I promise. Guys in Good. Oh, is these math pathways right that we've had this one pathway for hundreds of years that was geared towards calculus in mind, But now we're realizing and beginning to recognize the opportunity we have to set students up for multiple pathways.
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I know that you'll hear alternative pathways, and I don't want that language to be saying that other pathways are lesser, and I think that could be taken that way. And it's not. There's a traditional pathway that we've had for a long, long time, and we're just now learning to break away from that traditional pathway and realizing that we have mathematical pathways.
Yeah, we have lots of them, yes. And that we want to have students be able to be set up for. And I think that we are trendsetting by doing this right, we are trying to change the way that we think about mathematics, education.
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Yeah, yeah. And from that same American progress report that you cited earlier, there is a statistic in there that I actually pulled out around 80% of students.
These are college degree bound students. Around 80% do not need an algebra intensive curriculum nor calculus to be successful in their degree program. And yet and yet you're expected to take calculus for admission to top universities, right? Like even if you're not going that there is another quote in here, you're not going to get into Duke if you haven't taken calculus, even if you plan to major in French literature.
Right. So how do we think about that's to your point, like we're trying to bust a trend, we're trying to redefine that there are lots of meaningful, valuable sequences of courses, mathematical pathways, and we need to be thinking about those more carefully for our students rather than just assuming that the needs of everyone are the same for sure.
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All right, Joanie, we've been talking about this for a little while. I want to ask you a pointed question. I'm ready. You love those. So what is the key takeaway from this conversation for our listeners? What can we kind of be thinking about as we move into this school year? This is going to be released in in August.
So we're looking at beginning of school. What are the things that we as educators, teachers, administrators, whatever, what can we be thinking about and what can we be doing in light of what you and I have just been chatting about?
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Well, I'm going to I'm actually going to answer that by quoting from one of the articles that we read.
And then I'm also going to turn the question back on you, even if you just say the same thing you just said. But it's the opening statement of this Math Pathways article from the American Progress that a high school education and I would argue a K-12 education pre K-12 should prepare all students for their chosen next step after graduation, whether it be a two year college, a four year institution, military services, and then they're their to throw it in or immediate entry into the workforce regardless of their choice, their mastery of mathematics during their high school education is a gateway to success.
Yeah, and although we're making that sound like high school is where all the pressure falls, we know that's not true. We know that our elementary and middle school teachers are contributing to students high school successes too. So I think for me, the key takeaway is just the responsibility that we carry for our students and ensuring that we take that responsibility seriously.
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And I think the only follow up I would have, as you turned that question to, is to add to that advocacy, because one of the things that and I forget who said it this morning, it all ran together. Students often don't realize or don't know or aren't able to advocate for themselves. And so where do we as teacher get the opportunity to advocate for our students, both to them?
Because there's a lot of negative self speak out, there is a lot of negative self-talk. So where do we advocate to the student for the student and then also outside of the classroom, a system within the system, how do we advocate for them? And I realize that there's an incredible amount of pressure put upon teachers and the job is impossible.
Frankly, all of the things that we talk about are impossible to do as an individual and extremely difficult to do as a whole system in society. So I get that and I acknowledge and openly admit that. But that doesn't negate the importance of doing that.
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Well, that's it for this time. Be sure to check the show notes for the resources we mentioned and others you might want to explore.
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