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Mandy Jansen makes connections in math
57 Plays2 months ago
https://www.udel.edu/udaily/2024/march/faculty-excellence-awards-engagement-scholarship/
https://twitter.com/MandyMathEd/
https://jansenamanda.wixsite.com/professional
https://www.cehd.udel.edu/faculty-bio/amanda-jansen/
Book: https://www.routledge.com/Rough-Draft-Math-Revising-to-Learn/Jansen/p/book/9781625312068
Shout out to:
Frances Harper:
https://tpte.utk.edu/people/frances-harper-phd/
(She is actually an associate professor now.)
Peg Smith:
https://www.nctm.org/Grants-and-Awards/Lifetime-Achievement-Award/Peg-Smith/
https://www.lrdc.pitt.edu/people/researcher-detail.cshtml?id=55
Music by AudioCoffee: https://www.audiocoffee.net/
Recommended
Transcript
Podcast Introduction
00:00:00
Speaker
Welcome to the Learner Centered Spaces podcast, where we empower and inspire ownership of learning. Sponsored by Mastery Portfolio, hosted by Starr Saxton and Crystal Frommert.
Target Audience and Purpose
00:00:14
Speaker
In each episode, we will bring you engaging conversations with a wide variety of educators.
00:00:20
Speaker
both in and out of the classroom. This podcast is created for educators who want to learn more about how to make the shift toward learner-centered spaces for their students, schools, and districts, or education at large. The Learner-Centered Spaces podcast is a member of the Teach Better Podcast Network. Get ready to be inspired as we dive right into the conversation with today's guest.
00:00:46
Speaker
We are so excited to have Mandy Jansen on our show today.
Engaging Math with Mandy Jansen
00:00:51
Speaker
She is a mathematics professor and she has taught also in grades seven through nine, algebra one and general math, before she became a professor. Her passion is to help create math classrooms where students want to be. It's important to her to recognize and amplify strengths in students' thinking when teaching math and build on these strengths.
00:01:11
Speaker
Interesting fact about Mandy, she plays pinball, and she also received an award from her university in 2024 called Excellence in Scholarly Community Engagement Award. Please welcome Mandy to the show today. Thank you so much for having me. Morning, Mandy. We would love to know a little bit about your ah defining moment in your educational journey that led you to where you are now.
00:01:37
Speaker
Oh, thanks for asking.
Mandy's Journey from Teacher to Professor
00:01:38
Speaker
So yeah, I used to be a middle school math teacher, and now I teach future elementary and middle school teachers. And so how did I get on this path to focus on math teaching and learning? And I think about when I was in high school. And there were moments where I started to see that learning math wasn't just something to memorize. It should be about seeing new connections that are beautiful.
00:02:06
Speaker
And I remember you know i we had to memorize the quadratic formula. But when we learned about completing the square as another process, we could actually derive the quadratic formula through completing the square. And so recognizing that these are connected strategies was really eye-opening for me. And then it happened again in trigonometry, where the unit circle was actually representing what was going on in these sine and cosine graphs. And the larger idea there is how mathematics knowledge is an interconnected web. And so one way we could keep revising our thinking in math is finding new connections. And so then it's not so much about like fixing something that's wrong, but understanding more how these ideas are connected. Math and ended up becoming this really beautiful series of relationships. And I wanted to have had that experience when I was younger, not until I was in high school. and
00:03:03
Speaker
And it just led me to see math in a new way and wanting to help more people have that kind of experience. So as a non-math person, but who works with math people sometimes, can you share a little bit more about that shift to a space where where you were making math more than just what was on the page because I know I work with a lot of students who struggle with math and they'll say that they aren't good math students, but I suspect that that's probably just old programming and maybe haven't encountered the kind of learning you're talking about right now. So could you say a little bit more about that?
Teaching Math for Understanding
00:03:41
Speaker
Yeah, so I think a lot of times when we see ourselves as maybe not so much math people, it's often the case that what we've been taught to do is mimic someone else's solution strategy and not necessarily make sense out of it, but just execute it. And I really want math to be something that makes sense to people because it can, right? Math was invented by people. It's something that people can understand.
00:04:10
Speaker
So I think about like if you're solving a proportional or reasoning problem like I bought eight posters for a certain amount of money and I want to buy What if I needed to buy 12 posters? How would I solve that? And so some people have been taught a strategy where they set up two equivalent um fractions of proportions and they cross multiply, but they don't really know why that works. Instead of straight out teaching that algorithm right away,
00:04:41
Speaker
You can work with people to find strategies that make sense to them. Oh, I can find out how much one poster would cost and then I would be able to find what 12 posters costs or I can look for a scale factor. Like if I multiply eight times one and a half, I can get 12 posters so I could multiply.
00:05:00
Speaker
The amount of money that eight posters cost times one and a half to try in the price of 12 posters. So working on developing strategies that make sense to people, then people can view themselves like, oh, I'm capable of understanding this. I can do this. it' You don't just jump really quickly to something to memorize. Then you can build toward more standard algorithms, but they can be grounded in the strategies that make sense to people.
00:05:26
Speaker
So a more efficient way to do this could be. And then people will have some meaning to attach to that. I love that. And I wish that when my son was younger, he was one of these naturally smart math people who could do a lot of math in his head. And his teachers kind of kind of put that down, like he really wasn't allowed. And I think he struggled mightily to like write it with their prescribed strategies instead of just teaching all of them and let them choose.
00:05:55
Speaker
which one works for them. So i I appreciate you explaining those different ways of doing it. I think it'll help a lot of our listeners. I think that's right. If we require people to solve it, like you said, through an um prescribed strategy, that's only effective when the student understands why they're doing what they're doing, needing some meaning to why we're solving in a particular way. And so honoring what makes sense to the students in the room will really empower them to be able to execute these other kinds of strategies later.
00:06:28
Speaker
I totally agree with that, and I appreciate that you you know kind of making that really clear.
Collaborative Learning in Math
00:06:34
Speaker
um Can you tell us a little bit about what you think a learner-centered space looks like, feels like, sounds like to you in your space and how it might differ from a traditional classroom?
00:06:44
Speaker
Yeah, so my current spaces where I'm teaching is at the university level teaching future teachers both more about the mathematics that there will be teaching in the future to develop a conceptual understanding for math they may already know how to solve and then teaching pedagogical methods, teaching methods. But I find teaching the math content courses for future teachers is not that different than the kind of teaching I might do um in terms of the practice of pedagogy when I'm teaching middle school because I really want to center students thinking either way. So I think about whoever's doing the communicating, who's doing the talking, who's doing the writing, that's the person who's learning more.
00:07:29
Speaker
So if it's the teacher talking all the time and doing all the writing on the board, then the teacher is actually developing their own thinking more. So I really want spaces where students are up in the front of the room, students are at the board. I can't teach math anymore without a document camera.
00:07:46
Speaker
where you're projecting someone else's work. So bring a student's strategy that they have been working on up to the document camera, and then the students are workshopping that with one another. So we can talk about what makes sense, what um it we appreciate about that person's thinking that we're workshopping before we start critiquing and improving it. Because if we want, who is doing the communicating,
00:08:14
Speaker
to um be the students more, that we need to create a safe space where students um feel like or experience that their thinking has value, that they will be that they're thinking will be something we all try to take seriously and understand and try to make sense of, assume that the thinking makes sense. So having students talking in the front of the room in ways that we honor the strengths that are coming out of those solutions, but then also focusing on how we can keep growing and improving. We can revise our thinking even if it's correct. So if a student brings up a really great explanation of why something is true, we can then think about, OK, this is making sense. This is correct. But we can keep improving it to make it be maybe more precise, add in different mathematical terms. We could make the argument more elaborated. We can make it
00:09:12
Speaker
maybe more concise. We can add in different representations to help other people understand. So the focus is on constant improvement. Everyone can keep revising. It's not like some people are correct and some people are incorrect, but we can all keep growing. And then we're focusing less on performance at specific periods in time and more honoring and celebrating how everyone's growing in their thinking. So everybody's improving and we can recognize how we know something, um how we know more than what we knew at the beginning of class, the more that we learned, more that we know by the end of the week. Focusing on that growth really is motivating because you recognize how your effort and your um collaboration with your colleagues helps you all understand. and Then focusing more on collaboration with one another and building collective understandings in the classroom rather than competing.
00:10:10
Speaker
We don't want it to be a space where, oh, there are these two people in the room and they really know this stuff and we don't feel like we know as much as them. We're creating an environment where we're all learning from one another and we're developing collective knowledge as a community. I think that's really important too.
Enhancing Math Assessment through Drafting
00:10:29
Speaker
And in the spirit of revision, we have to talk about your book, which is one of my all time favorite math education books, Rough Draft Math. Can you talk about your book a little bit and how that connects to assessment, whether it be formative or summative in the classroom? Thank you so much for mentioning that. So I've been collaborating with classroom teachers about how we can create math learning experiences that are welcoming to students that are motivating to students. And through those collaborations with brilliance of teachers, we collectively developed ideas about treating math as a process of drafting and revising where share your thinking at any point, even if it's not done, even if it's incorrect or you're not sure if it's correct.
00:11:19
Speaker
We can learn from everyone's draft ideas. And also, as I was saying before, we can all keep revising all the time. And so creating explicit experiences where students are taking moments and documenting how their thinking has grown and changed. And so this question about assessment is so important because The assessment practices we create in our learning environments also communicate to students what we think learning is in the first place. And so a long time ago, I would say like five or six years ago, a teacher asked me, well, it's all well and good to welcome drafts and revising in the math classrooms. But what if your assessment practices undermine that message? What would that mean?
00:12:05
Speaker
And that was a really helpful question to send me myself on a journey because if I'm teaching myself, I want to think about how my assessment practices align with what I value. And so I have um been thinking about and working with classroom teachers on assessments where students are articulating the growth in their thinking. um So thinking about my pedagogy course for future teachers.
00:12:35
Speaker
I structure that class with a set of goals or standards of what I hope that they're thinking will develop toward over the semester. And then we have portfolios where we treat all assignments and classwork as artifacts of their thinking at certain points in time. So we have lots of different assessments or assignments that I've designed to help them learn. And then The students will write portfolios where they choose maybe two of the class standards, and for each standard they make a claim. So far, these are the ways that my thinking has grown in relationship to those standards.
00:13:16
Speaker
And then they will use their student um work, their classwork, their assignments as artifacts to illustrate how their thinking grew and changed. You can see initially in September, I was thinking about this standard along these lines. Evidence is here, da, da, da. And then they will bring in maybe journals from that class that they've written or larger assignments. And they will say, oh, you can see how my thinking has evolved in this direction. Here's evidence of that. And they will make conjectures about learning experiences that help them grow in those ways. That has turned out to be life changing for me because when I ask the students to teach me about their learning, I end up being surprised. And that's joyful for me to learn from students. So some of the surprises have been
00:14:05
Speaker
Maybe I create an assignment that I think is going to help the students develop their thinking about something. But the students actually, ah maybe, yes, they developed their thinking in ways that I hoped, but they learned something that I didn't anticipate that they would learn. And a more open-ended assessment allows students to celebrate the way they develop their thinking, what they value about their learning. And then I'm surprised because I didn't realize they had that opportunity to learn. And then it's meaningful for them. They're articulating um what they valued about the learning experience. And so then we're all learning together, right? I'm learning from them about their thinking and how the learning opportunities that we um developed in the class supported their learning in ways I couldn't have imagined
00:14:54
Speaker
And then the relationship in grading is less transactional. We're not debating about whether they should get a point back. We're celebrating the nature of their learning. It's particularly useful to have portfolio assessments like this in a class for future teachers because they're about to graduate and enter the teaching workforce.
00:15:16
Speaker
And as teachers, we're always trying to think about how we want to grow professionally, but no one is imposing something on us. Like we choose how we want to develop um as professionals. Like we go to a conference, we choose particular sessions we're going to attend to. And I'm hoping this is developing an orientation for the future teachers of how they want to reflect on their practice and growth in the future when they're no longer in a course setting and structure.
00:15:45
Speaker
Mandy, I really appreciate that you use portfolios with the teachers so that they could experience it as another paradigm of assessment. And i what you were saying about um giving more open-ended spaces where you could see the pieces that um aren't always visible when we're designing very specific assessment. What I'm really, really curious about is, have you experienced pushback with this alternative means of assessment or folks who are coming into teaching who don't understand the power of what you're suggesting?
00:16:27
Speaker
It's a really good point that if we haven't experienced something as a learner, it's hard to think about that as an educator or a teacher. So I'm hopeful that if they experience this form of assessment, they can think about it differently for their own students. The sort of pushback I've received tends to be at the end of the conference conversations around their um portfolios. I am required to put a grade in the grade book for them, right?
00:16:56
Speaker
and They are they are wondering like, oh, I'm proud of what I did. But how do I know that if it's an A versus a B and we have certain general um suggestions that I give to them like an A would mean you have a level of mastery that you can teach other people about this. That's one thing I use as a criteria. And maybe a B is um you feel like you have deep understanding for yourself, but you can't necessarily maybe teach other people.
00:17:28
Speaker
But that's just criteria that I'm trying to come up with a way to say what's really deep understanding. sure And I think the challenge is that some students maybe grade themselves extra hard because they're being hard on themselves, or they're afraid that I don't necessarily think it's good enough. So I think the challenges and pushbacks are around, am I really allowed to give myself a grade? Is that really OK?
00:17:55
Speaker
um They're wondering what I really think, right? Like if you were to grade me, would you have given this an A? And in some ways I wish we could just throw out the grade and celebrate the qualitative nature of the growth. So to me, that's one of the biggest challenges.
00:18:10
Speaker
And i I totally agree with that. And I would just say, just as maybe something you can do that might support that conversation, I used to keep a rubric behind my desk, that it was a mastery rubric, like a learning progression, so that my students could actually turn around and look at it when we talked about their level of understanding. And then when I asked them to use evidence to demonstrate what they were talking about, they had something concrete that they could lean on. Plus I let them, you know, bring their portfolio as I'm sure, you know, you let your folks do as well. But I did find having the language, the the mastery language learning progression was definitely something that helped them have that conversation.
00:18:54
Speaker
I think that's right. So if they want to talk about, are we sure this is the grade? We can go back to like the general rubric I was describing and I say, okay, so how does your argument in your portfolio align with these criteria?
00:19:10
Speaker
And as a class, we can even refine the mastery level criteria as well, and then they can develop a shared understanding about that. So it's not really about what do I think or what do they think. It refers to the criteria and did they make the argument aligned with the great expectation.
Influences on Mandy's Teaching Methods
00:19:28
Speaker
There are so many parallels of what you're saying with Dr. Sarah Zerwin's book, Pointless, and she's a humanities language arts teacher, but there's just so many parallels to to just the approach and the learner-centered nature of how you're assessing students.
00:19:47
Speaker
um To wrap up, we always ask our guests to share who would they like to shout out to people who along the way have influenced them, inspired them on their journey. So in terms of being brave enough to develop these portfolios um in my methods course for future teachers,
00:20:09
Speaker
two people that really helped me have a vicarious experience of this is actually possible. One is Francis Harper is a math education professor at the University of Tennessee at Knoxville.
00:20:22
Speaker
And I really model a lot of how I've been working on these portfolios with students through her work in that way, thinking about what ungrading might look like in mathematics teacher education. And then when I think about orchestrating student centered math conversations, I now use a practice of five practices of math classroom discussions where I'm anticipating what students might do, monitoring the room to see what solutions students are coming up with, strategically selecting and sequencing students to come up to the document camera to share their thinking, and then workshopping those strategies to work toward greater connections. And so I really think about the work of Peg Smith, who was a professor at the University of Pittsburgh, and her book around the five practices for math classroom discussions have really influenced my thinking as well.
00:21:14
Speaker
Thank you for sharing that.
Connecting with Mandy and Resources
00:21:16
Speaker
And where can our listeners find you online? So I'm i'm still active on Twitter. I've heard some people call Twitter Twix because it's Twitter and X. So I'm active there. um My handle is Mandy Math Ed. That's a great way for me to interact with folks. I always appreciate the intellectual conversations about education in that space. And my email, I'm at the University of Delaware. And so my email is my last name.
00:21:44
Speaker
Janssen at udel.edu. Well, thank you so much for being on the show today. I hope our listeners do follow you on Twitter or whatever we call it these days. And definitely check out your book and check out your work. So thank you for your time. Thank you, k Crystal. Thank you, Starr. It's great to talk with you both. Yes, thank you.
00:22:07
Speaker
We hope you enjoyed the conversation as much as we did. If you'd like any additional information from the show, check out the show notes. Learn more about Mastery Portfolio and how we support schools at masteryportfolio dot.com. You can follow us on X at MasteryForAll and LinkedIn in our Mastery Portfolio page.
00:22:29
Speaker
We'd love for you to engage with us. If you'd like to be a guest in the show or know someone who would be an inspiring guest, please fill out the survey found in the show notes. And we'd love your feedback. Please write a review on your favorite podcasting app.
00:22:47
Speaker
okay okay