The Extraordinary Educators Podcast
Best practices, tips, and stories to help you be extraordinary in your classroom and beyond, featuring Curriculum Associates' Manager, Voice of the Customer, Hayley Browning.
The Extraordinary Educators Podcast
Embracing Problem-Based Math Curriculum with Karen Gauthier
In today's episode, we sit down with STEM Coordinator, and veteran educator, Karen Gauthier to unpack how a problem-based curriculum turns learners into mathematicians who reason, justify, and connect strategies with confidence.
Karen traces her 37-year journey from classroom teacher to district leader and explains why shifting to a problem-based math curriculum changed everything. We examine the Try-Discuss Connect routine, showing how rich tasks with multiple entry points invite diverse strategies and deeper understanding. You’ll hear what can look like in real classrooms: students choosing tools that make sense to them, partners explaining their thinking before whole-group share-outs, and teachers curating student work to highlight mathematical structure rather than a single “right way.” Karen also shares routines that guarantee equitable discourse, such as structured partnerships with clear roles and timing, so 100% of students answer 100% of the questions.
If you want to build student agency, improve transfer, and foster a classroom culture where ideas matter more than steps, this conversation offers concrete moves you can use today.
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Curriculum Associates, an education technology company and the makers of Fiready, presents the Extraordinary Educators Podcast. Join host Kaylee Browning to hear tips, best practices, and successes to improve your teaching and leadership and drive student growth and learning. We believe all educators are extraordinary and we are here to support you. Hi everyone, welcome to today's episode of the Extraordinary Educators Podcast. Today I am joined by Karen Gothier, and Karen joins this episode to talk all about problem-based math curriculum. Karen brings tons of experience to today's episode, starting this work looking into more problem-based curriculum 20 years ago now. With that, we dive into things in today's episode like what exactly a problem-based math curriculum looks like, what triggered the shift to this type of curriculum in her district, and the power behind giving students the opportunity to be the authors of their own mathematical ideas. And with that, we hope you enjoyed today's episode with Karen. Hi, Karen. Welcome to today's episode of the Extraordinary Educators Podcast.
SPEAKER_01:Hi there, I'm happy to be here today, excited to talk about my favorite subject, teaching mathematics to young children.
SPEAKER_00:Yes, and we're so excited to have you, Karen. You wrote an incredible blog that we will make sure to link in the show notes for our listeners all about this idea of embracing problem-based mathematics curriculum and in turn supporting building your thinking classrooms. And with that, Karen, we're going to dive into that a little bit. But before we even do that, I would love to hear a little bit more about you. So can you introduce yourself, tell us a little bit more about how you got to where you are today?
SPEAKER_01:Oh, yeah. So I have been in education for 37 years. I started teaching at the age of 21 and spent 26 years in the classroom before stepping out of that role and becoming an instructional coach in mathematics for four years, then became a curriculum specialist in mathematics, supporting elementary teachers and students, and then stepped into an administrative role five years ago as the science, technology, engineering, math, or as we call it, STEM coordinator here in Capistrana Unified, which is the largest school district in Orange County, California.
SPEAKER_00:Wow, you bring quite a lot of experience to the table, ranging from classroom to admin. That's quite the range, which I think honestly really helps support the incredible work that you're doing with your mathematics students and teachers across the board. So with that, Karen, I would love to dive into this idea of problem-based math curriculum. In your own words, I would love to hear you explain what is a problem-based mathematics curriculum.
SPEAKER_01:Well, it's definitely one of my favorite topics as well. It's really how do we build student agency in mathematics? How do we create environments where students see themselves as capable thinkers, decision makers, problem solvers? And how do we be intentional in those practices and cultivate a classroom where students' thinking shifts from answer getting to sense making? And so in problem-based curriculum, you're really looking for the way they position the student as the learner, and that it encourages students to explain their reasoning, justify their strategies, explore multiple pathways to a solution. And so it reframes math as thinking rather than following a set of procedures.
SPEAKER_00:That's really powerful. I I love the it reframes math as thinking instead of following procedures. And I also like how you brought up that it focuses on building agency and creating this wonderful environment for your students that encourages them to kind of take the lead. And so with that, I'm wondering if you could touch on a little bit. If I were to kind of walk into a classroom that is utilizing this problem-based curriculum, what would it look like? What are the students doing? What is what's the teacher doing? Maybe what you're seeing from an observational perspective. What is going on?
SPEAKER_01:I'm going to take it back to in Classroom Mathematics California. When I think of Classroom Mathematics California and the way their framework of try, discuss, connect embraces that pedagogy I just described. If I walked into a classroom, what would I see? I would see teachers presenting problems to students that allow for multiple entry points, multiple solution pathways. While we will get to the same outcome and eventual answer, the road to get there looks different based on students' understanding of the concept. And so walking into a classroom, you would see students trying problems, you would see multiple different solution strategies, you would see teachers having students discuss their solution strategies with each other and the models they've built or the way that they unpacked a problem. And so when we think of building student agencies, the students in those classrooms are driving the knowledge. While the teacher is facilitating it and guiding it definitely has a part to play in highlighting certain aspects of the mathematics, the students are choosing tools and methods and representations that make sense to them. So they're really building their ownership of the mathematics. Teachers would then connect and compare their strategies, like, oh, look at what this student did. And how is that the same or different than this student's strategy? And so really just if you're a if you're a learner in that classroom, you feel like you are the mathematician in that environment.
SPEAKER_00:Well, that says a lot that you know students are leaving feeling confident in their skills and walking away thinking that they are the mathematician. That's that's really powerful. Thank you for sharing, Karen. And with that, you had touched on this idea of the students having their own role. They're driving their own knowledge, and the teachers are facilitating, highlighting certain things specific to what they're recognizing in the answers that students are coming up with. I'm curious if you could talk a little bit more about what teachers may experience as they're going through and maybe switching to a more problem-based math curriculum. It's definitely a shift in kind of pedagogy across the board. So, was there anything you experienced when you made this shift? Did you hear anything from your teachers in your district? And how did you start addressing and supporting these teachers as they were moving through this shift?
SPEAKER_01:Well, we learned by doing. So having teachers get to experience the mathematics in that way themselves as learners, and really valuing the fact that they were realizing that as they were solving mathematical problems, that the teachers around them in a common area were solving it in different ways. And that really brought to the forefront that we all approach mathematics, regardless of what level of ability we are as an adult or a young learner, that we approach things in ways that make sense to us. And so that sense making and building agency of students has to start with teachers realizing that themselves as learners. And so really centering student discourse and collaboration so that the teacher isn't the stage on the stage. Kind of a term that sometimes you hear in teaching. We want the student thought to be at the forefront of what they're hearing and saying in a classroom. So one of the things we've we've kind of taken on a mantra of, and this actually came from one of the TD specialists with um curriculum associates, they said we want 100% of the kids answering 100% of the questions. And so that's kind of become our mantra. And at first it was like, what does that mean? Does it mean does it mean that you give kids the problems and they have to answer every problem? And so, you know, unpacking that meant that when a teacher asks a question, we want the kids to talk about it with each other before we put their shared knowledge out into the open space in the classroom. So if a teacher were to frame a question that kids are partnered in a structured partnership, um, sometimes we call that an A B partnership and teachers get creative. Sometimes it's chips and salsa, or you know, at Halloween it was candy and corn and in all different ways. But we when we ask a question as the educator in the room, we want the students to partner up in a way that they talk to each other and listen to each other before that that knowledge comes out into the whole space of the classroom. And so that really is our our largest area of focus this year. This is our second year in the adoption. And and we've been seeing great success. And instead of just being turn and talk, if I were to turn and talk with a fellow colleague who loves to talk, I might not get my opportunity to speak. But if I know it's structured and we each have a role to play in that structured conversation, then we each have equal and equitable opportunities to talk and listen.
SPEAKER_00:Oh, that's really interesting. And it it says a lot about the environment and the wonderful school culture that you're fostering across the board where your students are able to feel confident and supported and encouraged to have these conversations and to work through that mathematical discourse. Um, and then in turn share their own strategies across the board. So hats off to you.
SPEAKER_01:I I I would hope that that in my hope of what I want all students to to have and seeing themselves as mathematicians is what I I wish I would have had the opportunity as as a young child as well, building my mathematical understanding of it. I want that for kids to experience something that a lot of us wish we would have had the opportunity to see math in that way.
SPEAKER_00:Yeah, yeah, 100%. And in your blog, you had mentioned that you kind of started diving into this this problem-based math learning uh many years ago.
SPEAKER_01:Yeah, 20, 20 years ago, yep. 2005. Um given an opportunity with other colleagues to experience um an approach to math called cognitively guided instruction, where it really did position the student sense making up front and the teacher facilitation on the back end and really using evidence of student thinking to guide the instruction in the classroom. We definitely had goals. It wasn't like it was just so open-ended that we were like, whatever we get today. I mean, there's ways to facilitate it that highlights certain aspects of student thinking and and ways to consider other um models and methodologies that that there is a part on the teacher's end to not just let it be so open-ended that we have learning goals and targets we want to get to, but we know that our students can be the ones that share those ideas, and then those ideas become front and center to the to the learning in the classroom.
SPEAKER_00:Yeah, 100%. And you also talked about this idea that students are the authors of their ideas, and that I think in and of itself says a lot about the power behind this problem-space math curriculum where students are able to have that ownership. And again, coming back to agency, coming back to all of these pieces overlapping. And it just becomes very clear that when you give students this opportunity to kind of take the lead, you end up seeing more in the long run. Would you agree?
SPEAKER_01:Absolutely. And and for our teachers and approaching um teaching mathematics that way last year, it was there was some level of um concern that kids wouldn't remember the content because they weren't bringing it to mastery each time they were learning a concept in a day. But what they saw is that kids were retaining the knowledge longer over time because they were building their long-term understanding and their working memory of why things work a certain way because they had the deeper understanding of the conceptual parts of that mathematics versus just going to a procedure and then, you know, when I try to retrieve that out of my memory and need to use it again, can I remember all of those steps? But if you build it conceptually, they hang on to that understanding longer because it they made sense of it in a way that made sense to them.
SPEAKER_00:Yeah, that's wow. I really, I feel like that's the perfect note to wrap up on. It's really building out this deeper understanding. We're really supporting these students to give them what they need in the long run. Um, and so with that, Karen, thank you so much for your time today. We really appreciated having you on.
SPEAKER_01:Thank you very much. I appreciate the opportunity to highlight how amazing students are.
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