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Desiree Harrison 0:00
It’s such an honor and privilege to have the very first Kids Math Talk Podcast guest today. We will be discussing the teaching framework for mathematics, which takes the 8 teaching practices, talks about their relationships, and how identity and engagement factor into those to build and sustain positive Kids Math Talk. If you are unfamiliar with these practices, here they are -
1.Establish mathematics goals to focus learning
2. Implement tasks that promote reasoning and problem solving
3. Use and connect mathematical representations
4. Facilitate meaningful mathematical discourse
5. Pose purposeful questions
6. Build procedural fluency from conceptual understanding
7. Support productive struggle in learning mathematics, and
8. Elicit and use evidence of student thinking.
Listen now for suggestions on how to use this framework for designing face to face or online learning and then later on head to my website kidsmathtalk.com/podcast to find a link to the actual framework.
Desiree Harrison 1:42
The 8 Mathematics teaching practices can be a lot to think about individually, and I’m so excited to learn from our guest about how to make these practices more manageable, so that we ensure that we continue to design and implement high quality instruction as children return to learning this fall.
Our guest today is a professor of mathematics education at the University of Wisconsin-Milwaukee, she was the chair of the writing team for the NCTM’s Early Childhood and Elementary Mathematics Catalyzing Change book, she’s a former NCTM board member, and lead writer for both the Taking Action and Principles to Actions books that I reference so often on this podcast, so let's welcome DeAnn Huinker.
DeAnn Huinker 2:38
Hi Desiree! It’s so nice to join you today and I'm honored to be your guest. I am really am enjoying your podcast.
Desiree Harrison 2:41
Thank you so much. So I do reference a lot of the books you have been so instrumental in on the podcast and I love Principles to Action, Catalyzing Change I’m getting more into everyday it just came in early… just a few months ago really early childhood version, and the Taking Action though, that came out in 2017 is what I really been drawn to. It truly resonates with me; I reference it all the time in my own work as math coach and I find myself picking it up and leafing through it at least once a week and I always end up coming back to that, I think it's in chapter 10, and it's the teaching framework for mathematics and it's just been career-altering for me so I was wondering if you could give us an overview of that framework.
DeAnn Huinker 3:38
Yeah, I would be happy to. And with that framework it’s so interesting...Matt Larson (past NCTM President) said he thinks we should have put it in chapter one rather than chapter 10 because people don't always find it so it's always the first thing I have people turn to and study first before really getting into the book itself and thinking about the teaching practices so in regards to the teaching framework; you know as educators we want every classroom to become powerful spaces for students to learn mathematics and for them to become doers, knowers, and sense-makers.
So the question then, is you know,
what does math instruction look like in these classrooms?
And that’s really where the teaching framework comes in. Because it’s a vision of what needs to occur really on nearly a daily basis in classrooms. So in Principles to Actions, we actually examined about two decades worth of research and that led to the identification of a core set of 8 high-leverage teaching practices for mathematics.
So, now the framework, which we then created and came out with in the Taking Action series shows how those teaching practices are related to and support each other in order to create these powerful learning spaces that we want for students in learning mathematics. Now the framework has four different parts to it that I’m going to refer to:
OVERVIEW OF THE MATHEMATICS TEACHING FRAMEWORK
PART ONE OF THE FRAMEWORK
So the first part of the framework shows that teaching begins by establishing clear goals for the math students are learning. So we need to think about - What are those math ideas we want children to understand and hold onto for a lifetime? What’s really that deep learning that we’re going after?
PART TWO OF THE FRAMEWORK
Then, the second part of the framework involves designing and selecting tasks related to those goals. Now the task as we think about these classrooms should engage students in problem solving and reasoning, and also focus on building strong foundations of conceptual understanding. Now that conceptual understanding is so important, particularly in the elementary school, and needs to be really firm and secure before we start moving students onto procedures. In fact, we get very impatient as teachers and we so often rush the development of conceptual understanding. You know, and this is, I would say, harmful to students, because when we rush that conceptual foundation, it results in gaps and holes in students knowledge, that really just hinders their learning for years to come. So we have to think about - what tasks are we selecting to really build that deep, strong foundation of conceptual knowledge and also engages students in problem solving and reasoning.
PART THREE OF THE FRAMEWORK
Then, the third part of the framework is really the heart of each and every lesson that we teach, and these are the discussions and discourse that occur among the teacher and the students. So, for example, the students might be working with different math representations to represent fractions. And as that’s occurring, the teacher is asking purposeful questions to surface students thinking, asking questions to support students in struggling productively to make sense of the mathematics - so it really embodies four of the teaching practices- to pose those questions, to use representations, to elicit student thinking, and to support that productive struggle- which is necessary component for student’s learning.
Desiree Harrison 6:58
I have lots of hearts next to that large box, so that what you just said really resonated with me.
DeAnn Huinker 7:04
I mean I love that idea! I’ll probably borrow that and put little hearts around it myself because I always say it is the heart of what goes on each day.
PART FOUR OF THE FRAMEWORK
And the fourth part, is really just the Feedback Loop. You know, the discourse and discussion that goes on, you know makes students thinking public and accessible, and then that serves as kind of the formative assessment that feeds back into the teacher’s, um, instructional planning and decisions for the next lesson. And then we just keep doing that over and over again, each day as we work with our young learners.
Desiree Harrison: 7:37
When you’re just flipping through, it looks like just another figure, but there’s so much to unpack within that, and that Feedback Loop was actually something that I hadn’t noticed the first few times that I looked at it, and then as I went back and read the narrative to go along with it, I was like, wait, what is this? There’s a whole new section for me to unpack and to talk about with teachers. So thank you for that overview.
So, on the podcast, we talk a lot about identity, and helping children form a positive mathematics identity, so
Can you tell us about how identity plays into, or factors into, this framework?
DeAnn Huinker 8:19
So, you know, we all want students to develop a positive relationship with mathematics and related to that is for each and every student to develop a positive identity or belief in themselves as capable and competent math learners. That’s what we all want - as teachers, as parents. So, the way we design and enact our math lessons, strongly impacts and influences a student’s math identity. We as teachers, have to take responsibility that the way we engage kids in learning, is going to have a direct impact on their identity.
And we know that far too many students form negative views of math, and negative views of themselves in relation to math - and this happens in elementary school. You know, by the time they leave elementary school, students have usually decided whether they like math or don’t like math, and whether or not they think they’re good at it.
And, that’s probably one of the things that makes me more sad than anything else, is when I see students that are starting to give up on themselves in mathematics. So when I think about the Math Teaching Framework, it really is about empowering students as math learners. So in any math lesson, students should be given choices in how they approach and solve problems, and they should have opportunities to share and discuss their different strategies.
So the Teaching Framework, provides a structure for teachers to think about viewing students as authors and owners of their math solutions, their explanations, their justifications, and then the outcome of all of that, really is, um, the development of positive identities and students seeing themselves as math learners, when they can really engage in that learning in very interactive, discourse-based ways, that the Teaching Framework is presenting.
Desiree Harrison 10:13
Right- empowerment and crafting a positive math story and math identity is really the mission, or the why of this podcast. So you’re talking about creating this vision and I wonder how this math framework can be used to help teachers and parents partner together.
DeAnn Huinker 10:32
Sure. I know teachers that are starting to use the diagram that shows the teaching practices as part of the curriculum nights, or, um, their parent-teacher conferences, and things so that it’s a way for teachers to kind of talk to parents, um, how things are changing in the math classroom. That look a little bit different than their own experiences. So I kind of see this as a tool for helping parents to envision how math classrooms are looking different and to start understanding why this is really important, you know, so the framework itself shows that math classrooms are becoming more dynamic and powerful learning spaces for their children and that a goal, which parents like, yes, I want my kids to engage in math, to believe in themselves positively about math, and to really understand math deeply and make sense of it. So I really see it as a tool for talking about how math classrooms are changing and how we interact with kids and why.
Desiree Harrison 11:37
I never thought about having this a part of a curriculum night or back to school night. That’s a great suggestion. Given that in a few weeks, a lot of us might be facing the reality of being in an online environment or having children who are in online learning situations,
What’s your take about how we can use this teaching framework to continue the process of, and the practice of, using formative assessments in the online environment?
DeAnn Huinker 12:09
Sure. The virtual environment presents so many challenges to us as teachers when we’re so accustomed to having kids right there in front of us where we can listen in and observe more readily. But then I’ve also been thinking a lot about how the virtual environment might provide some new opportunities for teachers and students. So, for example, we’re probably all amazed at how adept some of our students are at with technology, but I think the notion of having kids video record their math explorations and demonstrations is actually quite exciting because sometimes we, you know, students put things on paper and we say, ahh, I wish I had the opportunity for them to tell me more about this. And get to those learners.
So if students are recording their explanations and demonstrations, that actually provides new opportunities and even multiple entry points for students to demonstrate the strengths that they bring to their learning. Or if I’m thinking in an environment like Zoom or Google Hangout, you know a teacher could even record students explanations and then those could be tools that students could watch each others, they could watch their own, they could critique their own recordings and improve them.
Desiree Harrison 13:25
Wow. I hadn’t thought about using things like Seesaw or Google Hangouts or Flipgrid for critiquing yourself. That’s a brilliant idea.
DeAnn Huinker 13:37
Yeah, I mean esp-, I was thinking at first about older kids, ‘cuz they could, they can record it, watch it, and then they realize what they didn’t say. But I would also think very young kids, you know, they can look at theirs and say, oh I forgot to say this, I forgot to say that, so I think that would just kind of be fascinating.
Desiree Harrison 13:57
That leads me to thinking about how we increase discourse and I’m reading Classroom Discussions...
DeAnn Huinker 14:04
Yeah.
Desiree Harrison 14:05
...and one of the talk moves, one of the very first talk moves, is to get kids to be able to talk more about their own ideas before they even try to critique somebody else or agree or disagree with somebody else, so this strategy fits so perfectly with that.
Desiree Harrison 14:21
Before we continue with the interview, it’s time to announce the 2nd Kids Math Talk Podcast winner! Congrats to Deepak N. who writes - The podcast is exceptional. Desiree has explained how to cultivate math talk with children making small, planned steps to build their future and maths love. visualization, manipulatives, concrete ways of doing things, removing math anxiety and many more a parent/teacher can learn from podcasts. Thanks to her for this great initiative. And thank you Deepak for listening and for that review! Email me at kidsmathtalk@gmail.com to claim your prize. Next week another winner will be announced! All you need to do to enter is head to Apple podcast and leave us a review saying how you are enjoying the episodes. The reviews also help others find the podcast.
Now let’s transition back to our interview with Deann Huinker.
Desiree Harrison 15:22
So, if I’m a new teacher, or I’ve just never seen this framework before, where should I start?
DeAnn Huinker 15:30
You know, I always suggest starting with representations. You know, not with goals, rather, with representations, and to think about what are the different representations they’re using in our classroom. So, when I think about mathematical representations, the thing that often comes to mind is, you know, manipulatives, and concrete materials, or perhaps drawing lots of visual representations - pictures and diagrams - and those are super, super important. But the other, um, representation that I think often gets overlooked in classrooms is making connections to contextual representations.
And by that we mean, um, helping the children make connections to, like, their everyday lives, and to their real world contexts. To their lives, to their interests, and to their communities. And when I think of elementary students in particular, I also want to note that contextual representations don’t always have to be real. That we can tap into children’s imaginations and imaginary contexts, ah, you know, kids are ready to talk about traveling to another planet, or going on a safari, or whatever they want to imagine. And we can also use those kinds of context to help make connections to children’s mathematical work.
Whether if it's learning multiplication, or talking about comparing fractions, that we can tap into both their real world interests as well as their kind of imaginations. Yeah, so, in starting with representations, um, I kind of think of like these three questions:
(Question #1): You know first for a teacher to think- What representations are children currently to use in your classroom?
And then, Are you providing students with choices?
(Question #2): Do children get to make choices in the types of tools and representations they want to use to make sense of the mathematical work they’re doing?
And by giving students choices, we’re also helping them learn to make good decisions are which representations are appropriate or best for working on certain types of problems.
(Question #3): And then the third question is, How can we help children make connections among those different kinds of representations. Such as connecting fraction symbols to visual diagrams, and to real world contexts. So, I often think of representations as kind of a quick win area because it’s very, um, it’s something we can get a hold of and work with kids on very readily and bring more in and to think about representations. So I just think that’s always a good place to start. And then the other, um, teaching practices kinda start to connect to that and feed into it.
Desiree Harrison 18:15
I love that and the choice, and, to build within our children this idea that they are capable of making their, of making good choices for themselves is so important to build their self-esteem. And we’re looking at that framework to kind of start in from the side, that automatically starts that strong foundation of discourse which is the heart of the framework, so, alright. And I was not expecting you to say that!
DeAnn Huinker 18:45
No...Because I think as soon as you’re like, oh, well let’s look at your visual diagram, you have to think, what are the questions I’m going to ask children about their diagrams or their strategies? And then you want to start to draw out their thinking and reasoning, so that’s another teaching practice...and if they’re struggling with how to best use those representations, well then you’re supporting their productive struggle in it. So I think all the other ones kind of tie into giving those representations because they give us something to talk about. Right..
Desiree Harrison 19:14
Yeah. So as, as some of us have already started back to a new school year, and others are in the midst of planning some type of in person learning or hybrid or online learning...
What’s one piece of advice that you can give us as educators and parents?
DeAnn Huinker 19:34
So, as I think about the Math Teaching Framework, um, I like to envision it as a tool that we can use for strengthening our professional practice. So with the 8 teaching practices, each one of those gives us a lens for having these professional conversations with our colleagues and being able to talk about our practice in ways that we haven’t been able to before.
So I would suggest that you begin to use the Math Teaching Framework as a guide or a tool for conversations with your colleagues, whether they’re teachers at your grade level, or with your math coach, or even with your administrator, and then I would suggest that you pick one of the teaching practices to target. Then you and your colleagues can work together to study and strengthen that one aspect of your teaching, and what you’ll probably find is that as you’re targeting that one specific practice, you’re gonna just naturally start considering the other practices as well.
And, I guess I would add to that, you know, this is our year long work. This is what we do as teachers, right? We are continually working to strengthen our teaching practice. So it doesn’t have to be perfect right away, we just have to keep making that improvement.
Desiree Harrison 20:47
Yes. It’s a process, it’s a journey. Nothing is perfect.
DeAnn Huinker 20:52
Right.
Desiree Harrison 20:53
Thank you for that advice and thank you for being with us today at the Kids Math Talk Podcast and I wish you well and to stay safe and we’ll see you soon.
DeAnn Huinker 21:05
Alright. And thank you so much for the opportunity.
Desiree Harrison 21:09
So if you don’t already own this Taking Action, I suggest that you grab it, today. It’s available through the NCTM website. If you are a parent and you’re not really interested in the entire book, still head to the show notes because there’s some links in there to help you get more of a visual of the framework so when you’re talking with your child’s teacher, you have this visual image in mind.