Episode #278: How To Give Effective Feedback In Elementary Mathematics Classrooms – A Math Mentoring Moment

Mar 25, 2024 | Podcast | 0 comments



Episode Summary:


When you shift your teaching practices from “I do, we do, you” to a problem based approach that engages students to think first you will often be led to question how you give feedback to students. 

In this episode we speak with Diane Hamilton, an elementary classroom teacher from Toronto Ontario. 

Diane has been implementing the 14 strategies from Peter Liljedahl’s book Building Thinking Classrooms and is here to dig into how to give effective feedback to her students instead of grades. 

Stick around and you’ll: 

Discover innovative self-assessment techniques that empower students to take charge of their learning in mathematics, turning passive learners into active participants.

Learn how to develop and communicate effective success criteria, a crucial step in providing feedback that genuinely enhances student understanding and performance.

Gain insights into structuring self-assessment and growth-focused activities into your weekly routine, ensuring consistent student progress and deeper comprehension of mathematical concepts.

This is another Math Mentoring Moment episode where we chat with a teacher like you who is working through some problems of practice and together we brainstorm ways to overcome them. 

What You’ll Learn:

  • Practical self-assessment methods to facilitate student involvement and ownership in their mathematics learning;
  • How can I develop success criteria and share them with students so I can give effective feedback; 
  • How can I structure self assessment and growth in mathematics into my weekly routine;

Attention District Math Leaders:

How are you ensuring that you support those educators who need a nudge to spark a focus on growing their pedagogical-content knowledge? 

What about opportunities for those who are eager and willing to elevate their practice, but do not have the support? 

Book a call with our District Improvement Program Team to learn how we can not only help you craft, refine and implement your district math learning goals, but also provide all of the professional learning supports your educators need to grow at the speed of their learning. 

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Episode Summary:

The meeting involved discussions on technical difficulties, work-related topics, and personal experiences. Diane shared her unique teaching approach at an alternative school in Toronto, emphasizing the importance of conceptual understanding and visual learning. The team also discussed the challenges of teaching students at varying levels and the need for feedback and self-assessment in learning. 
Teaching Approaches and Community Atmosphere in Toronto Schools
Diane, who teaches at an alternative school in Toronto, shared her experiences and unique teaching approach. She emphasized the school’s social and emotional component and community atmosphere, and her focus on teaching math and French to grades 3, 4, 5, and 6. Diane also shared her personal journey into teaching math, including her struggles with the subject and the influence of a podcast on her teaching approach. The conversation also reminisced about the launch of an academy and Diane’s transition from a strong arts and literacy student to a math teacher.
Math Learning and Teaching Strategies
Kyle, Diane, and Jon shared their experiences and strategies in learning and teaching math. Diane emphasized the importance of conceptual understanding and visual learning, and highlighted the limitations of certain strategies. She also discussed the challenges of engaging students with different learning abilities and outlined their school’s non-traditional grading and feedback system. The group also discussed the implementation of thinking classroom practices, with Diane sharing her experience of incorporating all 14 practices. 
Teaching Challenges and Feedback Strategies
Diane, Jon, and Kyle discussed the difficulties of teaching students at varying levels and implementing new practices in the classroom. The main focus was on providing feedback to students, with Diane expressing concerns about the lack of feedback in her current methods. They agreed that feedback was essential and discussed potential improvements. Kyle suggested the concept of students ‘owning’ their math studies, but noted potential issues for students in the middle range. Diane was then asked for her thoughts on how to provide more opportunities for these students to strengthen their understanding. The discussion concluded with potential changes or additions to their teaching methods to better support students in ‘owning’ their math.
Self-Assessment and Growth in Teaching and Learning
Diane, Kyle, and Jon discussed a teaching method that emphasizes student growth and self-assessment. Kyle suggested using sticky notes with color coding to track student progress and allow students to self-assess. Diane proposed a self-assessment rubric for students to evaluate their own skills. The team also discussed the importance of self-assessment in learning, particularly in mathematics. Diane also shared her plans to observe her student teacher and provide more individualized coaching to certain students, with the aim of improving her students’ understanding of math concepts and reducing their anxiety. The team agreed on the need for clear success criteria and specific strategies for tasks. They also discussed the use of a ‘growth day’ to encourage individuals to own one concept at a time.
Educational Initiatives Progress Check-In
Jon, Kyle, and Diane discussed the progress of Diane’s educational initiatives and agreed to check in after six months. Diane shared her challenges and uncertainties in implementing all 14 practices and appreciated Kyle’s encouragement. 
Next steps
• Diane will consider implementing a self-assessment rubric for students to fill out after notes and check your understanding questions.
• Diane will try giving students one more day to self-assess and practice in areas they need work after wrapping up a unit. She will also observe her students more closely during a consolidation phase led by a student teacher.


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00:00:00:02 – 00:00:22:06
Diane Hamilton
I think many of us doing things in classrooms, we have that parable of. I’ve got a strong student working with a student that has more challenges and is hanging back and how do I get them both engaged. So that continues to be an issue for me. And I do walk around and give little prods and pushes.

00:00:22:07 – 00:00:54:00
Jon Orr
When you shift your teaching practices from I do we do you do to a problem based approach that engages students to think first. You will often be led to questions about how to give feedback to students. In this episode, we spoke with Diane Hamilton, an elementary classroom teacher from Toronto, Ontario. Diane has been implementing the 14 strategies from Peter the law’s book building to good classrooms and is here with us to dig into how to give effective feedback to her students instead of grades.

00:00:54:02 – 00:01:24:02
Jon Orr
So stick around and you’ll discover innovative self-assessment techniques that empower students to take charge of their learning and mathematics. Turning Passive Learners into active participants. You want to learn how to develop and communicate effective success creating a crucial step in providing feedback that generally enhances student understanding and performance. And finally, you’re going to gain some insights into structuring self assessments and growth focused activities into your weekly routines.

00:01:24:04 – 00:01:47:00
Jon Orr
This is another math mentoring Moment episode where we chat with a teacher just like you who is working through problems of practice. And together we brainstorm ways to overcome them.

00:01:47:02 – 00:01:50:09
Kyle Pearce
Welcome to the Making Math Moments That Matter podcast.

00:01:50:10 – 00:01:54:02
Jon Orr
I’m Kyle Pierce and I’m John or we are from math moments dot com.

00:01:54:06 – 00:02:04:05
Kyle Pearce
This is the only podcast that coaches you through a six step plan to grow your mathematics program. Whether at the classroom level or at the district level.

00:02:04:06 – 00:02:17:11
Jon Orr
And we do that by helping you cultivate foster. Your mathematics program like strong, healthy and balanced tree. So if you master the six parts of an effective mathematics program, the impact of your program will grow and reach far and wide.

00:02:17:13 – 00:02:32:05
Kyle Pearce
Every week you’ll get the insight you need to stop feeling overwhelmed, gain back your confidence, and get back to enjoying the planning and facilitating of your mathematics program for the students or the educate hours that you serve.

00:02:32:07 – 00:02:51:23
Jon Orr
All right. Let’s get to the conversation with Diane. Hey there, Diane. Welcome to the Make Math Moments That Matter podcast. We are pumped to talk to you and you’re pretty close. You’re in our neck of the woods being up in the Toronto area and us being down here close to Windsor, Ontario. So it’s nice to talk to a fellow Ontarians.

00:02:51:24 – 00:03:00:20
Jon Orr
But Diane, fill us in on the details. We know you’re from Toronto, but tell us what grade level you’re teaching and just a little bit about what life is like at your school.

00:03:00:22 – 00:03:29:13
Diane Hamilton
Sure. Well, I’m in the tdsb at an elementary school that’s actually quite unique from others. We are one of the alternative schools, Alpha Alternative. So it’s a Democratic alternative school. It’s very small. 80 kids altogether from K to six. And I teach the grades three, four or five and six math and also French. And so we have a big social emotional component to our school environment.

00:03:29:14 – 00:03:44:03
Diane Hamilton
It’s a great community school. And I’ve been teaching there for about six years, teaching math as really just had those six years to focus on teaching math. Before that, I wasn’t so much focused on math pedagogy.

00:03:44:03 – 00:04:06:03
Kyle Pearce
I’m actually very intrigued. You’re in, like you said, at a unique school, unique set up, and you’re teaching across a span of grade levels. So I’m sure more information will come out about that. And also something that is interesting to me. You had said before we hit record that you’ve been listening since pretty much the beginning of the podcast.

00:04:06:03 – 00:04:25:20
Kyle Pearce
And John, if we do the math and we work our way back, that’s probably shortly after you started at this school focusing in on math. So I’m kind of curious, just off the bat, were you searching on the Internet to try to figure out like, okay, I haven’t really been focusing on math. Like, what should I do or how can I do this maybe more effectively?

00:04:25:21 – 00:04:34:05
Kyle Pearce
What was your thinking? And is the timing about right when you say you started listening and you started this role with a heavier focus on the mathematics?

00:04:34:07 – 00:04:54:21
Diane Hamilton
Yeah, that’s right. I think I just did an online search for math educator podcasts and I listened to a few and I was really psyched to find one that was an Ontario based podcast. Little did I know then that you would sweep the globe as it was like you’ve done, and I think it influenced me quite a bit.

00:04:54:21 – 00:05:06:09
Diane Hamilton
Like I discovered Peter Lilienthal through your podcast, a lot of like Cathy Farr’s Not Joe or I think I found a lot of those big names through being a listener, right?

00:05:06:14 – 00:05:17:03
Jon Orr
Awesome. Great to hear about that. It’s partly our mission is to share different nuggets of insight, different ideas for folks to get started in their classroom and then go deeper when they need to go deeper.

00:05:17:04 – 00:05:27:22
Diane Hamilton
And incidentally, I was an early joiner when you first started the Academy. Oh four. Yeah, Yeah, very brand new academy. Wow.

00:05:27:22 – 00:05:29:03
Jon Orr
That’s old school. Yeah.

00:05:29:04 – 00:05:44:04
Kyle Pearce
Yeah. John, John, go down memory lane for a second. I’m curious if you know where we were when we hit launch on the Academy. I remember at the time we were so nervous because we’re like, I don’t know if it’s gonna break. I know. Like, I know where we were to where we were.

00:05:44:04 – 00:05:46:08
Jon Orr
We were in Delta, B.C. at.

00:05:46:08 – 00:05:47:20
Kyle Pearce
A kind of an Airbus B.

00:05:48:00 – 00:06:04:03
Jon Orr
An assessment conference, but we were spending the afternoon at an Airbnb. We were on the deck and we were just crunching through, getting this website ready to go and we hit send. And the folks like you joined over it that evening and overnight. And we woke up and there was a bunch of people signed up for the academy.

00:06:04:03 – 00:06:15:19
Jon Orr
So very exciting, exciting stuff. Diane, tell us your math moment, cause I know that’s not your math moment, but tell us your math moment about flashing back when we say math class. What is has stuck with you all these years.

00:06:15:22 – 00:06:49:15
Diane Hamilton
So I have a memory of being probably in grade three or four, maybe maybe three or four and maybe a little younger. Actually, I just remember stacking digits and doing the adding and that I had developed a system where for every digit I had mapped on to that digit dots of the same number so that I could count on it was eight plus four, Four had four little spots for me and I would start at the eight and then I would count up onto the digit four.

00:06:49:17 – 00:07:15:06
Diane Hamilton
And looking back at that, I just realized that I was one of those kids who needed the concrete representation for longer. I was moved on to Digits too soon, which I think is true for a lot of kids. The abstract digits before I had the schema in my mind and then having a sense of sort of catch up really ever since.

00:07:15:06 – 00:07:51:20
Diane Hamilton
In a way I was a good math student, but I didn’t own math and I was much more on the arts and literacy side. So it’s been a big surprise to me that I ended up focusing as a math teacher rather than arts and literacy, which seems like a more natural fit for me. Yeah, just that moment of working really hard to add single digits that were stacked and not having any sense of place value, just like doing the algorithm the way I had been shown to and working up my own little secret way to sort of cheat by counting on to the numbers.

00:07:51:22 – 00:08:07:16
Kyle Pearce
I love how you just said it. You felt as a student. I think there’s a lot of times where we pick up on a pattern or a behavior or a strategy, and somehow in our minds we were convinced that that’s cheating. Counting with your fingers is cheating. For a lot of kids, it’s like parents say not to do that.

00:08:07:16 – 00:08:27:14
Kyle Pearce
And in reality, it’s actually that’s reinforcement. You mentioned something that jumped out at me was this idea of not owning the math. And I think for so many people, even those who might have been considered good at math never really owned it. I never really owned it. I never had strategies like you had done. I just sort of, I guess, was lucky.

00:08:27:14 – 00:08:45:07
Kyle Pearce
And we’ll call it automatic. I don’t want to say automaticity because I didn’t have like a fluency with it, but it was just sort of I just did it. I didn’t have to think about it, but I also didn’t understand it, which meant if anything was out of whack, then anything broke the pattern. I was sort of lost.

00:08:45:10 – 00:09:18:16
Kyle Pearce
Oh, I’ve never seen that before. So I’m done right. And I often equate it to this idea of following. And if you always follow a GPS in the same neighborhoods and then the GPS shuts off, you’re stuck. You have no other sort of schema to try to work through it. And it’s really interesting when you hear different educators with different experiences, it seems like whether they were told through their grades that they own the math or whether they knew they didn’t own the math, it feels like everyone feels like they didn’t have a good grasp of it at the time.

00:09:18:18 – 00:09:39:21
Kyle Pearce
So I’m wondering, how would you say that impacts or influences your approach to teaching? And does it cause you to do anything differently for the students that you’re working with When you think about how you learned and how I’m sure many of the other students in front of you might be either similar or very different to the experience you had.

00:09:40:02 – 00:10:07:04
Diane Hamilton
Sure. Yeah, I think it causes me to really emphasize the conceptual side and try to keep things concrete and visual as much as possible. I’m always asking the kids, Does that make sense? You know, does that make sense to you? And yeah, just wanting to have those conversations and see those light bulbs go off rather than really kind of allergic to even teaching the algorithms.

00:10:07:06 – 00:10:34:07
Diane Hamilton
But I do after teaching a whole lot of other strategies. And it’s funny because the kids are often like, I like stacking the best, like stacking works. And I’m like, Yeah, it does, but it doesn’t always make sense. Just the other day we had 8.91 -0.99 and they were stacking it and borrowing and I was like, Come on, remember that over and back strategy we talked about it was a money contest.

00:10:34:07 – 00:10:48:08
Diane Hamilton
Why not just take off a dollar? A couple of kids came up with it. This was in the consolidation, but most of them were still their go to is stacking, even though I’ve been deemphasizing it. So anyway.

00:10:48:14 – 00:11:13:03
Kyle Pearce
Quick thinking brain loves to take charge. Right? Exactly. Slow and methodical thinker over here is harder to get going and it’s harder to motivate over here. It’s like, No, I know what to do. Duke, Duke, Duke. And I don’t have to even think about it. Even though it’s a lot more work to get there, it requires less thinking, which I think can really be a struggle to try to encourage a little bit more intentional thinking there.

00:11:13:03 – 00:11:20:02
Diane Hamilton
Yeah, which is like a stepping back first before you dive into the algorithm, it’s like, what are these numbers and what’s the best strategy with these numbers?

00:11:20:02 – 00:11:39:05
Jon Orr
Yeah, and think about the win you get because you can teach the algorithm like you said it, you teach it at the end. They want to rely on that. But when you start to see and you’re looking for kids to take that flexibility in that strategy to go, you know what the more efficient strategy is that one. And when you see that jump, that’s when you’re like, they got this.

00:11:39:05 – 00:11:57:01
Jon Orr
When you can look for the jump from moving from one strategy to the other and blocking for that selection because that when you watch for the selection or see that selection, that tells you a lot more than whether they can do this here, do this here. But it’s the selection that I always like to look for in the work that they do.

00:11:57:03 – 00:12:06:16
Jon Orr
So having said that, what’s on your mind, Diane? What is a pebble that is rattling around in your shoe right now that you want to shake loose in that we can dive in here together?

00:12:06:18 – 00:12:32:01
Diane Hamilton
Yeah, I sort of have to, but I’ll start with just one where I am in my first year of trying to implement all 14 practices of Peter Lilly, Adele’s Thinking classroom, I did just the upright boards and problem solving and random groups for the previous two years, but this year I’ve added in all the other stuff.

00:12:32:05 – 00:12:36:01
Kyle Pearce
I’m wondering when you say that I was going to just ask when you say that.

00:12:36:06 – 00:12:38:02
Jon Orr
Like a half, there was like a Yeah.

00:12:38:04 – 00:12:40:16
Kyle Pearce
I’m I’m just thinking because you’re like, I.

00:12:40:17 – 00:12:41:03
Jon Orr

00:12:41:04 – 00:12:53:13
Kyle Pearce
I started with two and then I tried to do all the rest the other 12. And I’m wondering if maybe we might already have one of the issues that might be happening. But keep going.

00:12:53:13 – 00:13:16:11
Diane Hamilton
Keep going. Well, there’s just so much. Yeah, it’s true. There’s so much. I mean, I think many of us doing things in classrooms, we have that pebble of I’ve got a strong student working with a student that has more challenges and is hanging back and how do I get them both engaged. So that continues to be an issue for me.

00:13:16:11 – 00:13:41:19
Diane Hamilton
And I do walk around and give little prods and pushes and comments. That’s just an ongoing challenge, I think. So this year I’m doing scaffolded notes at the end of every unit, which are highly scaffolded with really just sort of fill in the blanks for the kids, followed by check your understanding questions, mild, medium and spicy, and for context.

00:13:41:19 – 00:14:01:18
Diane Hamilton
Our school does not give marks. Our school does not have tests. We don’t give homework. The report cards are just comments, no grades, and we give feedback just sort of orally. And then in parent teacher student conferences, we give kind of what would normally be communicated through a report card.

00:14:01:20 – 00:14:22:23
Jon Orr
Diane, what would you say is the real kind of issue here that we can kind of dive in today? Because I know that it is like we’ve got varying levels of students in our classroom. We’re trying to implement 14 practices or 12 new practices in our classroom this year. You’ve got you’re in a school that’s kind of balancing feedback with making sure students progress.

00:14:22:23 – 00:14:27:16
Jon Orr
So think about all of those things. What would you say is the real struggle that you’re kind of battling right now?

00:14:27:18 – 00:14:50:05
Diane Hamilton
So I think the key thing I’d like to focus on is how to give the kids feedback about where they are and where they’re going in this very sort of complex web of the thinking classroom. There’s so many parts and do have that sense of not enough time that many of us have, which is not really helpful. But there it is.

00:14:50:07 – 00:15:23:13
Diane Hamilton
So I give them the scaffolded notes and they do their check. Your understanding questions, and then I launch into the next unit. And so according to Peter’s work, those check your understanding questions are really just for the kid’s own use, really. And we don’t want to mark them. We don’t want to even necessarily look at them. So the kids just feel like, yeah, I’m just going to do this and the value is in the doing of it, but I’m not sure.

00:15:23:13 – 00:15:44:05
Diane Hamilton
I don’t think the the kids necessarily know just from having done those questions what they know and what they don’t know. They do have an answer key so they can find out for themselves which questions are right, which questions are wrong. But like I have some kids who go through mild, medium, spicy. They want to do them all.

00:15:44:07 – 00:16:04:20
Diane Hamilton
They get most of them right. I guess for them they know like I know my stuff pretty well. I have some kids sort of at the other end to get through sort of two of the mild questions, and they’re not really sure what they don’t know or what they know. And I think most of the kids in the middle don’t really know.

00:16:04:20 – 00:16:27:23
Diane Hamilton
It might be for example, a unit on multiplication strategies. I use Pam Harris’s work a lot, so she has this wonderful summary of the most useful strategies for the four operations. So they’ll have the notes beside them, and then I ask them to try to use the strategies from your notes when you’re doing this. But I just feel like the feedback part is kind of missing.

00:16:27:23 – 00:16:34:15
Diane Hamilton
I don’t think it’s enough for them to just do those questions and then find out if they’re right or wrong, because that’s where it ends.

00:16:34:17 – 00:17:09:05
Kyle Pearce
Yeah, And I guess the wonder I was having, I was picturing like when you were talking about the mild medium spicy. And we can assume that students who are doing all three types and they’re doing fairly well are probably going like, I’ve got a handle on this. But those students in the middle, the question I was wondering is, do you feel that those students I’m going to use your word and say, do you feel those students own the math or do you feel that they’re not sure if they own the math or do they actually not believe they own the math?

00:17:09:07 – 00:17:32:13
Kyle Pearce
And based on that, I think that can at least help us to kind of figure out, okay, if they own the math, then and if they believe they own the math, then we’re in good shape. But if they don’t own the math and they don’t believe on the math and I might even argue some students might, even when we say own it, maybe they should feel like they own it, but they actually don’t.

00:17:32:13 – 00:17:58:10
Kyle Pearce
And that’s problematic as well. So where would you put, let’s say, those students that aren’t necessarily the ones that are having fairly little issues with these all three types of problems? And then I guess my wonder for you would be as for those who aren’t and aren’t owning it, it’s like what might we be able to change to give them more opportunities to own it?

00:17:58:10 – 00:18:25:20
Kyle Pearce
Right? Because if what I’m hearing as well is that if we’re not doing any formal types of assessment, let’s say actual summative, right? I mean, in our world everything is formative. But if we’re not actually doing that and then we’re not actually providing them with an opportunity to really test their knowledge, not just at the end of one lesson, but days later, then they might not really own it and then it might just kind of fade into space.

00:18:25:20 – 00:18:39:19
Kyle Pearce
So I’m wondering where is your thinking around that? And might there be something that we can maybe add alter shift to be able to provide that for our students?

00:18:39:21 – 00:19:20:13
Diane Hamilton
Yeah, I think you’re kind of hitting on it there that my sense is that they don’t feel like they own it and they don’t feel like some do, but there are too many of the students who I think do those questions and those I don’t think it’s necessarily building their confidence as mathematician twins or something. And I would say similarly, when I do the consolidation, I’ve got those few keen kids, but there are for me too many kids who I don’t feel like they’re walking out of the lesson going, Yeah, I really got that.

00:19:20:13 – 00:19:21:20
Diane Hamilton
That made sense.

00:19:21:22 – 00:19:45:21
Jon Orr
Do you feel like that you’re unsure if they’ve got it or, you know, they don’t got it? I’m just trying to decide. Like when they walk out the door and you’re saying some of them are unsure whether what that was today. I’m just curious. Do you do you have a good sense of that that day? Who’s got it and who doesn’t got it?

00:19:45:23 – 00:20:11:17
Jon Orr
You feel confident with that when you’re working with the kids and seeing that and you’re like, I do like I know exactly where everyone is. I think that’s really important, right? Because especially with if you’re providing feedback and it’s all about moving them along the trajectory of where they’re trying to get to on that particular learning goal for that lesson or for the unit knowing where your student is and being able to kind of give them the nudge or give them that that next step is really important.

00:20:11:17 – 00:20:16:01
Jon Orr
So do you think that they’ve got it or do you think there’s more to dig for yourself?

00:20:16:02 – 00:20:45:05
Diane Hamilton
Well, I circulate around and for sure connect with pretty much every kid during a problem solving class. So I feel like I know where each of them is with regard to that particular concept or skill. But I don’t feel like they know. And it is a very particular context where there aren’t marks and for good reasons that I believe in.

00:20:45:07 – 00:20:52:21
Diane Hamilton
But then without that kind of blunt instrument of a mark, then I need to find another way for them to know.

00:20:52:23 – 00:21:19:09
Kyle Pearce
Well, you know, my my thought is like something that could be as easy as a green yellow or maybe red might not be the right color, but you get the idea of giving them a sense, because I’m sure a lot of students, especially if, let’s say, use sticky notes, maybe use sticky notes, maybe avoid red, maybe avoid orange, or maybe you pick colors like blue, green and purple, and you have them have a meaning.

00:21:19:11 – 00:21:45:05
Kyle Pearce
Or you can go the other way and say like, red is spicy, that’s a good thing. Like, Wow, you’re really spicy at this. And you could potentially offer I’m thinking kind of two angles. First, if you already know, that’s amazing. That’s important. Like John said, very important for us to know. If you already know, then give them the opportunity with the stickies to kind of put a sticky note out based on where they think they are.

00:21:45:08 – 00:22:02:01
Kyle Pearce
And what that’s going to tell you is it’s going to help you align whether like, are they where I think they’re at? Do they think they’re at the same place that I think they’re at or are they missing something? And then that gives you something new to think about of like, oh, if they think that they’re spicy, which is good.

00:22:02:03 – 00:22:22:15
Kyle Pearce
And I think that you’re very mild, you know, or whatever, whatever you want to call it, right. I think you’re mild right now. And you know, you define what those things mean in your classroom and you make sure that everything is for growth and positivity and that this is not a judgment, but more or less an instrument to help you determine how we can get better.

00:22:22:15 – 00:22:47:04
Kyle Pearce
And this is a culture of growth. We’re always learning, we’re always getting better. The beauty is when students are are essentially putting down a sticky note that aligns with what you think the sticky note should be. And then the next question becomes, which is maybe the harder question is what opportunity can I give to that student so that they can actually make the progress?

00:22:47:04 – 00:23:13:23
Kyle Pearce
Because one of the challenges that teachers in general have is that time, as you’ve already articulated, is hard. But also if I don’t have, let’s say this typical end of chunk, end of unit, end of block sort of assessment, which everybody hates, like everyone who has that in their structure hates it because it’s limiting. But then when we don’t have it, sometimes we sort of like lose track.

00:23:13:23 – 00:23:41:24
Kyle Pearce
We’re almost losing an opportunity to kind of push to get better. It’s like a hockey team practicing, but there’s never a game. There’s never a game coming. So it’s like I don’t get to see whether it’s actually translates into something. So I wonder if there might be something like the stickies that you might be able to offer in terms of not formalizing it as a true assessment or as a true summative or anything like that.

00:23:42:01 – 00:24:04:09
Kyle Pearce
But just we go back a lot of times to our what we call our growth days when allotting time so that students can pick what they need to work on. And that might require you to help them as well, right? Because of a student pick spicy for everything for themself. And you’re like, actually, you know what? I feel like you’re more medium on this one.

00:24:04:11 – 00:24:30:00
Kyle Pearce
Then you’re giving them this opportunity to do some of that growth. But it’s also differentiated so that it’s not the same for everyone. It’s not a test that everybody has to sit and write and sweat and worry and cause stress and anxiety. But it does give them an opportunity and you an opportunity to work with students more individually as well as to actually allow them.

00:24:30:00 – 00:24:49:17
Kyle Pearce
And and what you can tell them is, hey, we’re doing this growth day or whatever we want to call it, because I want to give you an opportunity to own one concept today. Like that’s what we’re going to do today. You can’t own them all today, but we’re going to pick one concept individually and some of them are going to be the same and some of them are going to be different.

00:24:49:17 – 00:25:06:00
Kyle Pearce
But the goal here is we want you to own this. So if there’s something you don’t own yet that’s what we’re going to work on. And that would just require you to have maybe a few extra problems or material that they can use and try to use to grow from.

00:25:06:02 – 00:25:26:01
Jon Orr
What is also important in that you need for that type of system to go. When you said like, one of the things is like, how do I give them the right feedback and how do I get them to move when I know they’re not ready yet, is thinking about what Kyle is saying with these growth day or chunk of time where they’re at, say my medium child, and you want them to get them to medium.

00:25:26:03 – 00:25:52:01
Jon Orr
It’s like we have to have a really clear picture of what we expect for mild and then what we expect to see for medium and spicy. We need success criteria here to go. Like when I see this consistently, you are at the medium you’re doing medium level questions on this learning goal. But now because I see that I’m documenting it right, I’m going to write that down, that we’ve got this.

00:25:52:01 – 00:26:09:20
Jon Orr
It’s not a mark, it’s just a tracker. And it’s like saying like, this is where you are now. Our goal is to get you to the next level, the next stage, but we have to be clear on what that looks like. So when we see it consistently, we can go. Moving on, now you’re here, but the student also needs to know it, right?

00:26:09:20 – 00:26:31:04
Jon Orr
The student needs to know this is what medium looks like. And when you can do this consistently and here’s what consistently means on this particular skill, then when you can do that consistently, then you need to move to like you’re at this stage right now. But I want you to get to here and that’s your goal. Next. Like what Kyle saying is like you have a chunk of time.

00:26:31:04 – 00:26:43:12
Jon Orr
It’s like now you’re going to own this skill. Now you’re going from medium to spicy, you’re going from mild to medium, and that’s what you’re doing today. But here’s what it looks like when you get there so that we know what the target is.

00:26:43:14 – 00:27:10:03
Diane Hamilton
Huh? Yeah, that’s really good feedback. I’m wondering if after our notes and check your understanding questions, then I could be giving the kids a very specific self assessment sort of rubric really, for them to fill out, which then I can look at and see if I agree with them. And then that rubric could guide like a work they do on a growth day.

00:27:10:03 – 00:27:36:19
Diane Hamilton
I love that term growth day because, yeah, I mean, I know this is podcast, but I have a visual here of just this is the kind of notes that they’re doing. So say for multiplication we’ve got four different strategies. We’ve got partial products over under flexible factoring and doubling and having and they’re filling in the blanks and so then I’ll give them a bunch of multiplication questions.

00:27:36:19 – 00:28:10:02
Diane Hamilton
And the thing is they won’t necessarily use all these strategies. They’ll just use the one or two that they’re really comfortable with. So if I followed this up with the four strategies and are you not sure, pretty sure or really sure how to use that strategy or really confident, whatever it is, I could have kind of three levels then they could, after having done the questions, they could assess themselves and then they know where to focus on another day of sort of practice or consolidation solo.

00:28:10:02 – 00:28:11:06
Diane Hamilton
Not that the board’s.

00:28:11:08 – 00:28:38:24
Kyle Pearce
Right and something that’s really important as well, giving students the opportunity to self-assess, really assuming the student does it right. Sometimes some students are reluctant, actually put in the thinking required, but the goal, if they are encouraged to self-assess and they do try to self-assess, is it actually gets them to be reflective, right. So, you know, it’s metacognitive and they they look over and they go, what is this strategy really about?

00:28:39:00 – 00:29:01:15
Kyle Pearce
Because like, if I’m saying I understand that, do I really understand it? Or giving them a problem and saying, here’s a problem and I’m going to actually challenge you. I love using the word challenge. I’m going to challenge you to try that strategy. Right. Even though you might find this strategy easier, I’m going to push you to try that strategy with this problem so that you can get better at it.

00:29:01:15 – 00:29:29:07
Kyle Pearce
Right. And I think sometimes that can be hard in mathematics, especially when we’re trying to use strategies, is that as soon as there’s a strategy that seems to be one that works well for me, I’m going to lean on that heavily, right? So whether it’s stacking or whether it’s any strategy that I’ve used, compensation is one you’ll see once students learn compensation and oftentimes they try to use it in every number talk and then you’re not actually getting any better at any other strategies.

00:29:29:07 – 00:30:04:19
Kyle Pearce
So sometimes we have to almost say, listen, I actually want you to not use that strategy. It’s a great strategy. Love it. We want you to know it and use it whenever you feel it’s appropriate. But today, for this one moment, I want to push you here. And when they are self assessing and being given this opportunity to kind of give themselves a little bit of an indicator as to where they are in the learning that can really allow them to take ownership, not just of the mathematics, but ownership of the learning and like the responsibility of the learning for themselves.

00:30:04:19 – 00:30:27:03
Kyle Pearce
Because at the end of the day, that’s really what we want, right? We don’t always get it with every student, but what we want is for students to take ownership, to want to learn, to want to push themselves, just like we want everyone, every student, to be pushing themselves in all aspects of life. Right. Doesn’t always happen that way, but that’s what we’re trying to encourage.

00:30:27:05 – 00:30:51:07
Kyle Pearce
So it sounds like, you know, based on what you’ve you’ve been telling us today, is that you’re giving your students a lot of opportunities to do a lot of great learning, a lot of great collaboration, a lot of great thinking. And this particular pebble, I feel like you’ve got some ideas here to kind of shake that, oh, it might take some time as you try to strategize what that looks like and refine what it looks like.

00:30:51:09 – 00:31:02:16
Kyle Pearce
But when we wrap this conversation here today, I’m wondering, do you have any big takeaways or maybe next steps that you plan to put in action based on some of what we discussed here tonight?

00:31:02:18 – 00:31:27:18
Diane Hamilton
Well, I think I will try that. Just giving one more day, one more class after wrapping up the unit for kids to self-assess and then practice in the areas where they they’ve identified that they need more work for sure. And I think in general I think the kids are in a bit of a feedback vacuum because of not having the marks.

00:31:27:18 – 00:31:52:15
Diane Hamilton
And I think there’s a kind of an anxiety that can grow into that vacuum. So yeah, I want to figure out more ways to be giving them feedback. Just I’m here to make sure that you’re challenged and trying your hardest and finding out all the amazing things you can do. So yeah, that’s an exciting kind of direction to focus on.

00:31:52:20 – 00:32:00:15
Jon Orr
Yeah, awesome. That sounds like some really good next steps there. What would you say is an immediate, immediate next step for tomorrow?

00:32:00:17 – 00:32:43:15
Diane Hamilton
Tomorrow? Well, I have an opportunity right now because I have a student teacher, so I’m kind of excited to watch her teach the kids and do a consolidation so that I can step back and really check out how the different kids are participating in that really important consolidation phase. So I think in the next class with her leading the consolidation, I want to hone in on where those kids are at in terms of actually engaging in the consolidation, because I think this relates to their sense of owning the math and knowing where they are and where they need to go.

00:32:43:21 – 00:33:03:13
Diane Hamilton
That is a bit weak. I think I’m just going to try to make some really concrete observations about particular kids and then coach them a little bit more because I’m going to have this extra teacher who also needs coaching. But I think it’s a chance to step back and really observe my students.

00:33:03:15 – 00:33:04:19
Jon Orr
Awesome. Awesome.

00:33:04:22 – 00:33:05:22
Kyle Pearce
That’s fantastic.

00:33:05:22 – 00:33:12:09
Jon Orr
Would you be open for us to check in with you in six months or starting next year to see how things have gone? For sure? Yes.

00:33:12:15 – 00:33:15:09
Diane Hamilton
I would love to talk to you guys more. Yeah, that would be great.

00:33:15:13 – 00:33:20:05
Jon Orr
Awesome. Thanks so much for joining us on this episode and speaking with us this evening.

00:33:20:07 – 00:33:23:11
Diane Hamilton
Thank you, guys. Take good care.

00:33:23:13 – 00:33:47:04
Jon Orr
Okay, So we just got off the call with Diane and I think and conclusion to this episode, we often have to I like to think of our classroom tree. You know, we have our six areas of a strong classroom tree or a strong district program, a mathematics program. One of those areas is our mindset. We call that the soil, the water, the sunlight of the tree.

00:33:47:04 – 00:34:20:01
Jon Orr
And when I think of the mindset, a lot of times I think about how we perceive what others are doing in the classroom. Diane here was trying to implement all 14 practices, and it’s almost like she gave herself. She said one year she was doing the first few and then it was like, Let’s do all 14. And I’m going to argue that when I was in the classroom and we think about what we’re doing now versus what we want to do, this ideal, we’re always aiming for this ideal and we think we have to jump from where we are now to the ideal without going through the muck, without going through the trial and error.

00:34:20:01 – 00:34:38:05
Jon Orr
That has to get us there. We all do want to speed that up. That’s why books are written. That’s why we go to conferences. We want to learn from others mistakes. However, I think we have to also give self grace that we can’t go from here where we are now to the ideal without going through some learning curve at some point.

00:34:38:07 – 00:35:03:00
Jon Orr
So to go from where? Implementing a few practices to implementing all 14 practices and expect that to be like, Hey, I’m going to do a great job at that, I think we have to make sure we give ourselves that mindset that most people, we do have to go through a process to make sure that we uncover what’s involved and oftentimes in education, we look across the street, we look across the hallway, or we look at a conference and we want that.

00:35:03:05 – 00:35:22:07
Jon Orr
And we think we should be able to just get that. And also the leaders that we have in our buildings also think that that’s just maybe how it’s going to be. You should be doing that over there. But we have to consider that there is a learning curve to say pedagogical approaches to understanding the mathematics, the roots of our tree that we do have to kind of go through.

00:35:22:07 – 00:35:41:12
Jon Orr
And it does take time for us to develop those skills. So I just want to make that my big takeaway from the episode is think about the ideals you’re after and then think about the actual timeline of getting there. Don’t compare your bottom 20% or your bottom 80% to the person across the halls. Top 20%. We do that online all the time.

00:35:41:12 – 00:36:00:16
Jon Orr
We see people going, Hey, I want that. That looks amazing. And we compare. We’re not doing that well. I’ve got all of these problems and they’re showing me all these amazing things. But the reality is they also have some things that they’ve gone through that they’re just not showing you. So allow ourselves to realize that we can’t just jump from one to the other without going through that learning curve.

00:36:00:17 – 00:36:25:12
Jon Orr
Folks, we talked to Diane here and Diane reached out to us through our mentoring moment application and we encourage you to share or reach out to us. So you also kind of share what Pebble is rattling around in your shoe head on over to McMath moments dot com for such mentor quick form there fill out your pebble and we’ll be talking to you in a coaching call like we did with Diane and it will help the other educators in the math moment maker community.

00:36:25:16 – 00:36:28:16
Kyle Pearce
Well until next time I’m Kyle Pierce.

00:36:28:16 – 00:36:29:23
Jon Orr
And I’m John or.

00:36:30:00 – 00:36:32:22
Kyle Pearce
High fives for us.

00:36:32:24 – 00:36:37:03
Jon Orr
And high five for you. Oh.

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The Making Math Moments That Matter Podcast with Kyle Pearce & Jon Orr
Weekly interviews, strategy, and advice for building a math classroom that you wish you were in.


Download the 2-page printable 3 Act Math Tip Sheet to ensure that you have the best start to your journey using 3 Act math Tasks to spark curiosity and fuel sense making in your math classroom!

3 Act Math Tip Sheet


Each lesson consists of:

Each Make Math Moments Problem Based Lesson consists of a Teacher Guide to lead you step-by-step through the planning process to ensure your lesson runs without a hitch!

Each Teacher Guide consists of:

  • Intentionality of the lesson;
  • A step-by-step walk through of each phase of the lesson;
  • Visuals, animations, and videos unpacking big ideas, strategies, and models we intend to emerge during the lesson;
  • Sample student approaches to assist in anticipating what your students might do;
  • Resources and downloads including Keynote, Powerpoint, Media Files, and Teacher Guide printable PDF; and,
  • Much more!

Each Make Math Moments Problem Based Lesson begins with a story, visual, video, or other method to Spark Curiosity through context.

Students will often Notice and Wonder before making an estimate to draw them in and invest in the problem.

After student voice has been heard and acknowledged, we will set students off on a Productive Struggle via a prompt related to the Spark context.

These prompts are given each lesson with the following conditions:

  • No calculators are to be used; and,
  • Students are to focus on how they can convince their math community that their solution is valid.

Students are left to engage in a productive struggle as the facilitator circulates to observe and engage in conversation as a means of assessing formatively.

The facilitator is instructed through the Teacher Guide on what specific strategies and models could be used to make connections and consolidate the learning from the lesson.

Often times, animations and walk through videos are provided in the Teacher Guide to assist with planning and delivering the consolidation.

A review image, video, or animation is provided as a conclusion to the task from the lesson.

While this might feel like a natural ending to the context students have been exploring, it is just the beginning as we look to leverage this context via extensions and additional lessons to dig deeper.

At the end of each lesson, consolidation prompts and/or extensions are crafted for students to purposefully practice and demonstrate their current understanding. 

Facilitators are encouraged to collect these consolidation prompts as a means to engage in the assessment process and inform next moves for instruction.

In multi-day units of study, Math Talks are crafted to help build on the thinking from the previous day and build towards the next step in the developmental progression of the concept(s) we are exploring.

Each Math Talk is constructed as a string of related problems that build with intentionality to emerge specific big ideas, strategies, and mathematical models. 

Make Math Moments Problem Based Lessons and Day 1 Teacher Guides are openly available for you to leverage and use with your students without becoming a Make Math Moments Academy Member.

Use our OPEN ACCESS multi-day problem based units!

Make Math Moments Problem Based Lessons and Day 1 Teacher Guides are openly available for you to leverage and use with your students without becoming a Make Math Moments Academy Member.

MMM Unit - Snack Time Fractions Unit


Partitive Division Resulting in a Fraction

Shot Put Multi Day Problem Based Unit - Algebraic Substitution


Equivalence and Algebraic Substitution

Wooly Worm Race - Representing and Adding Fractions


Fractions and Metric Units


Scavenger Hunt - Data Management and Finding The Mean


Represent Categorical Data & Explore Mean

Downloadable resources including blackline mastershandouts, printable Tips Sheetsslide shows, and media files do require a Make Math Moments Academy Membership.


Pedagogically aligned for teachers of K through Grade 12 with content specific examples from Grades 3 through Grade 10.

In our self-paced, 12-week Online Workshop, you'll learn how to craft new and transform your current lessons to Spark Curiosity, Fuel Sense Making, and Ignite Your Teacher Moves to promote resilient problem solvers.