Episode #81: Creating Balance in Personalized Learning: A Math Mentoring Moment.

Jun 15, 2020 | Podcast | 0 comments


In another “Where are they now?” episode series we bring back on 6th grade math teacher Sam Brotherton from St. Louis Missouri. Sam’s back to talk about the changes he made in his classroom around assessment, lesson design and how practice fits in. He also talks to us about his new challenges around personalized learning. 

This is another  Math Mentoring Moment episode where we talk with a member of the Math Moment Maker Community who is working through struggles and together we brainstorm possible next steps and strategies to overcome them. 

You’ll Learn

  • The difference between Individualized Learning, Differentiated Learning, and Personalized Learning. 
  • How to create balance among different modes of instruction in your course. 
  • How we can spark the love of learning in our students.


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Sam Brotherton: If you have one student coming up with an idea, all of a sudden you have 10 students that have that idea, too. So how do I anticipate that to make sure that kids are having those light bulb moments, those moments that matter when they’re the ones kind of driving the learning? That’s kind of hard to do, but I think teaching kids how to brainstorm and how to get feedback from their peers and how to ask for feedback from adults, and also kind of coaching the kids through how do you give each other meaningful feedback and go beyond just saying, oh-

Kyle Pearce: In another, Where Are They Now episode, we bring back on sixth grade math teacher Sam Brotherton from St. Louis, Missouri. Sam’s back to talk about the changes he’s made in his classroom around assessment, lesson design and how practice fits in. He also talks to us about his new challenges around personalized learning.

Jon Orr: This is another math mentoring moment episode where we talk with a member of the math moment maker community who was working through struggles and together we brainstorm possible next steps and strategies to overcome them.

Kyle Pearce: Welcome to the Making Math Moments That Matter podcast. I’m Kyle Pierce from tapintoteenminds.com

Jon Orr: I’m John Orr from mrorr-isageek.com.

Kyle Pearce: We are two math teachers who together, with you the community of math moment makers worldwide who wants to build and deliver math lessons that spark engagement-

Jon Orr: Fuel learning-

Kyle Pearce: And ignite teacher action. Welcome to creating balanced in personalized learning, a math mentoring moment with Sam Brotherton.

Jon Orr: Before we get to our interview with Sam, we want to remind you that you too can join us for a math mentoring moment episode on this podcast. In these episodes, we talk with teachers about real issues that arise in their classrooms and together we work through possible solutions. We know that our listeners, math educators, like you will also get a lot of value out of conversation by listening in on that conversation.

Kyle Pearce: If you have a problem of practice or classroom struggle that you want to chat with us about, head on over to makemathmoments.com/mentor and fill out this quick form. We won’t be able to talk to everyone who fills out the form but we will make every effort to hear a variety of voices and classroom struggles. Again, head to makemathmoments.com/mentor to apply.

Jon Orr: Well, Kyle the ratings and reviews keep coming in and we couldn’t be more excited to read them. Like this five star rating and review from Escobar.

Kyle Pearce: Thank you. Thank you so much. I’ve been teaching for over 30 years and still struggle with some of the concerns discussed by you and your guests. It feels great to know that I’m not alone. My memorable math moments from middle school were mostly negative. So I am very focused on creating positive experiences for my students. In a recent episode, you talked about 3 ACT math tasks. I love the taco cart task, which thanks to you guys, I will use as an intro to the Pythagorean Theorem instead of a midway task. Thanks again and keep the episodes coming. #Bettertogether. I agree that reflection may keep me up at night, but it also keeps me fresh and young. Your podcast provide much food for thought and I approximate it, he says. Awesome stuff there.

Jon Orr: Wow, thanks so much for that fantastic math moment maker community review. That person took the time to help ensure the podcast reaches the ears of more math educators around the globe. Go ahead. What are you waiting for? It only takes a minute. Fire us an honest rating and review.

Kyle Pearce: Wow, do we have a lot of goodies to share with you and it all revolves around the math moment maker Academy.

Jon Orr: Right now, for a limited time we have a 30 day free teacher license available for any math moment maker from around the world to access our academy professional development courses including our courses on spiraling assessment, math tech tools, and even our latest course on how to Make Math Moments from a distance. These self paced courses are jam packed with videos and action items to get you reflecting and growing your math content knowledge and pedagogical practice.

Kyle Pearce: Also gain access to our monthly Q&A web calls both live and the replay recordings, the over 20 virtual summit sessions from this past November and our Make Math Moments problem based tasks and full units of study with teacher guides are available for you to access.

Jon Orr: Get on it because it goes away at makemathmoments.com/Academy. That’s makemathmoments.com/Academy.

Kyle Pearce: All right, on to our chat with Sam. Hey there, Sam, welcome back to the Making Math Moments That Matter podcast. It’s awesome to have an opportunity to do a check in. Where Are They Now episode here on the podcast? How are things going over in St. Louis?

Sam Brotherton: Well, things are great in St. Louis. Last time we talked the Blues were in last place and we know how they turned that around. As far as teaching goes, I’ve got some new things happening. So I’m excited to talk about it.

Jon Orr: Yeah, looking forward to talking about all of that stuff. Last time we chatted with you is way back in Episode 13, and Sam for all of those listening who that haven’t heard that episode just yet, can you do us a favor and fill everyone in on, we said that you’re from St. Louis, but maybe let us know maybe more specifically, and then also your teaching role?

Sam Brotherton: Sure. So last time we talked, I was teaching sixth grade math, and the big focus of our conversation was when you have these kids engaged doing 3 ACT tasks and then you come back to class two or three days later, it seems like nothing stuck. So what can you do to follow up the engaging stuff that you’re doing to make sure that kids are having deeper connections? So you guys gave me some good tools that I could implement, just to go over like on day to day lessons to make sure that all of the great discourse that we were having was actually getting the results that we were looking for. You want me to talk about what I’m doing now as well?

Kyle Pearce: Yeah, well, actually, it’s like you read our mind. We were about to just dive in there. I guess the only other thing I’ll do is if anyone who hasn’t listened to Episode 13, definitely a good idea to roll back to that one. Maybe hit that pause button, go back and listen in because, like you were saying there, Sam, you were talking about all kinds of great things going on. Like you were using 3 ACT math tasks, you even described like how you have almost like a vertical non permanent 360 room, like a big whiteboard room in there, getting kids up and doing all kinds of great things.

Kyle Pearce: You talked about Desmos, and how you were almost like Desmofying as many lessons as possible, trying to make it nice and interactive. One of those concerns was how that translated into assessment. So that’s kind of a, in a nutshell, what we were discussing. We did talk about consolidating and some practice structures. So yeah, definitely give folks an update as to like, where are things at there and like we always say, it’s always a work in progress. But how has things been going and how have things been progressing since we last chatted, back when the Blues were in last place?

Sam Brotherton: So I think just one thing to add on to that episode that we talked about, when we recorded that I was in my fifth year teaching and coming out of college, you can get online and just type in math lessons, middle school, and there’s so much stuff out there. Trying to synthesize everything and put it together can be really overwhelming. So I think listening to myself in that episode, a year ago, it’s like I have all these cool tools in my tool belt, and I just don’t know how to always put them together the right way.

Sam Brotherton: So I think that was something that we had some great conversations around, but as far as now, my district is starting to, I’d say we’re more than dipping our toes into the whole personalized learning movement. We have an elementary school that they built three years ago called Mosaic that’s all centered around personalized learning. So they’re trying to connect that idea of personalized learning to the middle school level. So just this year, I’m teaching a hybrid math-social studies class, sixth grade that centers around personalized learning. So taking some of my old practices, but evolving in a lot of ways and learning a lot along the way.

Jon Orr: Gotcha. Good to know that you guys are working towards that. Now, Sam, I’m wondering for all of our listeners, personalized learning can mean lots of different things. I think it’s running through people’s ears right now going, well, don’t I do personal learning or what is personal learning? What would you define personal learning to mean to you or your district?

Sam Brotherton: Yeah, that’s a really tough question. Because I think even within my district, if you ask different teachers that are in the trenches right now with personalized learning, we’re going to give you different answers. I think one misconception with personalized learning is that it’s kids do whatever they want. Kids don’t have deadlines, and they’ll eventually figure it out.

Sam Brotherton: I would say for me, personalized learning is when you get to that sweet spot where kids are identifying the problems, and kids are coming up with the solutions to the problems using the standards you want them to learn. That’s pretty much my definition.

Kyle Pearce: I love that I’m actually just coming back, just last week. I spent the week in Israel with one of our former guests from our math council episode, Craig Guthrie. We went over there to work with some math teachers and they’re very heavy into the idea of personalized learning. I know there’s some other terms we were chatting about it an email before we came online tonight to chat.

Kyle Pearce: There’s these other ideas like this individualization and differentiation. We use the term differentiation on the podcast a lot and like John said, I think what it looks like and sounds like to one person might be very different to another. So I know for me, it’s like, I think John and I have taken the approach in previous years or recent years, I should say, in trying to allow some of that personalization, but kind of mixing it in with this idea of differentiation.

Kyle Pearce: So it’s kind of like a bit of a mix of those two. How’s that looking and sounding in your classroom? Like, how are you feeling that your progress and maybe even just speaking in general to maybe some of the other teachers in your district, like, how has that more than dipping your toes in, as you mentioned, how’s that going? Because I know that that could be a really challenging idea to try to grapple with, if let’s say, you’re coming from a pretty traditional sort of approach to teaching a subject like mathematics.

Sam Brotherton: I think for me, just kind of the difference in how my philosophy of teaching is not as much, how can I get kids excited about math? Because I love math, but how can I empower my kids to be excited about learning in general? So it sounds kind of corny, but thinking with that mindset has pushed me to say, you know what, sometimes these 3 ACT tests that I think are awesome and fun, like that fruity problem that we linked in Episode 13.

Sam Brotherton: It was a really fun lesson, but then the next day, the kids are back in their same old routine. So what I’m trying to do in my classroom this year is think about how I can differentiate, how I can individualize and how I can personalize. In some ways, I have my own definition of those. So for differentiation, that’s just all the kids are learning the same skill, but they’re getting what they need to learn that skill.

Sam Brotherton: So if you’re talking about learning ratios, some students might need blocks to help them understand the concept of ratios, some students might be ready for a double number line, some students might be ready for a ratio table. Then there’s individualization, which might mean I have a student who’s on a second grade level and a student who’s on an eighth grade level. One of those students needs to go back and learn how to do perimeter, whereas one of those students is ready to start solving systems of equations.

Sam Brotherton: So when there’s time for students to work individually, I’m giving them the individual skill that they need to either close gaps or move forward. Then like we kind of talked about our like I said earlier, that personalization piece is, students are saying, okay, here’s a problem that I see or here’s something that I’m excited about. Can I demonstrate my warning and some different way? So we can talk a little bit more about that too.

Jon Orr: Gotcha. Gotcha. This is all good stuff, for sure. Things are running through my head right now on what this looks like in your classroom. So you’ve given me some suggestions on the definitions of these terms and thinking about personalization. So you said you’ve been using 3 ACT math tasks and other things, but you wanted that engagement but you were struggling with like how to keep that learning going, which is what we talked about on the last episode too. I’m wondering like, how does this personalization for you fit in with 3 ACT math tests? What does that look like for you? How are you taking this project or this new look plan with your district, and tying in these best practices that you already know about?

Sam Brotherton: For sure. So I have to go back a little bit last year to when I found out that I was going to be doing this. Our district did a ton of professional development. So I went and saw different schools around the area. We went up to Waukesha, Wisconsin, and saw some different school districts up there that are doing some personalized learning stuff.

Sam Brotherton: So then I kind of had to get out of this mindset of like, I’m always leading the discussions in my classroom. So when I found out that I was doing it, they basically said they wanted more open concepts in the room and my co teacher and I loved that idea. So I teach the math and social studies section to a cohort of about 50 students, and then my co teacher teaches the ELA science section to those 50 students and there’s an opening in our classroom.

Sam Brotherton: So on a day to day basis, I have kids for two 90 minute blocks and what that would look like in the classroom is I have different ability groups. So there might be a day where I’m doing direct instruction and when I say direct instruction, that might be a 3 ACT test. So I might have one group of students who are working on percentages, and another group of students who are still moving at a slower pace and might be working on ratios.

Sam Brotherton: So my group that’s working on percentages, we would do like a 3 ACT math test to introduce the topic and then they have different practice work to do and then there’ll be other times when we switch those groups and I’ll have the kids who are working on ratios. So that’s the beauty of having that open concept. Because we can kind of pick and pull kids as we need to, because we know that every classroom that you walk into, you’re going to have that student who’s on the second grade level and the student who’s on the eighth grade level.

Sam Brotherton: So having the luxury of being able to have a little bit more flexibility and moving them around is nice. Then where the personalization piece comes in is when we talk about assessment. So instead of necessarily doing a test, I have single point rubrics that I give the students and kind of put the ownership of the standards in their hands. So I’ll say okay, we’re learning about percentages, we go through it and then about halfway through the unit of instruction, I’ll kind of introduce this single point rubric and say, okay, you’re going to show me that you know how to convert from decimals to fractions to percents.

Sam Brotherton: You’re going to show me how you can use unit rates and relate that to percents, but then I want you to come up with a meaningful way to demonstrate that. So what that looks like is sometimes utter chaos. Sometimes confusion from the students, sometimes a lot of frustration, but it also can create some really awesome products and some awesome learning. So for example, last week, I had a couple students record their own cooking shows at home. They actually made their own recipes, and talked about the different percentages of ingredients they used.

Sam Brotherton: They created an ingredient list, talked about the pricing of the unit rate, the calories and all that stuff. So that’s really cool to see. When I see that, I’m like, okay, I know this student got it, and I know they’re going to remember this. The trade off those, will they still get that test question on the state test right? That I don’t know. That’s something that’s been a struggle to deal with as well.

Kyle Pearce: Right, right. That sounds similar to some of the ideas that we had come up with in that first episode back in Episode 13 was, again, how do we connect it all? It sounds like you’re feeling really good about how this is sort of unfolding. To me, it sounds like you’re doing an awful lot of what we would probably consider to be the approach that we use in our classroom where, although on the podcast, we often are talking about problem solving situations when we’re giving problem based lessons to students and we’re doing that more whole group and we’re differentiating throughout.

Kyle Pearce: The part that we don’t talk about as much, because I don’t think it’s interesting to talk about or to listen to on the podcast is, what do we do after that? That’s where that purposeful practice comes in and I think that’s where the individualization and the personalization can kind of fit. So to me, it’s sort of sounding like having kind of a happy medium or a balance of all three is seems really, really important.

Kyle Pearce: I’m hearing, you’re saying personalization, and it sounds like outside of those problem based lessons it’s very personalized, but yet, inside that problem based lesson, it sounds like it’s differentiated. Giving Students, the models, the different approaches and strategies that they want to bring to the task and they can approach it any way they see. So I really like the way that’s sounding and are there any other struggles? You’re mentioning this idea around assessment and like bringing it all together like, how’s that going to translate? Are there any other struggles that are on your mind that we can dive into here as well, while you’re kind of unpacking some of what’s happening in the classroom?

Sam Brotherton: Yeah, for sure. So one thing that we’ve been trying this year with some degree of success is like learner choice menus, we call it a playlist. So basically, the students have the assignments that they need to get done throughout the week and they can choose when they need to work on them. So like, if I’m not doing a whole group lesson, or we’re not working on some kind of project or having some sort of discussion, they generally do what’s called playlist time, and that’s where I can pull kids and conference, but they can choose.

Sam Brotherton: So some students might be working on a social studies debate, some students might be working on some sort of infographics. Some students might be working on their math practice that they need to do for that week. We also have some online platforms that they use, they might be doing that. That’s a real struggle to manage, especially when you’re working with 11 and 12 year olds, because I remember when I was in middle school, whatever my teachers would let me get away with to a certain degree, I would get away with, you know what I mean?

Sam Brotherton: We have the students make learner profiles at the beginning of the year. So it’s like Myers Briggs test, what motivates you, what distracts you, all that stuff, and we revisit that a lot. The idea is we have students create these learner profiles, so that they’re supposed to know how do I learn best, and then we help them set goals to make the right choices based on what they know. So our classroom has flexible seating.

Sam Brotherton: So they have choice in where they sit, how they sit, whether that’s like couches, standing and sitting. Then they also have choice at certain times on what they’re working on and then they also have choice on how they’re demonstrating things. So sometimes that can be really tough to manage, and that’s probably the same sentiment that you’ll get throughout the district with some of the teachers that are engulfed in this personalized learning right now, it’s like, this is awesome, but it’s like mentally exhausting and physically exhausting some days, because you have 20 kids that want your attention all the time.

Sam Brotherton: They constantly want to conference, they constantly want feedback. Then there’s also the aspect of I have 20% of kids who need my constant attention to make sure that they’re on task and doing what they need to. So kind of juggling all that while saying, I still want to do Desmos, I still want to implement the five practices of discourse. I still want to do 3 ACT math tasks, but I still want to do all this other stuff, too. It’s kind of like, you can’t live in the personalized arena all the time. You have to go back and forth between the direct instruction, differentiation, all that.

Jon Orr: It’s kind of like you got to pull them together and go, we’re going to do this activity today and we’re going to branch off and do these other things after or vice versa. Sam, I dabbled in that arena like the way you described that kids had a plan that these are the things we need to get done this week or in this time zone or this time or this unit, but I have freedom in choosing when I want to do that, or where I want to do that and how I want to demonstrate that.

Jon Orr: I had done a lot of that early in my career, and it is tough to manage, because you have to be able to track that well. You got to be able to say what learning goal is this kid on and have they demonstrated already? I totally get that. You said it’s tough. It’s mentally exhausting. I’m wondering, what have you done so far that’s been working for you to manage all of that?

Sam Brotherton: For sure. It’s been mentally exhausting but also I’ve had some probably the most memorable moments as a teacher from this particular school year. As far as managing things, Google Classroom is a big friend. We do standards based grading 1, 2, 3 scale, which I think helps too, because then I can talk to the kids about how, as far as math goes, I break that down by one is you, basically don’t know how to do the skill we’re working on. Two is, you know how to do the skill, but you don’t know how to demonstrate that in an applicable or meaningful way yet.

Sam Brotherton: Then the three is you can demonstrate that in a meaningful way. So being able to give that quick, specific feedback helps in my classroom on those whiteboards that are all over the place. We utilize those a lot. So I have a spot where students can sign up to conference with me, and they can sign up if they have a quick question or if they need to conference. So when students are working on different things, they can jot their name up there.

Sam Brotherton: So that helps me kind of manage the day to day stuff. Spreadsheets are super helpful. I just learned this year that you can insert checkboxes on spreadsheets, which helps me for a lot of stuff. Just have different tabs with all your roster on there and 20 different tabs under it for each assignment and you can go check, check, check, not check. So those are some quick little things that help.

Kyle Pearce: It sounds like you’ve got a lot of great things going on here and despite that fact that you have a lot of great things going on, like John and I were big Google Sheet fans. Before John started using FreshGrade, I was just leaving the classroom with John started FreshGrade and really focusing in on that standard spaced I think is really key, especially if you’re trying to do something like what your districts doing, which is really trying to put some of that onus in the students hands, giving them a bit of that autonomy to work on what they feel they need to work on at the time.

Kyle Pearce: Also with, it sounds like there’s a lot of that guidance with the teacher. You had already mentioned that it’s mentally exhausting. You’re running around and trying to stay on top and essentially, it sounds like observe and have conversations with students so that you’re not only looking at product, but really trying to triangulate data. So it sounds like a lot of amazing things going on, yet, I’m still getting this sense that you’ve got all these ideas.

Kyle Pearce: There’s all these things you want to do and trying to kind of fit it in there nicely and it makes me wonder, I’m going to mention Episode 54 was a mentoring moment episode where we talked about what an effective math block could look like and that was a big question that came up on that episode. We really tried to give this idea of balance in there. So on that episode, you’ll see there’s a graphic that was designed in our district for kind of giving teachers a little bit of that flexibility on what that could look like.

Kyle Pearce: I’m wondering if that graphic might be helpful for you to give yourself a little bit of a sense as to giving yourself permission that just because let’s say your district is really pushing personalized learning, that every day doesn’t necessarily have to look like that scenario you sort of painted for us where all students are working on different things. Today could be a problem based lesson, and then that helps you to jump off or leapfrog to the next stage in learning, but then also giving students those gaps in between.

Kyle Pearce: Let’s say it’s Tuesdays and Thursdays where they’re given that time. John and I would call those, what we’d call leveling up days or assessment days or check in days, which really sounds an awful lot about, like what you’re doing in your classroom.

Sam Brotherton: Yeah, I think you’re on the right track, though, I’m still having some of the same types of struggles as I was when we last recorded, it’s just now in a different setting. When we first started the whole personalized learning thing last year, and when I say we, there’s a group of eight sixth grade math teachers that are all in this for the first year together. So we met a lot. We went to different businesses in the area, different schools, but we created our own vision about what we think personalized learning is and essentially it’s what I was saying before, where students are identifying problems and students are asking questions, and students are coming up with solutions.

Sam Brotherton: So I think when we first started this, I felt like I always had to be doing that. Every single thing had to be students coming up with questions, students coming up with problems, students finding solutions to that. It’s just not realistic to think about having a classroom that runs that way, and I think I got away from some of the things that made me a strong teacher in the first place.

Sam Brotherton: So I’ve given myself permission to not necessarily structure class like that all the time. So I’d love to check out that graphic that you were talking about from Episode 54 because I think it could definitely help me. One thing I have done to just create a little bit more structure for me and for the kids is just to have two overall, and we’ll call them ability groups, but two groups that are working on different units from Open Up Resources.

Sam Brotherton: So I printed out, again, they’re basically little packets from Open Up Resources with the practice problems for the unit and then I’d give the kids those packets. So the way that I see it as kind of like, that’s where I can do a direct instruction lesson from Open Up Resources. Then they have the practice to go with that. That’s my way of making sure, I am teaching the sixth grade standards, I’m making sure that they’re getting all the skills that they need, then we use the online platforms to either fill in gaps or push kids.

Sam Brotherton: Then with that playlist time, that’s where I can start to try to get that personalized learning piece, whether that’s a project that we’re doing or that’s saying, okay, we’re learning about this. Now, what can you do with it? How can you take it and apply it? How can you find the problem? How can you ask the question, how can you identify a solution to your problem or question? So another thing is with those learner choice menus, I know you’ve talked about how you had the level up days.

Sam Brotherton: You’re right, it does sound similar, but what we tried to do at the very beginning of the year was say, okay, here’s your playlist. Here’s all the things you need to do this week, and we’ll be here to help you. That really stressed kids out and it stressed us out and it wasn’t productive because there’s these arbitrary timelines that didn’t really work. So what we’ve started to do is introduce the playlists when it makes sense. So Monday and Tuesday might be direct instruction, Wednesday, we may be working on a project in science class.

Sam Brotherton: Then it may be Thursday where it’s like, okay, now we’ve got these three or four different things introduced, these are the things that you need to work on, here’s your playlist for the next four or five days. I think that’s helped me manage the kids. It’s helped the kids manage their time, it’s helped the kids manage their assignments and it’s given them the confidence to take ownership of the learning.

Jon Orr: I think there’s a lot to be said for the instruction of a quality teacher, and sometimes there’s like, there’s lots of phrases that sometimes when we think kids are going to be able to direct where they want to go, and I think it’s you hit the nail on the head that most kids are going to freak out about that being like, what do you mean? There’s that phrase, you don’t know what you don’t know, sometimes it’s like, how are kids expected to be like, I’m going to teach myself the curriculum, or I’m going to all of a sudden try To explorer and then where do I go?

Jon Orr: Then the teacher is going to pull the math from that, which is a great idea for sure. Then that’s what Kyle and I, and lots of people who have made those 3 ACT math tasks have talked about that we can present these situations where we show real world scenarios, or we show curious scenarios, and we get the kids to feel like they’re directing the learning.

Jon Orr: There’s a lot to be said for the teacher who’s actually directing where that learning goes because then we can pull the math from it. I think there’s a lot to be said, for that quality math instruction from a teacher. Sometimes I think, Sam, that when we say kids are going to teach themselves on a certain day, and here’s a list of topics that we have to accomplish. It’s almost like in that zone of like, okay, here’s the list of topics, and here’s YouTube and Khan Academy and go learn.

Jon Orr: I’ve seen that model of math class, and it scares me and I’ve been in classes where they said that, like, oh, we’re all moving at our own pace, which is great but I feel like we’re there to inspire those kids to love Math. Sometimes if we just kind of let it go, they’re not sure where to love math or what math to love and how to appreciate it and see the power of equivalent expressions. I think there’s a lot to be said for those really nicely crafted lessons that you’ve been doing.

Jon Orr: I think you’re completely correct to say, we can do some of this and some of that, and it’s a great balance, because you want to be in that position to spark that curiosity for your kids so that they love it and want to explore, because it’s like all about lifelong learning. We’re teaching them skills to learn what they can, but I think the difference there is, we’re telling them what to learn, instead of sparking curiosity, so that they want to learn. I really love that you’ve got that balance, or you’ve realized that that balance has to happen. So I think that’s super important.

Kyle Pearce: I was just going to pop in there and mention to like, I’m visualizing because Sam, you’re saying certain days of the week kind of look certain ways and I’m visualizing in mind as well, picturing the idea, the menu, you were saying if you didn’t feel it was super productive when you were giving, let’s say the list to students at the beginning of the week. I wonder if even taking that same idea, and trying to do it and almost slowly releasing that.

Kyle Pearce: It’s kind of like similar to our curiosity path where we withhold information. It’s kind of similar in that regard, where early in the school year, John and I were setting up our course. A lot of times, we would do a few lessons and it was like the topics for students to work on wasn’t very broad initially, because it was the beginning of the year, but as the year went on, then it was like those doors opened the gates swing wider for students to have more opportunity for choice and to decide where they need to go next And at what pace they’re going to do it.

Kyle Pearce: So it’s kind of like maybe a little bit of both there, trying to find that happy, medium, that balance. It makes me wonder, too of how to try to make those experiences, those, we’ll call them the curious experiences, those curiosity path sort of experiences, where you’re doing a problem based lessons and these more personalized lessons where students are working, and you’re walking around the room and trying to conference with students as you’re going.

Kyle Pearce: How can you bring those two scenarios and link them so that they feel connected instead of disjointed? When you’re thinking about that, what John’s just mentioned, and this idea of trying to smooth out that ride a little bit and make it feel like, instead of it being like, today’s this type of day, and tomorrow’s that type of day, it’s sort of like it’s, this is the week, and as we progress through some of the learning, it’s like you’re shifting through these different modes instead of it being like, today’s this and tomorrow’s something completely different. What are your thoughts on that?

Sam Brotherton: Yeah, a lot of thoughts. I want to go back to one thing John said about the Khan Academy thing, putting kids on the computer and all that, because I think that does tend to happen when you start to get into this idea of personalized learning and individualized learning. It’s that sometimes it gets defined as how fast can kids move through stuff and it’s like, I have a sixth grader who’s doing calculus.

Sam Brotherton: So this is personalized learning, but then those light bulb moments that you were talking about, of making the connections in class, those kind of fall off. So I think personalized learning is more of an idea than necessarily something you could see or touch and thinking about how you can take that idea and help your instruction. Kyle, you were saying, how do you make class go smooth, so you’re not just I guess, going from different format to different format for the kids, which can be hard for them to follow. Is that kind of what you’re saying?

Kyle Pearce: Yeah, and I guess too, also for you, as the educator, I think it’s really hard on us when we’re doing one thing this day and something different the next day. I guess what I’m envisioning is, we always come back to this idea of planning with intentionality that the work that students are going to do in this more of this, we’ll call it personalized setting, is linked to that problem based learning lesson so that it’s kind of like built off of it.

Kyle Pearce: It’s like that part John’s talking about, about inspiring students and helping them to see the beauty and essentially helping them bump into really interesting scenarios, because that’s the other thing that we often miss when we go into a more independent sort of student driven experiences. What if they don’t bump into the math and see, and really sort of catch on to some of those strategies that you’re hoping they’ll arrive at, unless we really intentionally craft those experiences.

Kyle Pearce: Then there’s always time for them to build on those skills and that would be that purposeful practice where I see some of this personalized approach fitting in really nicely, but then it’s kind of like it goes together. It’s almost like you’re picturing it as a block of multiple days that are connected. So it’s not like we’ll do this sometimes and do that sometimes. It’s like this is the process we go through.

Kyle Pearce: We’ll call it almost iterating through a cycle of this is how we learn, like we were inspired by this new idea. Then from that idea, sparks all these other associated related ideas and topics. Then there’s still choice as well for students to explore in different areas.

Sam Brotherton: Yeah, it’s kind of funny as I’ve taken the five practices for orchestrating discussion and applied that to my whole planning process. So take last year for example, for doing a 3 ACT task, you were going to take the five practices and think about what are the mistakes they’re going to make? How am I going to monitor this, which pieces of work am I going to select and then how am I going to connect all that? Well, I’m kind of taking that same idea but thinking about it in almost an entire unit.

Sam Brotherton: So if we’re learning about, I keep going back to ratios. Let’s change it up and say we’re learning about solving equations. Well-

Kyle Pearce: Hey ratios are so messed for kids, right? So let’s keep talking about ratios.

Sam Brotherton: I feel like that’s sixth grade. If you got ratios, you’re going to be great. I anticipate, and almost going back to when you read Peg Smith’s work like step zero, what can I select to get kids interested in ratios right off the bat? That’s where I think the 3 ACT tasks or any other interesting lab or lesson that you’re doing in your class is something where you can have a launching point, but then anticipating where the math mistakes that kids are going to make and where kids going to resort to, if I give them a chance to show mastery in a way that they want to.

Sam Brotherton: What I mean by that is, if you have one student coming up with an idea, all of a sudden you have 10 students that have that idea, too. So how do I anticipate that to make sure that kids are having those light bulb moments, those moments that matter when they’re the ones kind of driving the learning. That’s kind of hard to do, but I think teaching kids how to brainstorm, and how to get feedback from their peers and how to ask for feedback from adults, and also kind of coaching the kids through, how do you give each other meaningful feedback go beyond just saying, oh, that’s cool, that’s good and talking about, hey, what if you did this?

Sam Brotherton: What if you connect it to that, so I think that helps too. Then just monitoring where kids are at, and what progress they’ve made on certain points, and then selecting certain students to highlight their work, to display that for the rest of the class. I think, as far as planning all this out, there’s still just the straight up, this is the sixth grade math that we’re learning and I’m still planning out how to teach the direct instruction and how to go through the practice and how to teach kids to connect a double number line to a ratio table, and then how to take that a step further and calculate unit rate.

Sam Brotherton: That planning and also happens and all that progressions still happens, but then it’s also planning out with that, how do you make sure that you’re monitoring everything else that’s happening in your class?

Jon Orr: I think it’s a really interesting way to think about planning for big ideas and units. I think that’s a great way to frame out for all those benefits you just mentioned, by taking the five practices and not thinking about as at a micro level, like a lesson level, but think of it as a macro level, like a bigger, multiple lessons where you’re building in huge ideas like peer assessment, self assessment, confidence. I really like how you’ve used those same five terms and you built on these ideas for kids for deeper learning than just the math content, but also big skills that they would take with them to other grades. So I think that’s really great of you to see that connection between the five practices lesson wise.

Sam Brotherton: I think that connection piece at the end is the most important part now for me. Thinking back to when I would normally plan a lesson, I don’t know if you can say like any particular step is the most important. I know we always say step zero, pick an exciting task but I would say probably the selecting process was my most important. So knowing sequencing, knowing how I was going to select and sequence things was the most important, but for me now, it’s the connection piece.

Sam Brotherton: How do I make sure that the students are making a connection with whatever skill or topic we’re talking about, so that they remember it? That’s what I want. I want them next year, or next month or in 10 years to remember, hey, I made a cooking show when I was learning about unit rates and percents. Maybe I don’t remember the exact math to it, but I know there’s a connection with math and cooking. I know that’s something that I’ll remember and think about.

Kyle Pearce: Well, to me, it sounds like you’ve got a lot of good connections going on here and it’s probably maybe buzzing around in your mind a little bit like still a few things that you’ll have to grab and reflect on after, but what I’m hearing is that the process, like the problem based lesson process is a really important part. I think that’s one thing that in my experience, visiting a lot of classrooms that are focusing on personalization in math class is that what I find is that those lessons, we tend to go too far, too away from our problem based lessons, and now it’s kids working at their own pace.

Kyle Pearce: Then at that point, I worry about the last discourse opportunities, I worry about my ability to create an intentional experience and for, you had said that consolidation and making connections, like the connections piece at the end. So to me, it sounds like you’ve got all the elements right there waiting for you and I know you’ve been using the Curiosity task tool inside the Academy here and there.

Kyle Pearce: I know that you’ve mentioned to us that that’s been helping you with you’re anticipating and planning out that process, those five practices. So I think if you look in there now, there’s actually more and more of these problem based units that we’re releasing. I just mentioned this to you in an email earlier in the week where now what we’re trying to do is actually taking this idea of, instead of it being a one hit wonder sort of 3 ACT math tasks style lesson, it’s that task that first day actually launches like four, five, six days, where we build in math talks, where we build in purposeful practice.

Kyle Pearce: Those days that are kind of organized in a way that builds off of the connections that we’ve made in the consolidation from the previous day, really, I think will give you an opportunity to dive deeper into this personalized learning piece, because for John and I the personalized piece is really all about helping us with assessment, helping students to be able to continue getting better.

Kyle Pearce: We didn’t talk about it today, but for those who are listening, this idea that to personalize learning, one of the biggest things we can do is that standards based grading that you had already mentioned that you’re using, and the ability for students to be able to come to me at any point in the school year to show me what they know and that they can up, we always call it leveling up or whatever you want to call it, where we’ve personalized the assessment process.

Kyle Pearce: So to me, it’s like that personalization is really heavy towards the assessment piece where students can move at their own pace, and at the speed of learning, as Graham Fletcher would like to say. Really, we still want to keep those problem based Lessons at the core of what we do. So that to me is kind of the engine that keeps things moving. So we’re getting close to the end here. I’m wondering if we flip it back to you one last time to maybe reflect with us live on the air here, what’s something that you’ve taken away from this conversation that you’ll walk away and sort of chew on a little bit as we continue on along this journey we call math learning?

Sam Brotherton: I’ll give you a couple. One, I think knowing where to find your resources and how to use those resources, like your guys’ platform is super helpful for me when I’m looking at like that hot chocolate, I think you guys have like the whole week planned out for that lesson, and that’s ratios, right? My favorite. I think a lot of what I’m trying to compile together, like taking Open Up Resources and taking different 3 ACT tasks and trying to mash all that together, you guys have nicely weighed out there.

Sam Brotherton: So knowing where to find your resources, if you’re going to try to push yourself outside of your comfort zone, I would almost say that’s your step zero as a teacher. The other thing I think you guys said, one of the fears with personalized learning is losing out on the rich discourse. I think that’s absolutely a valid concern. I think one approach that I’m having is maybe not having as much math discourse with the kids, but having discourse like I talked about with giving feedback and discourse about more character skills.

Sam Brotherton: So what’s your self awareness when it comes to this lesson? How are you approaching this lesson with a growth mindset? How are you thinking about how you’re being a global citizen, when you’re coming up with this new invention that you want to invent? Is there going to be some adverse effects? So I think there is definitely a trade off, because you only have so much time in your classroom.

Sam Brotherton: So if you’re thinking about doing something where you’re saying I want to personalize, I want to give more opportunities for kids to identify problems and kids to create, that is sometimes less time for talking about what did you do on your ratio table and what you do on your double number line, and which is better, the ratio table or the double number line?

Sam Brotherton: So I think you just have to be intentional about what you’re trying to accomplish for your classroom and your kids before you just say I’m going to jump into this because then you’re going to end up with probably those negative definitions of personalized learning where you have kids sitting on a computer, working through continuums as fast as they can, and kids are not getting chances to go back and show their mastery on different topics. So yeah, I’d say that’s kind of what I’m thinking after our conversation.

Jon Orr: Awesome. Sam, as always, you’re such a reflective teacher, a teacher who puts it all out there, it’s pretty brave of you to come on here to talk about things that you’re working through. So we got to put our hats off to you. So that’s pretty awesome of you and I think you’ve got some great takeaways there. Thinking about, especially that whole, when we start those lessons, like what do we value in education? What do we value in our students? How can I get that out of them?

Jon Orr: So awesome job here, Sam in this episode, and we definitely want to thank you for joining us here. Next year, we’d love to bring you back on see how things are going, like keep this going. To see this progression would be awesome for us to keep these talks open and going and if you’re okay with that, we’d love to have you back next year to do the same old thing here.

Sam Brotherton: Yeah, hopefully we’re not doing the same old thing next year. Right?

Jon Orr: Right. True.

Kyle Pearce: If you keep progressing like you have, you know what, you’re definitely reflective. We appreciate you and I know your students appreciate you and the math moment maker community I’m sure appreciates these conversations. So thanks for taking the time and we really look forward to continuing to follow along in the journey with you.

Sam Brotherton: Yeah, thank you guys for all the hard work you guys are doing for math in general. We all appreciate it as teachers.

Jon Orr: Well, there you have it. Sam Brotherton from St. Louis. Thanks, Sam, for joining us on another, Where Are They Now episode? We know that you’re working wonders for your students and we’re proud to have you in the math moment maker community.

Kyle Pearce: This was another math mentoring moment episode with many more to come where we’ll chat with folks like you from the math moment maker community who are working through common challenges and struggles, and together we’ll brainstorm ideas and next steps to help overcome them.

Jon Orr: If you want to join us on a podcast for an upcoming math mentoring moment episode, where you too can share the big math class struggle you can apply over at makemathmoments.com/mentor. That’s makemathmoments.com/mentor.

Kyle Pearce: Have you registered for the Make Math Moments Academy yet? Remember, we currently have a 30 day free teacher license available for any math moment maker from around the world to access our academy professional development courses, including our latest course on how to make math moments from a distance. Join in or watch the replays of our monthly Q&A web calls. Watch over 20 virtual summit session replays and access our make math moments problem based tasks and full units of study with teacher guides.

Jon Orr: It’s all in the Make Math Moments Academy. Get on it before it goes away at makemathmoments.com/Academy

Kyle Pearce: That’s makemathmoments.com/Academy.

Jon Orr: In order to ensure you don’t miss out on new episodes as they come out each Monday morning, be sure to subscribe on Apple podcasts or your favorite podcast platform.

Kyle Pearce: Also, if you’re liking what you’re hearing, please share the podcast with a colleague and help us reach an even wider audience by leaving us a review on Apple podcasts and tweet us your biggest takeaway, by tagging @makemathmoments on Twitter, on Instagram @makemathmoments and find us on Facebook.

Jon Orr: Show notes and links to resources from this episode can be found at makemathmoments.com/Episode 81. Again, that’s makemathmoments.com/Episode 81.

Kyle Pearce: Well, you know what that means. Until next time, I’m Kyle Pierce.

Jon Orr: And I’m John Orr.

Kyle Pearce: High fives for us.

Jon Orr: And a high five for you.

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