Episode #144: When is drill and kill appropriate in my math class? – A Math Mentoring Moment
We’re speaking with David Alewine in this Math Mentoring Moment Episode. David is home-schooling his twin 6 year olds and doing a fantastic job at weaving different curriculums and resources together to reach his kids and help them with what they need most.
David shares his story of how he chose to home-school, the benefits and drawbacks that he faces, and he’s seeking advice from Jon and Kyle about how and when to include “Drill and Kill” lessons!
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.
- When is drill and kill appropriate in my math class?
- How do I structure my math blocks when home-school teaching.
- How can I help my children learn math and still love math!
David Alewine: The great thing about having time was I said, okay, we're going to start all over again. We're going to go back to the beginning. I'm going to find a new curriculum. I'm going to find something else because I don't want to just go back to the beginning of this one and redo it. But what you need to happen is we just need to go back to the beginning and we just need to do it again. We just need to do it again. And that's okay. And so I found a new curriculum and we just started over, and that kid is thriving now.
Kyle Pearce: We're speaking with David Alewine in this Math Mentoring Moment episode. David is homeschooling his twin six-year-olds and doing a fantastic job at weaving different curriculums and resources together to reach his kids, and help them with what they need most. David shares his story of how he chose to homeschool, the benefits, and the drawbacks that he faces. And he's seeking a little bit of support from us in the Math Moment Maker community on how and when to include drill and kill type lessons. Should we be doing them? Should we not be doing them? Should we have something in between? What is that in between? We're really excited to dive in here.
Jon Orr: This is another Math Mentoring Moment episode, where we talk with a member of the Math Moment Maker community person, just like you. And they're working through some struggles and together we overcome and brainstorm some possible next steps and strategies for them.
Kyle Pearce: Awesome stuff, Jon, what'd you say we hit this? Let's do this.
Jon Orr: All right.
Kyle Pearce: Welcome to the Making Math Moments That Matter podcast. I'm Kyle Pearce.
Jon Orr: And I'm Jon Orr. We are from makemathmoments.com and together-
Kyle Pearce: With you, the community of Math Moment Makers worldwide, who wants to build and deliver problem-based math lessons that spark curiosity and fuel sense-making and ignite those teacher moves. Jon, we get a treat today. We've got an active member of the Math Moment Maker community coming in. David Alewine is coming to hang out with us and talk all things homeschool. I got to say, I had no idea. I knew that this individual had a lot of math background through some of the things we see sharing on social media. But I did not realize that this is a homeschool parent who is working so hard to try to provide the best that he can for his children.
Jon Orr: And I think this is the first time we've had a homeschool parent on the show from all of our past Math Mentoring Moment guests. So pretty excited to share this interview with you. But also impressed with David's knowledge of curriculum and resources. So you'll want to watch for that here in this episode. So let's get it. Let's get to the episode with David. Here we go.
Kyle Pearce: Hey there, David, thanks for joining us here on the Making Math Moments That Matter podcast. How are things going over in your world? And actually really excited to chat with you tonight because actually you're going to be a Math Mentoring Moment episode with a little bit of a unique experience, which I'm sure we'll dive into a little bit. But how are things going on your end? How's your day going, your week going? Tell us on how things are going in your world.
David Alewine: Yeah. Things are going really well. I mean all the days now blend in together, don't they? So things are going well, but yeah, a normal week over here. I spent today going back and listening to a lot of your past episodes that really inspired me with Cathy Fosnot, and Dr. Nicki. So yeah, I just going back and listening to those and getting reinspired again. So that's been really nice.
Jon Orr: Awesome, awesome stuff. Yeah. Cathy Fosnot and Dr. Nicki some great episodes. We've actually gone back and listened to those just because they help us learn even more every time we listen to episodes. So David, let's take a little tour into your situation and what you're coming to us for a little bit, just because normally we talk with teachers in this segment, but you've got a little bit of a unique story. So why don't you fill us in a little bit about that and tell us that unique teaching backstory that you've got?
David Alewine: Well, it's not necessarily a teaching backstory. I actually was a professional dancer for 17 years. So that's what I did for my professional career from the time I graduated high school until I was about 35, gives my age there. And then my husband and I decided to have kids. So I decided to be a stay-at-home parent and doing the at stay-at-home parent thing. Having kids always thought, yep, kids are going to go to school. I actually had a friend who was like, "I'm going to homeschool my kids." I thought you are insane. What are you even talking about?
And sure enough, here I am decided to homeschool, we're going to do like a half day kindergarten with my kids. Sorry, I have six-year-old twins, boy, girl twins. And so it was going to do a half day kindergarten with the kids and send them to a Waldorf school for half days and COVID hit. And thought, you know what? I'm already teaching.
Kyle Pearce: Here we are.
David Alewine: Yeah, here we are. So already teaching preschool to them. I had already started that last December and thought, you know what? We're doing fine. Let's just keep going, here we are. So I just continued along with that and completely fell in love with it, with teaching my kids. And it's just been amazing. And it just sparked something in me that I had no idea was even there.
Kyle Pearce: I love it. And you mentioned this in the email and you said it again here tonight about this idea of I don't really have a teaching backstory and in reality, I mean, you're doing I think some of the hardest teaching that there is. Jon, his girls are a little bit older than my children. My kids were home for the last spring COVID and then we just had our stay-at-home orders lifted recently. So kids are back in school. But that is some really hard work. So the fact that you are doing that, you're loving it, that's something that's really awesome.
And it's also, I think, a unique experience that, well, I guess it's less unique now because of COVID. So some people have some experience with it, but the fact that you're carrying it through, I think, is really awesome to hear. And we do want to dive in more. I know you mentioned Cathy and Dr. Nicki, and you had shared some resources with us in an email. So hopefully we'll get back to that shortly. But before we go any further, though, we ask every person who comes on to this podcast-
Jon Orr: Yes, that come in.
Kyle Pearce: ... about a math moment they remember from their own learning. Yes. And we will love hearing.
Jon Orr: inaudible now.
Kyle Pearce: Yes. We love hearing it. So go ahead. Don't make us wait any longer. What's the math moment that pops into your mind when we bring up math class?
David Alewine: Okay, okay. I've been waiting for this because this is you guys. This is your signature. So I have two. One of them is, I think, super common. It's those times tests. It's that I was in second grade and we did those times tables and they were timed. You needed to do it at one minute for each timetable. One times one, one times two, one times three, you got to get through all of those in one minute, and then you would get literally a gold star. And it was the first thing that was on the filing cabinets when you walk into the room, it was on the left.
I don't remember my teacher's name, but I remember looking at that chart every day, when you walked in, it was on the first thing on the left and the door, and it had everyone's name, and it had the numbers of the charts up above, and a gold star. And I had no gold stars. And I was the worst one in the class. And I know it sounds dramatic, but I swear it stuck with me for, I mean, obviously till now.
Kyle Pearce: Well, it has.
David Alewine: It's a vivid memory I have. And I always just from that moment on, I knew I wasn't good at math because I couldn't memorize. You guys have said, you guys talked about that a lot yourselves back then for what math was, was memorization essentially. And I did not know how to memorize. So, yeah. So that's a downer one.
And then the good one I have actually happened just a few months ago with my own kids. And I was brushing my daughter's teeth and she was asking me, "What's six plus six?" And I said, "Well, what do you think?" And she goes, "One 10, two." And I was like, "Yep, yep, that's right." And then she said, "Okay, what's seven plus seven?" And I said, "Well, I don't know, what do you think?" I could hear her little voice and she's standing there. And she said, "Okay, well it's 10 and then there's four left over, one 10, four.
And I was like, "Cora, you did it. Yes. How did you do that?" And then she explained it to me, you have a 10 and then you have four leftover. And I could see the rekenrek in her mind. I could see it. And I knew right then she had it. And she started reken through just over and over and over. And I was like, "And she has it. There it is." She has a strategy.
Kyle Pearce: I love it.
Jon Orr: Mm-hmm (affirmative). Nice. That's definitely a big win to hear something like that. I can hear it in your voice that your pride and the joy that the two of you experienced through that. And if I go back to your other memorable moment there for a moment, and on that say negative moment that you had in something that we like to ask as a follow-up sometimes chew the memorable moments is how you felt or how you think that moment that it clearly has stuck with you? Because clearly it's carried forward. We wonder how do you think that that moment back then influences you now as a teacher of your own kids?
Most people who listen to our show are teachers in the classroom or coaches and we ask them that same question. How does that influence their classroom teaching practice? However, you're teaching your students, I wonder how you think that moment is now influenced your teaching style?
David Alewine: Yeah. I think it has really made me want to just allow them to be where they are at, and to not let them just be where they're at, and not trying to push them farther, just because something somewhere says that they need to be doing this thing at this point. They're not doing times tables yet, but if you can't do that, if you can't subitize the five, well, then let's stop and let's figure out how to do that. I'm not going to try to make you do five plus five if you don't even understand what five is yet. I don't want you to feel like you don't understand what's going on. My big thing is just, I want them to be where they're at and be okay with that.
Kyle Pearce: Yeah. I think it's a great answer. Well, first of all, through your email and some of the things you had shared in the email, I had a sense of what this conversation would look and sound like and it's playing out as I anticipated. You just said subitize, you were talking about the rekenrek. Some of these words, there are teachers listening to this podcast, I'm going to say probably more teachers listening to this podcast may be familiar because they tend to be a little keen. They're pretty eager for professional learning.
However, there are many teachers out there who have not heard of subitizing is, or rekenreks are, or some of these researchers and resource creators that you've already mentioned. You mentioned Cathy Fosnot, Dr. Nicki. And I'm hearing obviously some quick wins here. We're hearing how some of your experiences are shaping how you're delivering this math learning, approaching it. It's interesting because a lot of times when you ask someone about their math moment, they might say something and I'm talking about an adult in general, not necessarily from this podcast. But sometimes people would say things like I'm no good at math, but then they'll advocate to learn it in the exact same way that they learned it, even though it didn't work for them.
And what I'm hearing from you is you went the other way and you were like, "Well, wait a second. This didn't work for me." And you clearly remember how you felt in that moment, that experience. And you've done something about it. I've already heard a couple of quick wins here, but I want to give you an opportunity to share. I say quick win, but I'm going to say I'll open it up to any win you want here, because I'm seeing you've done your research, is what I'm going to say. You've got a lot going for you here. And I don't believe you have a teacher certificate or qualification. So you've done your homework here. And I'm wondering what would you say a quick win would be for you as a relatively new homeschool parent?
Because, I don't know, I guess I'm impressed with how far you've come given the fact that you didn't have a couple of years of schooling or to help prepare you for this, or maybe you didn't. We just didn't hear about it yet.
David Alewine: Yeah. Well, I know. I don't have any school. I didn't go to college even. So nope, no school. Very intimidated to come on the podcast. I will say, by the way, the people you have on here are just the most inspiring. The teachers are the most inspiring. It's just incredible. So I will say that Cathy Fosnot I have nothing in common with her and a lot in common with her I feel like. I've actually emailed her. She is insane. She just gave me her email and just emails back and forth with me. And she is unbelievable.
And her passion for it when she was talking on your episode about staying awake at night and just wanting to learn how to teach the kids, that was me. That is me. Not every night, but many, many, many nights, one o'clock in the morning, I'm just, "How do I teach this doubles? Okay. What is the best way to teach them doubles? I know that's our next trajectory so what's the best way to do that?" And then thinking about how their brain has been working during the last few lessons and what we've been building up to, and then saying, "Okay, is doubles best on this, the tens, 10 frames, or would it be best on a math rack? When I do it? What's best. What do I see?"
And so just really going in and yeah, just how she always wants to learn how right along with the kids. I think she was talking about that something in your episode with her and how she wants to learn. She's learning as the teacher just as the children are learning. That is 100% how I feel. I feel like I am learning math all over again. And I'm excited about it as you can tell, probably. It's just every single lesson we do, I learn that first. I do that lesson first, I learn it, I think about it. And then I go in to teach them. And it's very different with them because they're six years old. I have five minutes. You have about a five-minute window where you can really get that-
Kyle Pearce: Even you've already lost two of them.
David Alewine: Exactly, exactly. That goes to where I felt you were asking about I don't have a teaching education. I don't have a teaching background. How am I interested in it? And I think trying to answer that question for you, I'm interested in it because I can see them learning and it is mind blowing to me how they can take in this information and just learn it and understand it. And then they just move on even faster than I do.
So to go to a win, I would say it's been a lot of learning like I've just talked about. But things that I have had successes with are how I structure our learning. So I do it in, what I consider our book learning, two 20-minute sessions a day because with six years old 20 minutes, I mean, you're burning oil at that point. So within that 20 minutes, I set up probably about three to four different little work areas. And we will do maybe five minutes in each little area. One be like a floor desk I have with some chairs. And then we'll move over to sitting on the floor with some whiteboards and doing another activity over there. And then we'll get up and we'll move over to a regular desk, and we'll do maybe a little bit of a worksheet over there.
And in between that we'll do some physical stuff. So in between each one, all right, stand up, run into your playroom, grab your favorite toy. How long do you think it's going to take you to get there? Can you tell me how many seconds you think you can do that in? Okay. 15 seconds. Okay. I'm going to set the timer and go and run in. They grab it and they come back. They need that to really get them their brains back in it.
So the way I set up the day with them basically, and I do those two of those a day. So I do 20 minutes in the morning and a 20 minutes later in the afternoon, different subjects. And that's been a big win for me, learning how to capture their attention span and really focus in on what I want them to learn.
Kyle Pearce: Yeah. That sounds like a huge win for you. And I think to go back to when you said that Cathy was learning with the students and you're learning with the students, and I feel like all of us teachers who had our eyes awoken to what information we can learn from our students. I know the math. When I'm teaching my high school students, I got the math covered. But what I'm learning every single day along with my students is how they're thinking, and how they're approaching the math, and where they are on a progression.
And that part is so exciting. Just like you're excited to work with your kids because you're seeing that same progressions, you're seeing how they're going to grasping what you've put in front of them, and how that learning unfolds it's so rewarding, but also curious. I'm very curious to see what my kids are going to do or how they will respond to a particular lesson, and what I can learn from them so that I can help them. I think that is a big win. I think that we're all learning in that way, which is totally different than say the way I thought math teaching was for a really long time.
I'm really glad you shared some of what your day looks like in terms of math, because I think that's also so eye opening to say us teachers, who've never really taught our own kids other than during the pandemic times. crosstalk. Yeah, that was still like, "Hey, your teacher's online, go over there and sit in front of the computer because I'm going to go teach my students in front of the computer because what you're doing is not math." So I'm really glad you share that.
And it just occurred to me, one of the biggest hurdles teachers will say, when they're teaching their students is time. You'll say teachers, we're like, "We got to cover this. We got to make sure that we get this ironed out before June," because then they're going to go off to a different teacher. And I just can't help, but think how that constraint that most teachers feel, because the course will end. They will go to a different teacher. You don't have that. You're going to see those kids every single day. And then you're going to see them next year. And then the year after that.
So if they don't master timetabling right now, you're like, "Hey, we're going to get there." It's almost that freedom that says like, "We're going to go where you need to go. And then I know that we will get there down the road, but it doesn't have to be by April 23rd, or it doesn't have to be by because I have to get a test result in." I feel like you've got this nice freedom and I know that's probably put some struggles on you because you don't have a pacing guide and you figure all this out. And that might lead into what you want to chat about with us here tonight about what struggles you're having and where you want to lead this conversation. But I just wanted to comment on that.
How are you finding that time aspect? Did you kind of clue into that? You're going to have all this time to work through, or is time still an aspect for you that you're still thinking about?
Jon Orr: Yeah. Or is it like stressful knowing that you're the ultimate decision maker here? Because there could be maybe that pressure you're like, "Well, it is my own kids." There might be that pressure and it's not my principal breathing down my neck, but it's my own want for my students too. I don't want to "mess" them up. Everybody always worries about that in your classroom. You're like, "I don't want to damage these children." And of course you probably feel a little bit of that, but I am curious about that. What's going on in your mind? Clearly you're loving this role, you're enjoying it, but is that time a factor for you? Or there other struggles that maybe we're not seeing here that you can share with us?
David Alewine: Yeah, yeah. I think that time it's a blessing and a curse like anything. I think at some point our kids will go to school. That's the plan at some point. When that is, we're not 100% sure, but so there's always that in my back of my mind. For sure. So there's always that in the back of your head of like, "Well, if they're in kindergarten, then they should be doing what kindergarteners are doing." Just trying to keep up. And then because I don't have, like you said, a principal breathing down my neck, first there's this example where when I first started, it was about a year ago, I started with formal curriculum with the kids with math.
And we started with RightStart. I don't know if you know anything about RightStart, if ever heard of it. But it's a spiral homeschool curriculum. And amongst people who are, "Mathy people," it's considered like a very good program, and it's heavy spiral, very spiral. And I started off with Level A, which would be their kindergarten level and it was great, and then until it wasn't. And I realized that for one of my children, it was too spiral and it was trying to move on too quickly. It's trying and they just weren't getting, I could tell that their subitizing was not where we needed it to be and they weren't feeling confident on it. And this curriculum was trying to move forward and I could just see it.
And some of this comes back from, I will say, I was a teacher for dance when I was dancing and just picking up on slight cues, people's facial expressions, just how they check out when you ask them a question. And I could see that one of my kids was just they were into it. And then all of a sudden I could see, oh, they're struggling a little bit. The great thing about having time was I said, "Okay, we're going to start all over again. We're going to go back to the beginning. I'm going to find a new curriculum. I'm going to find something else because I don't want to just go back to the beginning of this one and redo it. But what you need to happen is we just need to go back to the beginning and we just need to do it again. We just need to do it again." And that's okay.
And so I found a new curriculum and we just started over and that kid is thriving now. It's amazing. That kid was the one who was just like, Ooh. And then now if we went back way, way, way ahead. I'll just say that.
Kyle Pearce: I love it. The part that's so difficult with teaching, whether it's math, any subject area when you're teaching and your experimental group is the control group at the same time, that's also difficult. So trying to art, pinpoint what it was that did it like, is it the fact that maybe they just needed that little extra bit of time? Is it maybe the curriculum? I'm wondering from your perspective. So you had mentioned maybe this first curriculum, which I think you said StartRight was maybe almost like the-
David Alewine: Yeah, RightStart.
Kyle Pearce: Sometimes this can happen in RightStart. Jon and I had this, I think it sounds a lot like what we did when we started spiraling ourselves in our classes where we just threw it in a blender and we were just trying to mix it all up and now we try to be a lot more intentional about it. And I wonder with this new curriculum, was there anything to the approach as well? Because I'm really curious to see how maybe Cathy's work has influenced some of how you're teaching.
Because I know for me after reading Cathy's work, after using some of her contexts for learning units and mini lessons, I know that you're familiar with mini lessons, it really made me look at mathematics differently, especially when it came to just number sense and operations. I looked at it completely differently with how important strategies and models were. I'm just wondering did this new curriculum change the approach and how it was being taught, or was it just that it stuck to a concept a little bit longer? What's your thinking on that?
David Alewine: So the new program that I started it's called the Good and the Beautiful, and it is a religious based program actually, which a lot of homeschooling stuff is, but it doesn't really have a lot of religious stuff going on it. We're a secular homeschool. But the way they approach the math is more mastery based, but still spirals. And it was just like you were saying, it did have a slower approach yet they continue to go push forward with something that might be just a little bit out of their knowledge base.
But then circles back around to it later and that nice spiral. But it was definitely hinting more towards mastery base and just moving through things slower. RightStart is very quite literally black and white. It's the texts, everything is black and white. There is no color anywhere in it. And the Good and the Beautiful really incorporates tons of color and art, classical art, contemporary art. They incorporates lots of stories, and different cultures, and talking about right now we're doing on Chinese culture.
And so they just do everything talking about children in these cultures and it tells stories about them. So it's nice because it opens up deeper conversations, maybe not about math at all, but just about other things in general. But at the same time, to answer your question, it just spends a little more time and things and the stuff with Cathy Fosnot, all of the things I've been pulling in.
So the thing about the Good and Beautiful is it's a really good trajectory. That's what it does well. If you go to Doug Clement's work and Julie ... What's her last name? Sorry.
Kyle Pearce: Sarama.
David Alewine: Sarama. Yeah, yeah. So if you go to their amazing website, the learningtrajectories.org and you look at it, the Good and the Beautiful, it does an amazing job of just following that along basically. It just takes you step by step. Maybe not everything within there is the best way to do it. And so then that's where I have gone and found Cathy Fosnot work. I have found, I wrote it down in the thing I sent you guys I can't remember her name, Christina-
Jon Orr: Tondevold.
Kyle Pearce: Oh, Tondevold.
David Alewine: Tondevold, yes. So her work incorporating that stuff and to really understand the best ways to teach all of these principles through the trajectories. And so you're trying to hit all those trajectories, but what's the best manipulative or what's the best, big idea to talk about, to get you to all of those things. And so I use the Good and the Beautiful as a roadmap, essentially.
It's my roadmap. I don't follow it verbatim, but I do use it as my roadmap. And then it does have amazing spatial reasoning activities in it with tangrams and it does Sudoku, it does all these different kinds of things. So it really does follow all these trajectories and it hits all the different points really well. And then I supplement with all these other things going into it.
Jon Orr: Yeah. That's great stuff. You gave lots of resources for our listeners to go check out because teachers are always looking for another great resource to add in. And I think that's also a benefit of what you can bring to your students too, is that sometimes we have to follow a certain curriculum that the school district will set out. And you got like, "You know what? I'm going to take a little bit of this, and I'm going to take a little bit of that, and I'm going to take a little bit of this, and I'm going to just mold it this way."
And it's like, you're a chef. You're taking all the best work and putting it into front of your kids. So that's awesome stuff. And we'll put all of the links that you've just shared in the show notes page for sure. I'm wondering David though, if we wanted to narrow down into a focus that you want to talk about here with us tonight so that you can go back tomorrow and work with your kids on something, what would you like to chew on with us tonight?
David Alewine: Yeah, so the thing I struggle with a little bit is not knowing when is drill and kill, is there a time and place for this because I'm not a teacher, I don't have this. And so I've been trying to find out like in these young years what we're really trying to do is the number sense. And we're doing that, but then at the same time, so they have that fluency and then do you drill and kill it all. I mean, I know you do not drill and kill, but is there a place for that? Yes, that's my question.
Kyle Pearce: And you had mentioned that as well. Yeah. Ahead of time. And I was really interested to chat about this because I think first off in education, in math education, sometimes terms like one person's interpretation of something looks this way and then somebody else's interpretation looks some other way. And I think at least my perspective with drill and kill is usually repetition without maybe connections or explicitly thinking about something. So I picture probably your math minutes or whatever they were called that you remember from your past. Going and doing the timed one minute test and you go, go, go, go, go.
And when you really think of the part of the brain that's being triggered there, it's more of a reactionary thing. Where it's like, I have a phone number that's memorized. There's no connection there. I can't apply any reasoning with a phone number, but I can do that with multiplication. I can get there a different way, just like one of your children who when they were saying like what's six plus six and they reasoned through it.
So the benefit that I think people see from drill and kill, or at least in my interpretation, what they see and what you're after when you do drill and kill, is this ability for students to not have to think about the math so much, but we would argue and I'll argue that your good friend Cathy Fosnot would say that how we get there would be through more of that thinking and the reasoning. And what you did that example of six plus six and then seven plus seven, those opportunities, I think you want to do those as often as possible in order to get the repetitions in that you would get from drill and kill, but you're not killing anyone.
Imagine that you don't want anybody to be harmed in the process or have any negative memories. Now that said, we would argue that there's always an opportunity. I would say the younger the children are, the more they want to be older kids. Your kids probably love it when you go to the desk area and they sit in a regular desk and they have to write stuff on paper. That's such like a thrill for my kids. They love it. They feel like they're older. And so doing some of that work, I think, is completely fine. But I think at the end, and you're very intentional, I can tell from the conversation today and all of the work that you've done, it's like if the intent at the end is to give students this automaticity, not just rote memorization, but automaticity where eventually they can not have to think about it.
But if they ever do, if somebody asks them about it, they'll be able to unpack it. I think that's what we want to push towards. And you can do that in a variety of different ways. But the one thing that I think we try to advocate against is making it timed or making it maybe too competitive. Some kids thrive on that though. So, I mean, you get to be flexible based on the personality of your children. I just think you want to make sure that whatever it is that you're doing with them, that they don't misunderstand or misinterpret what mathematics really is. Jon and I both admit, like you said earlier, we thought math was just memorizing a bunch of stuff. That's how we got through.
And we were lucky enough to be able to do that. We had that, I'll just say we were lucky that my brain can see patterns in that way, but I didn't understand any of it. Jon, what are your thoughts on that? I know it's a sticky subject. And I don't think there's a clear, hard, fast rule about it, but it sounds like you're on the right track. Absolutely.
Jon Orr: Yeah. I think you're right there, Kyle, I guess there's definitely, you want your students to feel, like you said Kyle, automaticity towards the skills in the ideas that want to bring out or emerge. And that's different than memorization. I think you talked about this before about this memorizing for these gold stars. I think that's what a lot of us were doing back then versus understanding the mathematics so that it is automatic and not, I'm just memorizing, but I don't know why. That's the difference. It's like, we want to get to the deeper level of why we're doing things so that when things get tough, you could have strategies to work around this process.
So I guess we're going to throw it back on you, David. What do you want your kids to have? What relationship do you want your kids to have about mathematics? Do you want them to have that memorization where it's just that? Or do you want them to have that mathematics is more than just memorizing a set of procedures?
David Alewine: Yeah, yeah. Yeah. So with my kids, for instance, so we'll get down, we'll sit down and the worksheet has 10 problems on it and there are not like your children. They're like, "Yeah, no, this is not fine. Nope. Not interested." And so I'll say, "All right, totally cool. Why don't you pick two, pick two of those." And they can just do it. It's not a problem. Just bam, bam. And then I'll say, "Okay, so you did those two and you wrote the answers down. All right, I'm going to do two more with you," and we're just going to talk it out and boom, boom. It's not a problem.
And I'm like, "Okay, you have this. You have strategies for it." I guess my question is, at that point you just keep moving forward because they have all our doubles. They understand how to make go to 10 and make more, one less. They understand they have these strategies. It's almost like they are wanting to move on. They're like, "I don't want to do, why do I need to write that down? It's not interesting." And it's goes to what you were just saying.
Kyle Pearce: Yeah. Sorry to cut you off there, David. I was just envisioning like my son, Landon, he loves talking about numbers, but he doesn't love sitting down and writing it out. My daughter, however, she likes pretending that she's the teacher and she likes making the worksheet of 400 problems. And she wants to make Landon do it or make me do it or whatever.
So yeah, I think working with your children, of course, it's like, I would say forcing them to do something wouldn't be helpful in the long run. It wouldn't be productive I think. And then also too, I want to also keep in mind that your children are young, six, you said. Twins, six years old?
David Alewine: Right. Yeah. Mm-hmm (affirmative).
Kyle Pearce: So six years old, that's pretty young. So I mean, doing two on a piece of paper might be enough. And then maybe it sounds like you're number talking it out. Or if you go mini lessons style, like a Cathy Fosnot string of problems where something I always find that's interesting is you can get. I think anyway, if you have a string of problems that are related, like Cathy Fosnot mini lessons, what you can do is it's almost like they're strategically selected. For those who have used mini lessons you'll see they're strategically selected to have a low floor at the beginning and then they build on each other and it tries to emerge a specific model and a specific strategy.
David Alewine: Yeah. They give you the answer right up front.
Kyle Pearce: Yeah, it's like you have something to work with. And then it's almost I find it's easy to like the curiosity path where you suck them in a little bit. You do this one, then they're like, "Oh, well that was easy." And then you do this next one. The next thing you know, you're doing some pretty complex things. If it was multiplication, for example, you might start with three times four. And then all of a sudden, now it's six times four and they're using this doubling strategy. It's like, "Oh, well, if I double one of the factor," I mean, we're talking a little out of our shoes here for your kids.
But for those who are studying multiplication, they might be looking at a doubling and halving strategy. And when kids ... I find they're fascinated when they pick up on these strategies that actually work. My son, for example, was adding, he wanted to multiply, he's in grade one. He wanted to multiply. He heard his sister talking about it. And he said four times six. And he was, you could tell, just blank. And I was like, "Well, this is one six." I'm like, "So let's do four of them."
And we just of showed them and you could almost see him separate the five and the one. And he knows how to count by five. So just by doing this, he went 22. And I said, "Oh, well think about other." He goes for 24. And I'm whoa, why do you know that? And of course over time, I want them to know that six times four is 24. But right now in this moment, I want him to have these strategies that'll help him get to all these different places. So that confidence builds. And then over time, of course, we surely want them to have automaticity.
Eventually your children are going to know six plus six is 12, and they're going to stop thinking about five and one, five and one. They're going to stop using that strategy or the 10 and two, like you said, the one 10, two. Eventually that's just going to happen and it doesn't necessarily have to happen through sitting down and doing what I would call the not thinking drill and kill, if that makes sense. That just that repetition, that mindless repetition. So I like how Jon framed it. It's like, what do you want that relationship to be with math? And is there a way that you can achieve it in different ways? And I would argue that doing some problems on paper, you can still keep a productive disposition towards that experience depending on how you approach it with them. Right?
Jon Orr: It sounded like when you send your 20 minute blocks, you were already breaking the script a little bit. You were already changing gears and going we're going to do a little this, and then we're going to come over and do a little this. And I think that's a great approach. You could be doing a little bit of these questions and then all of a sudden we can change gears, go over here, and do some of these. And then, you know what? Maybe we're time to come back and do some of this. I think to mix up the way these skills are presented, but also practice can add to that automaticity.
You could do some on paper, but then maybe you're doing like what Kyle suggested all of a sudden that your next station is like, "Now we're going to have this little math talk with our whiteboards. We're going to draw pictures and we're going to represent the mathematics this way." And it's like all about connections. So it's like, if you can make connections to this visual model, to this paper model, that's how you're going to build the automaticity because that's what is going to give kids the strategies.
David Alewine: Yeah, yeah, yeah. That's great. That's great. So a question I had, in your experience with this young age, and I know you both have kids so I know you haven't taught this age, but you've been around the kids this age. How important is it the actual physical of writing down of information? Because what I have found is it slows my kids down because they're learning to write, correct? They're learning. That is a skill unto itself that they are still developing.
So I have noticed, and I don't know if this is from being a dancer or what, but as soon as they have to do that physical thing with the pencil in their hand, and they put it down on the paper, it all changes, everything changes. And they suddenly go into their head and they're no longer with me thinking about it. It's a complete shift. And I actually there was a time when I noticed early on when I was like, "Oh, we got to shift this too." One of my kids was we would do great mental math, just very early on doing stuff two plus two, five plus three. And then we got over to start writing it down.
And I noticed one of my kids started drawing dots on the paper as soon as we started drawing it down and counting the dots. And I'm like, "Whoa, okay." I mean, that's fine, but we just saw that problem over there and you didn't need dots. But now because we've made it physical, you're making it physical now.
Kyle Pearce: Yeah. That's interesting. And what immediately pops into my mind, again with that age group is right now, at that age, when you think like they're still developing language, I mean, we're all continuing to develop all of these skills, but just not as intensely now as we get older. But they're developing their language, their understanding of language, their ability to speak and articulate their thinking. They're thinking mathematically. So that's developing.
And now they're trying to even just to get that dexterity and to get that coordination, to take my thinking also at the same time as thinking, tell this limb to do something. So I want you to go here and I'm also trying to not make my the number nine as big as the entire page. Kids always write super big, or this number is huge, and this one's small, and crosstalk my nine is backward.
Yeah like all those inaudible going on. So I would say that is absolutely a developmental thing. And I wouldn't necessarily say to move away from it, but to also almost anticipate that that slowdown is going to happen. And I think what you're saying and what you told us, and it makes me be more hyper aware of it is that if I want them to be practicing their fine motor skills, if that's the intent of this activity, perfect.
And I'll say number one in 10, because there's always other intentionalities there as well. So you wanted to do a math problem, but also have them write it down. So it's, I think, trying to figure out your priority list. And I would argue that you'd want to have some of that because you do want them to develop that skill, but then maybe you're not assessing them as intently on the mathematics portion.
You might just be assessing them more on their writing, their ability to communicate their thinking. And yeah, I feel like I just had an epiphany based on what you shared there because we don't want to avoid it by any means, but at the same time, it's like, we also don't want to feel, or avoid it, or judge them on it, if that makes sense.
David Alewine: Yeah. It's like you were saying, it's two totally different skills.
Kyle Pearce: Absolutely. And we're trying to make them do it all at once. That's really difficult.
David Alewine: Right. And I think that was my question. And I'm sorry, I'm not great with words. I was a dancer. Give me some grace. My question was that was kind of it is, is it okay at this age? And I guess that's the thing too. It has to be okay at this age. For those to be two totally separate things, there's no other option because it is, that's what I'm seeing in front of me. I'm seeing their math brains are way ahead of their physical writing brains and bodies. And so I guess my thing of like drill and kill-
Kyle Pearce: That's like a good place be.
Jon Orr: That's crosstalk by the way.
Kyle Pearce: That's cool to think about too.
David Alewine: Yeah, yeah. And thinking I have these worksheets, but my kids, they are not interested in doing these worksheets. So we just need to draw seven, and eight, and nine, and five, because they understand that those represent that. But in two years, they will be more comfortable with writing and then we can work on math problems. But right now they're good with just the math problems in their head, this point. And so, I think, basically sometimes you need permission for someone to say, yeah, those are two different things and you can do those separately and move forward with your kids mentally.
Kyle Pearce: Yeah. I wonder, you do a math activity, you do it verbally, you may be modeled their thinking on a whiteboard, but then maybe part two of the task or the second portion, you can still go to another area to do it is now them restating their thinking. So it's like the thinking has happened mathematically and now you're almost journaling it. In our Make Math Moments units, we do consolidation prompts, which are often based on trying to figure out who heard what? What did you take away from this lesson?
Well, with young children, it might just be okay. So we talked about, hey, we did this thing called doubling like six plus six. Wow, those are doubles. You did six plus six, you did seven plus seven. You even did eight plus eight. I want you to go back to your seat and I want you to write those three down and I want you to fill in the blank, whatever it is that you're hoping that they will do, will they be able to write it down? And then also the answer, did you want them to model it?
But it doesn't have to maybe be new thinking. It could just be them getting an opportunity to reflect on their thinking and practice their communication of their thinking, which is something that's like an adaptive reasoning skill. So that's a really important skill. And maybe that would take away some of your concern or worry about there being too much happening at the same time. Now they can focus on this task, but also be reflecting at the same time and getting a little bit of that benefit as well.
David Alewine: Yeah, yeah. I like that. I liked that. Yeah.
Jon Orr: David, we've been pretty impressed with the amount of thinking that you're putting into your teaching. It's eye-opening, it's been inspiring, and we've actually learned a lot about, say the homeschooling aspect of things. And I just wanted to say that you're doing such a great job and I think that you will continue to do a great job with your kids. So I'm wondering as we wrap up here, what would you say right now is a big takeaway from the conversation we've had tonight?
David Alewine: I think the big takeaway I had was it's okay to separate out, like say, the physical writing from what mental math that the kids are doing. So for me, and maybe that's just because it's the freshest thing that we've talked about, but that's the biggest thing I've taken away. Is that with kids that are at this young age, I'm seeing it. I see it in front of me. I see. Yes. I know you are learning this as you're doing it. So you can't possibly learn math and learn writing and do it all on the paper at the exact same time. And it's okay. That's totally fine. We're going to work on writing over here and we're going to work on math in our heads over here. And one day they will catch up and we'll be fine.
Kyle Pearce: I love it. I love it. And yeah, I'm feeling energized from this conversation. I'm so happy that you reached out to hop on this call. I mean, initially you reached out for a different purpose and I said, "Hey, this would be a great conversation to have on the podcast." So thank you for being vulnerable and brave for coming on the show. I'm feeling great. I can tell Jon's feeling great.
So we want to put it back to you here before we wrap up, how are you feeling after the call? You came into the call, had some questions. How do you leave this call today feeling in terms of going back into the classroom, into the basement classroom with your children and getting those stations started again tomorrow?
David Alewine: Yeah. I'm feeling really good. I feel like coming into this, I was very nervous. I even emailed you guys and said, "Are you sure you want to have this conversation? I am not a teacher. And I don't have the experience of all the amazing people on your podcast. And I'm not sure I have anything to offer you for your time or anyone listening." But I will say, I feel I'm on the right path. And I feel like that. I feel I trust in myself maybe a little bit more than I did when I first came into this. So that's a great feeling.
Jon Orr: Awesome, awesome stuff. And I think we know that you're on the right path too. David, I'm wondering if it would be okay with you if we check in with you nine, 12 months down the road and see how things are going and seeing any progress you've made, any new setbacks that we could redo this conversation and catch up?
David Alewine: Sure. Yeah, that'd be great.
Kyle Pearce: Thanks for bringing up so many great names. And again, it just shows how much effort, how much time, and dedication you put in to doing this work for your children. I hope that one day down the road, assuming podcasts still exist when they're older, they can go back and listen to this episode and say, "Wow, my dad really worked hard in order to teach us at that prime young age of six years old." So good on you. And thanks again from the Math Moment Maker community.
David Alewine: Well, thanks so much. Thanks for having me and you guys just do amazing work and I always look forward to every time to podcast out. I'm like, "Oh, high school, let's talk about high school. Awesome. I'm going to learn something. I'll pull something out of it." Awesome. So I appreciate it.
Kyle Pearce: I love it.
Jon Orr: Thanks so much, David, have a good rest of your evening.
David Alewine: Thanks. You too.
Kyle Pearce: As always Jon and I learned so much through these conversations as we work as a team, as a Math Moment Maker team to try to get that pebble out of our shoe that we're currently working on. And with David there, we hope that he's walking away with some new ideas or new perspectives to think about and to stew over before we touch base with David again.
Jon Orr: Yeah. And if you have not yet reflected on this episode, do that. Great way to hold yourself accountable is share with someone, share with a partner, a colleague, or with the Math Moment Maker community. Hit us up on all social media with our handle @MakeMathMoments, or get on over to our free private Facebook group, Math Moment Makers K to 12.
Kyle Pearce: Awesome stuff. And friends, if you're interested in joining us in an upcoming Math Mentoring Moment episode, just keep in mind, just like David, you might not be a typical or traditional classroom teacher, but we all have different mass struggles out there. So if you're a homeschool parent, or if you're in a unique situation, don't let that hold you back from submitting an application over at makemathmoments.com/mentor.
We basically ask you just a handful of questions and the most important one is, what is that pebble in your shoe right now that you're working on? We know there's many in there, but what's the one that you're really thinking about and really reflecting on to try to put into practice. Head over to makemathmoments.com/mentor. And we might reach out to you to get you on so that we can all work through that challenge together.
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 your favorite podcast platform, Kyle, show notes. Tell them.
Kyle Pearce: Show notes, links to resources, complete transcripts can all be found from the web, or you can download them and take them with you over at makemathmoments.com/episode144. Note, also that all the links in those show notes, we tend to try to help. So for example, in this particular episode, we talked a lot about different curriculum resources. So we got links there. We also have links to our problem-based math units. So head on over to makemathmoments.com/episode144, 144. We'll get you there. All right, my friends until next time I'm Kyle Pearce.
Jon Orr: And I'm Jon Orr.
Kyle Pearce: High fives for us.
Jon Orr: And a high five for you.
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