Jon Orr: Hey, hey, there, Math Moment Makers. Do you find students give up too easily when working on math problems that are unfamiliar? Do you find yourself stuck pre-teaching concepts to students before they have a chance to truly engage in the problem-solving process just so they can get through the problem? Our constant pre-teaching of concepts is just one of the reasons students struggle with word problems and they throw their hands up in frustration. In this episode, you'll learn five reasons students struggle with word problems and what we can do to overcome this common math class challenge, including how we can engage our students by planning and delivering lessons that ditch the I do, we do, and you do model of instruction to teaching through rich tasks, to leverage student curiosity and promote resilience through problem-solving.

Kyle Pearce: All right, John, let's get into it.
Welcome to the Making Math Moments That Matter podcast. I'm Kyle Pearce.

Jon Orr: And I'm John Orr. We are from Make Math Moments and, together-

Kyle Pearce: With you, the community of Math Moment Makers worldwide who want to build and deliver math lessons that spark curiosity-

Jon Orr: Fuel sense-making-

Kyle Pearce: And ignite your teacher moves. John, I am super excited to dive into this episode where it's just you and me hanging out, and we're going to chat about this very common math teacher struggle. I don't care what grade you are teaching, whether you're working with our youngest learners or if you're working all the way in secondary math or high school mathematics. This is one of those struggles that I know both you and I have been on this journey. And we hear so many Math Moment Makers who are also struggling to get students thinking and reasoning in their math classrooms. So we're pretty geeked to get going here.

Jon Orr: Sure. Yeah. And word problems have been notorious, right Kyle, for giving teachers headaches and giving students headaches. And we've talked to so many teachers here on the podcast about memories of their math moments. And so many things come up over and over and over again. And sometimes kind of most of my students would argue that word problems, applications from my old teaching days where the tough thing to accomplish. And what we want to do here in this episode is talk about the five reasons that kids were kind of ditching those and then saying like, "Those are so hard to do." And then we're going to talk about some ways to fix that and how you can make that word problems a thing of the past as the thing that is tough for kids to learn.

Kyle Pearce: And John, you and I actually, we've carved out a date in our calendars. The date is Wednesday, May 5th, 2021. So if you're listening to this well into the future, the replay would be out by then. But if you're listening this now, In the now, when this is being released here in April, 2021, we've got a date for a webinar where we're going to take these ideas and these struggles. So if you're listening and you're kind of head-nodding going like, "Yeah, I see that," or maybe there's a struggle there that you want to help overcome, you can hang out with us. We're going to do a webinar where we're going to actually dive into these. So we'll reframe them. But then we'll actually dive even deeper to show some examples and how we can actually transform some of these resources that we use. Because as many of you heard us say before, we are not advocating that we just ditch the resources we have, right? There's so many resources out there and every resource does certain things well, and then there's other things that maybe it doesn't do too well.
So if you want to dive even deeper, definitely mark it in your calendar. Wednesday, May 5th. We're doing this at 7:00 PM Eastern Time in North America, which is 4:00 PM Pacific time in North America. So hopefully we're going to hit a lot of North America. If you're in other parts of the world as well, which we know there's many of you. We hear about it. Every time we do a webinar it's like, "It's in the middle of the night for me." We apologize for that, but there will be a replay as well. So make sure that you get yourself signed up at makemathmoments.com/webinar. That's our standard webinar signup page. Anytime there's a webinar coming up, that's the page you want to be hitting, makemathmoments.com/webinar. John, what do you say we dive in here and frame out what these challenges really are? And then maybe a few tips that people can take to kind of get started on this journey before we hit this webinar coming up?

Jon Orr: Definitely. I'm really excited for the webinar, because as you said, Kyle, we're going to dive into some practical examples of what we're doing in our classrooms, what teachers in the academy are doing in their classrooms to mitigate this belief that we have that word problems are the enemy. And I think that's one of the big things that we're going to talk about here. It'll come out in the five different reasons. It's kind of saying it's not the enemy. We can do this better. And so we want to talk about that. We're going to give you all those examples in the webinar. But let's go through five reasons kids are saying or teachers are saying it's tough to teach word problems. It's tough to teach this problem-solving aspect of our math classes. Not in any particular order here, folks, but the first reason that kids are saying or teachers are saying it's tough to teach word problems is that it's partly our fault. It's partly our fault.
And it was just partly my fault as a teacher that taught this way for so long is I was pre-teaching all the steps and the procedures and the algorithms. That was me. That's the first reason we're saying it's tough to teach word problems. It's definitely tough to teach word problems, Kyle, if we just are trying to teach math as a procedural thing. It's a get done subject. It's procedures, one after the other. "Here, follow this list of steps like a recipe and you're going to have this wonderful math come out the other end." It's not that easy, right, Kyle?

Kyle Pearce: Yeah, absolutely. And I think too, one of the big things that sort of popped into my mind as you were saying that is I think it's our perspective in general. Like you had said, it's like when we try to teach word problems. And that's kind of a psychological shift that we have to make in our mindset. It's not about teaching word problems. It's about actually teaching mathematics, right? And word problems are a part of that journey. So it's not like we're planning out and working towards word problems, but rather helping students truly understand the mathematics. And I know for myself, and John, I always say you and I, we've been on such a similar journey, and lucky for us that we were kind of in a similar place in this journey as we went along. And that's where we sort of teamed up and decided to do a lot of collaborating.
But I would almost hold off on all of these word problems because I looked at them as too difficult. Students in my class, there's no way that you'd be able to attempt a problem that I haven't already somehow pre-taught you these steps and procedures ahead with just what we call these naked problems. Right? We'll dive into naked problems a little bit later as well. But this idea that we can't possibly have students do something like that until way later in the teaching journey. So we're just going to very slowly kind of breadcrumb them along with these very... We'll call them knowledge-based problems, very simplistic problems that don't require a lot of thinking but more a lot of mimicking.
John, I'm picturing in my mind, in my classroom. It was like, I thought as I was breadcrumbing students along what I eventually would see is like, "Okay, now I can do this word problem. We could do problem-solving." It was near the end of the unit and we're going to introduce problem-solving. And then I don't know about you, but my students, as soon as we did this, it was like we just hit a wall.

Jon Orr: For sure. And my students as well hit that wall. And I can imagine when I was teaching at that particular way... And this is the way I would teach word problems, right? It's like now we have to bring in context into the situation. And if you've been teaching procedurally like step one, step two, step three, when you're solving equations or when you're using a proportion problem or whatever the math happened to be, I would often write the step-by-step procedures out right at the beginning. And when you go to bring in now context later on, kids are only used to seeing those mimicking type questions that you were talking about. And now it's like, well, how do you teach where problems? Well, if you've been teaching the mimicking, mimic my procedure, then the only way I could do that... and I'm sure this is true for some of you listeners out there... is that you would highlight or underline or we're used to plugging numbers into this algorithm or this formula or this scenario, this procedure.
And we're like, "Okay, well, we got to pull the numbers, right? Pull that info. Which info goes where? Well, what's that? We got to highlight that." And it was this whole... Now teaching word problems had its own set of procedures which are a little different than the other ones because it was like you're solving equations, whatever, you're solving a proportion, had step one, step two, step three. And now you're going like, "Okay, well now in word problems, we have to push one, two and three steps down a little bit. We've got to introduce a new step at the beginning of that steps. But step one is read it and underline the key words. And then now try to figure out where those go in the other procedure."
So no wonder our students are like, "I can't do this," because it's like, "Now, which set of procedures goes where?" And it's becomes this thing in their brains. They're saying like, "I just can't figure out what set of rules to use when," and that is where we hit the wall. And some kids hit a wall early. Some kids hit a wall late, but definitely that wall comes for a lot of kids because it's like I'm only seeing mathematics as which list do I pick from now?

Kyle Pearce: Yeah. Yeah, totally. And you kind of briefly mentioned this idea of context. An example I have... This is more of like in my own context. Yet when I go in, I think back to my own experience, my own context. My daughter was working on division recently and she came up to me with a few problems. And I hope everyone who's listening realizes by all means, I do not judge any of my kids' teachers or anything like this because again, we were all on this journey at some point, right? Some people are earlier in the journey than others. Some people are later in the journey. And by all means, it's like I don't want anyone to feel this blame game going on or anything like that. But she came back and she came to me with pretty typical approach that we just highlighted, this idea that we're going to, pre-teach this idea of division and we're going to do so with these contextless problems, these naked problems.
So my daughter came up to me and she had a series of problems and she's saying, "I'm working on these problems." I said, "Okay, well what are these?" And she said, "Well, it's like when you have the two numbers and then the thingy," and then she held out... Those are watching on YouTube right now can see. But she held up her finger horizontally and then took two other fingers and was using the dots to show the division symbol. So she couldn't even name what that symbol was. So it was very clear that at least for my daughter, this might not be the entire class, but for my daughter, first of all, looking at these problems without any context and looking at it symbolically was probably not really helpful for her because now she was kind of looking at this and she was essentially grasping for whatever the step or the procedure was that she's supposed to do.
Now there's also a caveat here with this example that because there's no context, when you have a scenario like division or an operation like division, there's actually more than one type of division. And again, this is something that we've talked about on previous episodes. I did not know this for the majority of my teaching career, the majority of my life. So again, no judgment here, but basically what it does is it tends to get students thinking that division is only one thing. So if you were introducing division, as many people do, oftentimes division is introduced as a fair share sort of approach. That's called crosstalk-

Jon Orr: How do these go in here?

Kyle Pearce: Yeah. Well actually, that's the opposite there. That's like how many of these go into there is quotative. And this is how confusing that is. So if it's fair sharing, it's like I've got this many people and I've got this many cookies and now I'm going to like hand those out one by one is typically the strategy, the earliest strategy a student would use where they just manually hand out one to each person. And that was the approach that she was sort of using. But the challenge would be is... Imagine this though, John. So first of all, she's looking at these numbers. She's like, there's 12 of something. There's four of something. I don't know what they are because there's no units, there's no context. And then there's this symbol in the middle that we're going to call division. And then we're going to use a fair sharing strategy, which is a partitive division strategy in order to solve all these problems, sort of suggesting that that's the only scenario that you would ever see.
And what's going to happen ultimately is she's eventually going to bump into a real-world problem, which is again, word problem. And she's going to have to do this stuff. And some of the contexts are not going to be a fair sharing context. They're going to be the quotative context. How many of this go into that? Which is a different type of division. And then all of a sudden, what do you think students are going to say? They're going to go, "None of this makes sense because it's like I've been doing all this over here. I'm getting all these right answers. But now you're telling me that that is the same as this over here, where there's a context, a rich context. There's words."
Well, of course that strategy you were talking about, John, is going to take place where now it's like, "Well, if I know how to do it with problems that are just numbers, If I go in there..." And as Graham Fletcher, I've heard him say before, "If I go in there and I number pluck, I could pluck my numbers out of the problem and I could try to put them in the right spot and then do this stuff that I was doing earlier and mimicking in order to get a number. And then I'll take that number and I'm going to go put it back into this problem."
And then what ends up happening? We see wrong units. We see numbers that were plucked and put in the wrong spot. And then at the end we think it's like, "They just need more practice. We just need more practice doing this." And of course, if we want them to mimic this whole process, that is absolutely a strategy that will work over time, but not for all students. So it's like when we look at this and we think and we go, "Holy smokes."
Imagine one of the things we're kind of advocating here and we'll show in this webinar is imagine if we approached all new learning through context. Now it doesn't have to be words. We'll talk about that a little bit as well. It doesn't have to be a word problem, but through context so that we can make sense of the mathematics in the world around us, and then work our way towards more of these symbolic represented problems over here.

Jon Orr: Yeah. Like you said, Kyle, we're going to do that in the webinar for sure. And it doesn't have to be this word problem that has like, "Sally went to the store," or, "Joey was doing this." We can do this abstractly as well, but there is context to the abstractness as well. So if we're just kind of recapping here, the two reasons that students right now are struggling with word problems, one that we started here with was we teachers are pre-teaching steps, procedures. And the second one Kyle just talked about was this context idea of how do we bring context in? We got to teach through context, teach through problems. It's just something that we've been doing for a number of years now and seen significant gains in not only problem-solving skills with our students, but the understanding is coming along with that, which is totally different than what we used to teach.
So those are the two. Now the third reason we would say is kind of related to some of the other two, which is something that we've talked about many times here on the podcast is this idea of thinking and where the thinking happens in your classroom. We've talked on the podcast with Peter Little, though, who argues that most teachers are doing all the thinking or most of the thinking in their classroom when you are doing the pre-teaching, the procedures, the algorithms, the setups, or the I do, we do, you do model. And that's something that we've been changing too.
So another reason kids are struggling with word problems is we've never really given them an opportunity to think, and we want to change that. How can we bring that into the classroom? How can we bring thinking more? What are the things that we're doing? What are the strategies that we are doing in our classrooms, our members of the academy are doing in their classrooms to change the thinking dynamic in our classrooms?
Because there's our quote from Peter that we've used many times is that we would plan our lessons under the assumption that kids can't think or won't think like, "Kids aren't going to do any of that." Well, if we assume that, you're right. We will design our lessons to make it real easy on ourselves. We will just show them how to do everything because they're not going to think. Well, we don't give them that opportunity enough to think. And if we want kids to become better problem-solvers, we do have to put them into situations where they are the ones thinking and we are the ones guiding or assisting with feedback.
And sometimes we think that kids won't think and just won't do this problem-solving aspect. Kids need that cognitive engagement. This is why kids hate math class and hate word problems is because they're not actually thinking while they're there, right? They're just mimicking. They're like, "Why do I need this? I don't see the point of this." But if they were cognitively engaged throughout that whole time, your whole class, your whole period, your whole lesson, then I don't think you would get those comments from students because they're cognitively engaged. And we don't need perfect context to do that. Kids love video games. And why do they love video games like today's video games? Because they're cognitively engaged the whole time.
So many video games are built around puzzles and solving little problems here that lead to bigger problems. It's been a while, Kyle, since I've played video games. But when I did, I was an adult still. The average video game player is a 38-year-old person. It's been a long time because I haven't had a lot of time to play video games anymore, like 10 years ago. Those video games are super complex. They are full -on worlds where you have to make so many complex decisions to progress yourself or in the game. And kids thrive on that. That's why it's such a big business is because it's cognitively engaging our students. That's proof that kids can cognitively engage and do these things and have fun or learn deep things along the way.
And I think we're not doing that, right? We're not cognitively engaging our students enough. So that's our third reason is kids are not enjoying or not understanding word problems because we actually haven't helped them become the thinkers that they need to be.

Kyle Pearce: Yeah. And the other piece too that like you've touched on here, John, that I think is so important is we hear this all the time. We hear it in our Facebook group, for example, our Math Moment Maker Facebook group, other Facebook groups as well, where a lot of times, people are seeking out a way to make math relevant to students' everyday lives. There's a confusion here because I was like this too, where I was like, "All right, I need to make it about their life and what they're interested in now." But the reality is, is that's actually not the relevance that we really need to seek.
We need to get them cognitively engaged in something, get curious, that curiosity piece you've kind of hinted on in the video games and puzzles. It's like it's cognitively demanding. And for what purpose? When you think about video games, students aren't doing it because of like, "Well, one day I'm going to have to race a car. So that's why I'm going to do this."

Jon Orr: It's not relative to their life. Nobody's saying in a video game, "When am I ever going to use this again?" Because they're probably not. But like you're saying, it's cognitively engaging.

Kyle Pearce: Yeah. And if we do that in our math class, there could be... In some of our best experiences teaching mathematics... And John, I know you'd agree with this... Is some of our more abstract math problems that we give, but it's how they're delivered and how we give it to students to do the work.
If I give them something abstract and I tell them exactly how it works, it's like I just took the remote control out of their hand. I took the game controller and I beat the level for them. And I was like, "There you go. That's how you do it. Now you go back and do it." How many of your kids out there or students out there would actually want to play the video game if the teacher kept taking the remote from them and doing the levels and being like, "There you go. I just hit another top score. Now it's your turn to hit that top score."? And I feel like that's what we tend to do in math class.
And we don't even get them interested about the thing we're going to show them how to do. We often just show them whether you like it or not and then say, "Here's the game controller. Now you go." So it's like, how do we make math class feel more intuitive? And that's another thing that these video games do is they kind of just feel intuitive. My son right now, he's in Roblox and he's working on building a grocery store. I don't think that he ever cared about a grocery store before Roblox, but that's something that he's doing. And he feels a reward when he overcomes these challenges that are out there. Same with Minecraft. Right? So that to me is really important. And then if you want to talk about how do we go and do this practice? Because a lot of students will have to practice. If they're playing a video game. You're not going to just go into every level and then just beat the level the first time.
So of course, practice is important in math class. But again, we have to think about how are we going about that practice? Are we just repetitively doing it over and over again where there's nothing interesting or intriguing going on? So we want to be cautious here because John and I, of course we don't want to get you in the mindset of like, "You're never allowed to print anything to give to students," because that's how I think some people feel now, right?
Worksheets have such a bad name. I think it's just how we go about the practice and the routines that we use in order to, first of all, set students up to prepare them for purposeful practice, and then also by that point, I feel like... and if we do it in a reasonable way where students are understanding the concepts that they're actually practicing, we can ask them more interesting, deeper, cognitively demanding questions that require them to use a little bit of that metacognition, right? To explain what's going on in the scenario and help us better understand where they are in their journey versus it being again, a bunch of naked problems where you're clearly just following the same steps over and over and over again.

Jon Orr: I agree. And that's the fourth reason the students are struggling with word problems and we are angry or... I guess not angry, but we are-

Kyle Pearce: Frustrated.

Jon Orr: ... with teaching word problems is how are we setting up the practice for students like Kyle has just outlined? Are we using just rote memorization worksheets or are we carefully crafting? And I know this will take more work, but we're going to talk about what that looks like in the webinar because the webinar's a great spot for us to showcase and show you what you can do because we'll use video. We'll walk through. You'll be in the chat with us so we can walk through what that looks like in our classrooms so that you can kind of walk away from the webinar with purposeful practice examples for many different topics ranging from grades three through 10.
So that's the fourth of the five reasons. Kyle, the fifth reason, the final reason here that we're going to talk about in the webinar is probably one that we've shared or talked about the most, but also it's underlying in everything that we've talked about in creating a math class, where we make math moments that matter. And it's about psychological safety. How are our classrooms structured for the culture of that room? I know that when I taught for so many years in my old, very traditional way, that I did not create a culture that was open enough, that kids could share different strategies, just problems. It was always the teacher strategy. And I think when we want students to solve word problems and kind of solve those real-world problems, how have we set up that culture so that they have the freedom and the license to try and be risky and solve problems?
Or going back to number one, are they trying to go back and go peg, "What of the procedures that I was I shown, which one do I use to solve here? Can I have the freedom and can I have that creative license to try something here and see where it goes?" Because I think that is huge. And that's about culture. That's about allowing students to have psychological safety about their risk-taking and also just be comfortable in the room. We've talked about that many times too.

Kyle Pearce: Yeah. And one of the big pieces for me that helps with that psychological safety is again, if we're changing how we logistically set up our math classroom, both from environment perspective, so making it more of a collaborative culture, but then also flipping it and getting rid of this pre-teaching idea because with pre-teaching, this goes all the way back to number one. If I'm pre-teaching you procedures. And basically I'm sort of saying this is how we're going to do something, the prescribed method, let's say, students very quickly know whether they can do that one way or they can't, or if they're uncertain.
And even students who can do it a certain way, if they're not making sense of the math... So this is that fueling sense-making piece that we're always advocating. This is a part that we really struggled with for many years was trying to get our students to actually make sense of what we were doing. There was a time where I was able to help my students that traditionally struggled in a math class. I found ways to help them do well on standardized tests, but it still involved pre-teaching and it still involved them mimicking steps. And while that was celebrated at the time, I thought that things were going well.
What I realized is at the end of the day, that test result, that was higher actually didn't do a whole lot for those students. They still didn't feel safe in my math class because they didn't know why they got the answers correct. Right? If it looked like a problem they had done before then they were good to go and they knew it was right. They couldn't tell you why it's right. But they knew it was right because it looked a lot like this one over here. What we want is to build this so that students are using... When we say prior knowledge in our math class, prior knowledge should feel intuitive, right? If you think about that for a second, it's not about, "Okay, you need to use section 3.6 in order to help you for section 3.7." Like we're talking about the things that we've learned previously in our math class over time, as we have more experience, and as we're making more connections in our brains and understanding why those things work the way they do, understanding the behaviors of the mathematics that we're exploring, then it feels intuitive, right?
When you think about intuition, what that is, a lot of people say like, "Oh, it's just intuitive to do something." A lot of people think of it as though it's something you're born with. But intuition is something that is really influenced by your experiences over time. So we want to build that psychological safety by students feeling like the progression of mathematics is intuitive to them, that it feels logical, that the next step is logical to do this thing versus them sort of going like, "Huh, I've got to go back and try to map out all the things we've done before and try to somehow make sense of why those things work." So for us, this big idea... And I know we've listed this one last, John, but I would argue, this is something we need to be working on immediately in our math classes.
Because without that, all of the other work that we do is going to at least be hindered. I'm not saying we can't make any progress by changing some of these other pieces. But if students aren't feeling safe in the classroom environment, in the math scenario, in the math context, in the math world, then all of this other work, we're going to be spinning our wheels quite a bit because they're still not feeling confident and they're not feeling like they themselves are mathematicians. So these are things that we really want to push through and ensure that students are truly like, "I can do this," just like that video game that you referenced earlier there, John.

Jon Orr: Yeah, totally. And I'm glad you summarized that one being one of the most important. We've talked about that one being so important to start with. Anytime you're changing some of the lessons, ideas that you're going to be making in your class, you do have to start with building the culture. And it does take time that you build psychological safety. You can't just flick a switch and, all of a sudden it's like, "Now I have it." And so that's why we want to make sure we include that in the webinar. We're going to show you what we've been doing in our classrooms to change that psychological safety in small steps. So throughout the year, you can overcome that and kids will feel confident about problem solving, but also confident when they go to solve these kinds of word problems that we're talking about here in this episode.
So that's five. Let's just do a quick recap, Kyle, of the five reasons kids were saying our kids and teachers struggle and are frustrated with word problems. Number one, we said was the pre-teaching of steps, procedures and algorithms. The second one was about context. How are we introducing context? Is it all very abstract? Or do we have context? And the context can come in different ways. Kyle, the third and the fourth?

Kyle Pearce: Yeah. The third is this idea of cognitively engaging our students. Right? So getting them thinking in our math class. Math class should be about getting them thinking and getting them to problem-solve, not about preparing them to be ready for when problem-solving comes. The fourth though, is this idea of purposeful practice. We'll talk a little bit more deeply in the webinar about this one.
I know we talked about how it's important, but again, worksheets aren't bad, but it's the questions we're asking on those worksheets. That's what's important. So looking at them more clearly and then also thinking of ways that you can actually provide that purposeful practice in more of a spaced manner. And then finally the fifth one and again, probably most important... I would say probably... It absolutely is the most important, is the psychological safety of our students. Are they feeling safe in our math classroom? We're going to argue that everything we've talked about here can help you work towards that psychological safety and that we can overcome this challenge. Word problems themselves are not the issue. There is so much more to it.
And coming up in May, 2021, on May 5th, the Cinco de Mayo, I think it is there, John, come and have a math party with us here at 7:00 PM Eastern time in North America. That's 4:00 PM Pacific time in North America. You can join us by going to makemathmoments.com/webinar, get yourself signed up. And even if let's say it's the middle of the night or the middle of the teaching day where you are in the world, get yourself signed up so that you can get informed of the replay when it's made live. And then of course over time after time, we end up putting that into our academy, which now has over 10 courses in it and all kinds of awesome PD goodness inside there.

Jon Orr: Yeah. I'm really looking forward to that webinar, which we're going to debrief and build examples for all of the five reasons we talked about here about why our students give up on word problems and what we can do to fix that. So looking forward to seeing you all over there. Kyle, show notes and links to resources from this episode can be found over at makemathmoments.com/episode124.
Again, that's makemathmoments.com/episode124.

Kyle Pearce: Yeah. Make sure you check us out over on all social media platforms. Also, if you're listening to this in the car or on a run or wherever you are, keep in mind we're also doing our best to provide video versions of the podcast. Probably a little more raw in the video form as well. So whenever there's something that goes wrong, John's cat shows up on the scene or Land Bando shows up to say hi when dad's in the middle of a sentence, most of those get... We keep them in on the video. So if you want to check that out, check it out on the YouTube channel. We've got weekly videos coming out on how to teach a little bit... We'll say differently than how John and I taught when we were growing up. So go check that out on our YouTube channel, Make Math Moments. And my friends, until next time I'm Kyle Pearce.

Jon Orr: And I'm John Orr.

Kyle Pearce: High fives for us.

Jon Orr: And high five for you.