 Fantastic. So I will be monitoring the chat area and let you know if there's things you should be paying attention to. And if you all have specific questions about any of the information, there actually are going to be a couple of places where I'd like to get your input. But at any point during the presentation, if you have some questions, feel free to type those into the chat. I can get those from Carol. Obviously, the format is a little tricky for interaction, but we like for it to be as interactive as possible. So again, I'm a physics teacher here at the School of Science and Math in Durham. I've been here five or six years now. I actually started my career in Harvard County in eastern North Carolina. So when I was there, I taught physical science and physics and chemistry. So it's kind of been in a couple of different settings and had the opportunity to teach with some different types of students. And while what I'm presenting today, I've developed at science and math for physics classes. I think there are some themes and pieces that would work. You know, if I were still back in Carteret County teaching with my students, I could still use some of this. So hopefully regardless of where you are and where you're coming from, you'll find some misinformation useful. So I'm going to use this acronym, I guess this symbol p squared in part because I didn't want to keep typing purposeful problem solving over and over again. And p squared is sort of a nice compact way to say that. So I'm going to talk a little bit today about what purposeful problem solving is, why it's important, and what education research has to say about the problem solving process. And then what we do at science and math to kind of help our students get better at problem solving. So here's a brief agenda, kind of what we're going to look at. We've asked some folks this question already. But if you wouldn't mind just typing in the chat box, kind of give us a sense of what your background is or where you're from in North Carolina and what is your specialty area, your day-to-day job. Are you a teacher, are you an administrator, are you a curriculum coach, do you work with high school kids, do you work with elementary and middle school kids, college kids, that sort of thing. If you could just type that information into the box so we can kind of get a sense of who's here while we're going. Seventh grade math teacher. That's good. And teacher from Thomasville City, teacher from Cleveland County, secondary math curriculum coordinator. So yeah, actually at the scaling STEM conference there were a number of biology folks in the room. I know some of the content can differ a little bit from physics, but some of the strategies that we were using, they seemed to think were helpful. So hopefully we'll be able to find some good information here as well. Problem solving is often a very interdisciplinary endeavor, so I think it sort of touches on a lot of different areas. Well, great. That seems like we've got a nice diversity of people here, which will give us some good perspectives. So we're going to briefly get into a warm-up activity and then talk a little bit about this idea of purposeful problem solving and then get into sort of what the research says. Talk a little bit about science and math. I also want to touch a little bit on technology, so how can you use technology to make the problem solving process more interesting, generate more interesting conversations with your students. And if we've got time at the end, I'd actually be really curious to learn from you all what do you currently do to encourage problem solving with your students. Okay, so that's sort of our agenda. But I want to kind of warm up a little bit and get everybody thinking. No, it's probably towards the end of the school day, but we'll see what you can do with these questions. Oh, excuse me. So these are three questions. They're actually, if you Google them from Fermi questions, you can get a lot of questions like these. They're pretty interesting, but three questions here. And I'd like for you to just pick one and spend maybe about four or five minutes thinking about this question that you got. And see if you can talk with an answer. So take a look, pick a question, write down some thoughts, and sort of think about how you're going to go about solving this question. So at the time of the panel, we have a clock here. 319. Okay, great. So we'll give you about four or five minutes here. And you're welcome to use whatever resources you have at your disposal while you're doing this. And these are the only questions to do. They're sort of the classic back of the napkin calculations. There's a good list of these in the physics teaching journal. The physics teacher, they always have two of these in the journal. It's kind of nice to... If you think you have an answer by all means, please type it into the chat box if you can come up with a number for each of these. Well, the first one, how far should you be willing to drive? There is no absolute answer for that one. The word should. It's a special word to be sure. Some of these are sort of different types of questions. The first one is sort of almost a value statement, personal preference, that sort of thing. Four miles, all right. And I should know the answer of how much it costs to keep my hot water. But I haven't paid attention. Are you the typical American household with the... Oh, 1.8 children. Yeah, 1.8 children and then 1.2 pets. Okay. Yeah, all right. Okay. 2.3 rooms. Okay, this person would... Right, so. Good point. Yeah, so far you can travel for four cents. Yeah, Victoria, you bring up a good point, right? I mean, so you need to know some information. And depending on the starting point, what is your starting information? What are your starting assumptions? You're obviously going to influence the answer that you get. How many people are there in the typical household? How large is the typical house? Right, then those are all good questions. So another minute or two here and then we'll discuss what kind of appliance is right, right? You have an energy star water heater. What is your cost of electricity per kilowatt hour, that sort of thing. So I think North Carolina is relatively cheap. I think our energy is fairly cheap. It's 10, 12 cents a kilowatt hour or something like that. It looks like we've still got a few people joining then. So if you're just joining us, we're starting off with a warm-up activity, just having people think a little bit about each of these three questions. We're sort of talking about problem solving, so it seems reasonable to start with a little bit of problem solving as well. So just having folks think individually about these and asking some new questions about the answer that you get is going to depend upon some things 5 times 10 to the 13th power. So looking at these questions, the first thing I think about is the kind of research that I have to do in order to start answering them. Okay, absolutely. Okay, so yeah, regardless of where we are, we'll go ahead and proceed. I mean the point of this is just to get you sort of thinking about the problem-solving process and about how there are different types of problems and different types of questions that require different information. Ultimately, we're going to take questions like these and sort of contrast them with the traditional textbook problem, which generally contains about as much information you need to solve it. And often than not, that information is sort of explicit within the problem and you sort of contrast that with something like this. The answer you get could depend. There are multiple correct answers depending upon your starting assumptions. And you know, in theory, for a question like two, there is a number out there somewhere that exists that we could potentially go out and research what that number is. If we're sort of forced for time, we can always make some assumptions about what those numbers are and do some estimations. Whereas the first question is kind of more of a value statement, writing how far should that word should is very important as well. But kind of the point of these questions, again, thinking about the approach, how did you think about these problems? What was your starting point? Is there a process that you can generalize for how to go about solving problems? And that's something that we're going to talk about today. I mean, have you ever thought about that before? How do you think about and solve problems? What kind of process do you use? So, you know, I've studied and taught physics for a long time, so I've always kind of had this physics problem-solving process in my head since I've been in high school. And I've found that to be a very valuable way of solving problems. But that's really not the only way to solve problems. So, Barry came up with an answer for number three, and he said that it was $800. So, Barry, my question to you is did you Google it? Did you or did you just know it because you've been investigating? How did you get to that answer? Because this generation is much more likely to go right to the Internet and look for the response to a question. And it's important the way you phrase the question, what kind of answer you're going to get. Sorry, that was scientifically, and then yes, yes, it's sort of an order of magnitude approximation answer. So, the Fermi questions are kind of notorious for, as long as you get about the right order of magnitude, you're okay. It's kind of the process that matters more. And sometimes you've got to do that. Sometimes you have to guess. So, anyway, let's go ahead and move on. But again, just trying to get us to think a little bit about the problem solving process as we talk more about how we encourage problem solving in science. So, to kind of get a definition out on the table, when I say purposeful problem solving, what does that mean? How do I like to think about it? It's a method of solving problems that is very goal oriented. It's guided by process. And you kind of have a sense of where you're going when you set out to solve a problem. You're not just sort of proceeding randomly and just sort of trying things because I don't know what else to do, so I'll try this strategy. Although sometimes good problem solvers have to be flexible, so they may start off on one path and realize, well, this isn't getting me where I think I need to go, so I need to adapt and switch gears a little bit. And perhaps most importantly, this idea of purposeful problem solving is very good for solving what I would refer to as ill-defined problems, problems that aren't necessarily obvious. It's not necessarily obvious what the answer is, and there may be multiple answers for these problems. And that sort of ill-defined problem is much more consistent with sort of a real-world problem where there could be multiple solutions. And so someone who's good at this or purposeful with problem solving is going to be better equipped to handle these kind of real-world situations. It's important to ask the question, is this a good thing? I'm assuming that it is, but why do we care? Why is this a valuable skill for our students to have? Because currently, I'm not sure that we explicitly test for this on sort of a state level. If we look at the U of C's, I don't know how many ill-defined problems that you're going to find in a scientific or mathematical context. So, you know, if it's not tested, why should we care? Well, we've got the next gen science, what is tested in life, right? So, that's certainly important. And as the next gen science standards roll out, problem-solving the ability to solve real-world problems via engineering and design is a major point of emphasis in the next generation science standards. And I am not familiar enough with Common Core and mathematics to know how prevalent problem-solving is. I'd love it if somebody who is familiar with Common Core could potentially maybe speak a little bit to how problem-solving should, real-world problem-solving shows up there. But I know in science, of course, this idea of real-world problem-solving engineering and design is really important. So, you know, in that regard, I think if the next gen science standards dictate how we do education in North Carolina in the next 10 years or so, this is going to become very important. But also, yes, as someone alluded to a minute ago, you know, teaching people for life. So, problem-solvers are desirable, you know, when you're trying to get a job and you're trying to get in college, people want people who can solve problems. I heard a quote, you know, five, six years ago, you're never going to get paid to solve a problem that you've already solved before, right? You're going to get paid to solve new problems that you haven't seen before. So, it's a valuable skill that can translate across a variety of different jobs. So, sort of taking the definition of problem-solving a little bit trivial here, so I think it's important to define problem-solving. So, this is the definition from sort of the primary source education research article, but I actually like this next definition a lot more. So, what is problem-solving? What you do when you don't know what to do? By definition, the problem means that you're in a novel situation. You're kind of out in the unknown a little bit and you have to think about how to navigate that situation when you don't know what the answer is. So, kind of contrast the notion of a problem with what we're going to call an exercise. We'll kind of get into what that is in a minute, but I want to get you thinking a little bit more about sort of this idea of what you do when you don't know what to do. So, think about these four questions for a minute, all right? So, you've got sort of a question about San Diego, Chile, the distance between there and Durham, how many feet are there between here and San Diego, how many gallons of gas does it take to drive there, how many Snickers bars would you have to eat to be able to walk there as well, okay? So, if you think about a problem and sort of the situation that's potentially ill-defined, kind of a real-world type problem, it contrasts that with what we're going to call an exercise, which tends to be sort of a little bit more cut and dry concrete. If you think about these four questions, which of these questions is more sort of an exercise than a problem, okay? Which one sort of has a definite answer? Which one is concrete? Which one, with respect to a problem, which one are you going to have to think a little bit more about? Which one are you going to have to potentially make some assumptions? Which of these questions are ill-defined? And hopefully, as you look at these questions, it's obvious that sort of the first question, I mean, there is a right answer, right? So, it's something you could look up. It's a piece of information, it's a fact. You know, contrast that to the fourth question, how many Snickers bars would you have to take to walk? Kind of like a firmy question, you've got to make some assumptions, you've got to think. That's a hard question to do. I'm not sure I know how to answer that question immediately. So, I would consider the last question more of a problem than the first, which I would consider an exercise. Because exercises tend to be situations in which there's one correct answer. You're applying something familiar. There's a small number of steps. Generally, the process is pretty rigid compared to a problem, which hopefully, as we've seen already, is potentially a little bit more ill-defined. Might have a lot of steps, might have a variety of pathways to get to the answer as well. So, you know, problems, when I teach, I really like to emphasize this idea of problems. Now, exercises are important, and I don't want to downplay the importance of an exercise, but I think a problem is going to invite more thinking on the part of the students. It is a little bit harder. And it's also important to note that what might be an exercise for one student could be a problem for another student. There may be one student in your class who knows exactly what to do when you put a question on the board, in which case that would be an exercise for one student, but for another, it could be a problem. And so, there's sort of a differentiation issue with this difference. For the same question, you could have two different students kind of approach it differently. So, getting back to this idea of encouraging purposeful problem-solving, kind of knowing what to do, being goal-oriented. A situation that invites purposeful problem-solving generally is going to be open-ended, potentially with multiple solutions and pathways. It's going to involve real-world situations, which we're often able to find. Like most real-world problems, you're probably either going to have too much information through which you have to filter or too little information. You have to go out and research more information. And I think perhaps most importantly, when you think about a problem-solving, you might think about a traditional textbook problem that you could solve in five minutes. I would argue that perhaps the most interesting problems take a lot of time to solve. And so, problems can range in scope from very, very short to very long as well. And they're both valuable, but I think kind of having an opportunity to solve both types of problems is really important. So, here's an example of what I would consider to be a question that might invite more purposeful problem-solving on the part of students. How fast do electrons move in a lightning strike? So, as folks pointed out earlier, there are a lot of pieces of information that you might need to know before you can arrive at what you would consider to be a good answer for a question like that. Well, how high is the cloud? What's the weather like that particular day? What's the humidity? What's the moisture? There are a lot of factors that could potentially make getting an answer to a question like this difficult. And so, you have to potentially make some simplifying assumptions to be able to do this correctly. But this is a lot, if you contrast this with sort of a traditional textbook physics problem about there's a capacitor plate with a potential difference of 10,000 volts. How fast will an electron be moving at the end of that? In essence, this problem and that problem are testing similar concepts, but this problem is doing it in a much more open-ended fashion. And the answers can be varied depending on the starting assumptions that a student has. So, hopefully, at this point, we can agree that problem-solving is important. So, the next question becomes, well, how do we get students to become better at problem-solving and more purposeful at problem-solving? So, I thought I'd spend a couple of minutes talking about what science and physics education research say, because ultimately I think we need to sort of look to the literature and use that to guide what we do in the classroom as much as we can. So, what do science and physics and researchers tell us about how to get better at problem-solving? So, kind of in a nutshell, if we look at characteristics of experts, people who are really good and really purposeful with their problem-solving, we see that these people have what's called sort of a strong physical intuition. They kind of have a general sense of what to expect in the situation. If you give them a question, they may have a gut instinct that generally tends to be right. A lot of times, that's a function of experience, and that's a hard thing to do when you're dealing with younger students. These people tend to be very persistent, so they're not easily dispersed. They're gritty, if you've heard that term before, grit in psychological literature. They're willing to keep going, even if they don't get the answer immediately. Which actually can be a problem with some of the students here at Science and Math. They're so used to getting the answer immediately, and I saw this with the honors students that I would teach when I was at Furlattan in my previous job. They weren't patient. If they couldn't get the answer immediately, they would get frustrated and be quick. So, that's a tricky thing to do. It's a hard characteristic, but it's one that purposeful problem-solvers has. They're very efficient in what they do, high task efficiency in their goal oriented. So, they kind of know what they're doing, and they're also efficient with the process. And finally, they're flexible. So, they kind of know if what I'm doing now, they can evaluate what they're doing. So, they're metacognitive as well. They can kind of self-monitor what they're doing and look at whether or not the strategy is successful and changing, if it needs to be. Okay. This is a little bit more physics-related, but I think there's an analogs to these ideas and other disciplines as well. But one of the strategies that good expert-like physics problem-solvers have is one of the characteristics that they have is that they can represent a similar idea multiple ways. So, if you look at the bottom three pictures, each of these is a different way of representing the concept of force Newton's second law, basically. Over here on the right, there's a mathematical statement that represents this idea that unbalanced forces cause an object to accelerate. Here, you've got a traditional, it's called a force diagram, which essentially is communicating this similar concept, this idea that unbalanced forces cause things to accelerate. And then over here, you've got on the left, you've got a picture, sort of a real-world diagram about what would happen. And so, in physics, people who are really good at problem-solving, people who are really purposeful with problem-solving, are very good at moving back and forth between these representations. So, they might think about the situation in a diagram form first. Maybe they draw a force diagram and introduce an mathematical equation, but they can also jump back and forth. They can think about the problem in multiple ways. They can sort of analyze the process. I mean, this issue of analysis versus exploration is all about exploration implies that you're kind of just searching for a process. What does analysis mean? You kind of know what you're doing in our proceeding in a logical, purposeful fashion. And again, there's this idea of flexibility as well. Another big issue, especially in physics, one of the things that's kind of interesting, and those of you that teach physics may know this, students in an introductory physics course often try to map their way out of doing physics by memorizing equations. It's pretty common here, and it's a challenge we have to deal with. And I like to compare that strategy to reacting to a loose screw by grabbing tools randomly until you can find the right one. So it would be as if I see a loose screw. I'm just going to randomly reach into the toolbox and grab a hammer. I'm going to try it if that works great. If it doesn't work, I'm going to go get another one. And so ultimately it's a strategy that I guess over time can work, but it's not very efficient. It's not very purposeful. And I would argue that probably the better thing to do would be when you see a loose screw, think first before you grab the tool about what kind of problem you've got and then find the appropriate tool. So what physics and researchers find is that people who spend more time on the conceptual and qualitative side who think about physics first before they grab the math are much better and much more efficient. And so that's something that we value with our students here is this idea of emphasizing qualitative and conceptual reading. Excuse me, reasoning and using that as a way to plan as well. So that's another characteristic that in physics expert problem solvers have is they know how to reason qualitatively. So some of the characteristics of experts, and I think our goal as teachers is to help our students become more expert-like. So how do we do that with our students? Well, one way is to explicitly instruct students, teach students how to reason like experts, encourage them to think about their thinking, encourage them to monitor how they're thinking about situations, and start this kind of internal dialogue with themselves, conversation, well, what am I doing and why am I doing it? And we'll talk in a few minutes about specific ways that you can do that as well. I think it's important that students understand why a particular process is structured in a certain way. So when I teach classes, I find it important to justify to students why we are doing what we are doing. So I like to ask the question why a lot. And in this case, if there's a particular problem-solving process, well, why is it important that you draw this force diagram or draw this energy bar chart, that sort of thing? And then again, getting at this idea of qualitative and conceptual reasoning, encourage both. So don't just give students an equation, give them the corresponding concepts. I find often that conceptual reasoning can be much more difficult than the math, which sometimes you can sort of do a problem without really understanding it. And then kind of like with most things, you get better at most things by practicing, but purposeful practicing. So if you want students to get better at solving open-ended problems, you've got to give them open-ended problems. You can't give them exercises and expect that they would be good at problem-solving. So it's an issue of selecting activities that align with what your goal is for the students. So if your goal is to create great problem-solvers, then you need to give students opportunities to practice problems, not opportunities to do exercises as well. So give them some new opportunities that are challenging. So specific examples of how we do it at the School of Science and Math, here's sort of a list of strategies that we use to encourage our students to be a little bit more purposeful. So the first one is hopefully fairly obvious. We want to model the approach. So most students come in to our courses not used to sort of thinking about problems in a very systematic fashion. So we had to do a lot of work to convince them, one, that they should, why it's important, and then to help them develop those skills and those practices. So we model that as teachers in class when we write up problems on board and write up solutions as well, trying to model that approach. We also do a lot of group work, both in and out of class, because oftentimes when you have situations that are open-ended and they'll define, having multiple perspectives and opinions is a very, very important way to deal with the complexity and to kind of break through if you're getting stuck. Having multiple people at the table can often help. So we do a lot of group work, both in class and out of class. And not just on projects and labs, but even on homework assignments. We encourage our students to collaborate within reason when they're doing the work as well. Two strategies that I really like a lot. The first one is called show and tell. So what we'll do with something like that is we'll assign a problem. Sometimes we'll assign a really difficult problem for homework just to kind of see how the students react to it. And then the next day, we'll sort of randomly select a student to present her or his work and then talk about what she or he did and then get feedback from the class. So give the students some constructive criticism on her approach or his approach. What did she do well? What are the aspects of the solution that were not included that she needs to include for next time? Did other people do the problem differently? Kind of the point in the show and tell, it gives students an opportunity to practice, but it also gives them an opportunity to talk about what they've done. And one of the particular philosophies of learning that I like a lot really emphasizes the idea of conversation. Conversations are really important. Students learn a lot by talking to each other and making their ideas explicit. So in my classroom, I tried to generate as much conversation about that. And show and tell is one way to do that. Another activity that I like to use a lot is called pass the problem. And this works when you have certain groups. So kind of the way this works is I'll have, imagine I have four groups of students in my class. What I'll do is I will generate four folders. And inside of each folder is a problem prompt. So I'll pass out a different problem in each of the four folders to each of the student groups. So all four student groups have a different problem. And so they'll spend maybe 15 or 20 minutes working on the problem kind of coming up with a solution. Then I'll call time. They'll put the work that they've done back into the folder and then we'll rotate. So another group has the folder that they just worked on. And so that second group will work on that problem, but they'll work on it without looking at the first group's work. So they'll independently come up with a second solution to that problem. Then we'll rotate again so there'll be a third solution to that problem that's independent of the first two. And then on the fourth pass, what we do is we ask that fourth group to take a look at all three previous solutions, look at those solutions, analyze those solutions, think about which of those solutions is the best, which is the most convincing, which is the best solution, the most comprehensive solution. And then their job isn't to work the problem. Their job is to write up and synthesize using other students' work what the best solution was. And then they present that solution. So they present a solution to a problem that they haven't worked. They're kind of taking that information and synthesizing it. So I've found in the past this is a really good way to expose students to multiple ways of doing the problem, to multiple assumptions. Some students make different assumptions than they might. They may have different strategies. So it's a good way to expose students to those multiple ways of solving problems. And again, it encourages conversation so students are talking about, well, why did this group do this? Why didn't they assume that? And so it gets them thinking about and talking about different ways of solving problems, getting at that notion of flexibility again, being able to do a problem in multiple ways. So also with all of our courses, kind of the second two bullet points sort of go together, we encourage multiple representations. And one of the ways we encourage that is by incentivizing students with our point rubrics. So kind of to give you an example of what this means, if I give my students a problem, let's say that problem's worth 10 points. It's on a homework or a test. Probably of those 10 points, two of them will be the answer. So if all the student does and is right down the answer, even if the answer is correct, they get two out of 10. And students hate this when they get to science and math. They get really, really frustrated by this idea. But what our goal is to get them to think about and communicate explicitly what their thought process is. So maybe a picture of the situation is worth two points. Maybe the force diagram is worth two. Maybe there's a list of assumptions that they're making to simplify the problem is worth one. Maybe the math and the algebra is worth two. So you're sort of incentivizing each aspect of what you want in a solution by assigning points to it and grading appropriately. So there's actually a document that we'll post on the website with this presentation that has sort of standard problem-solving procedure that we use with a lot of our courses in science and math and what the steps are. If you want to take a look at that, that will be available for you. But like most people, students respond well to it in the Senate. So if you incentivize it with your grading rubrics and your point values, assign a lot of credit for the work that you want to see, not just the answer. You're going to get students to think a little bit more about the process than just the answer as well. And one thing that I've started doing recently in the last, I think, two years is I've had the students start to think about and write down what their assumptions are when they do a problem. So everybody makes assumptions all the time. We have to. Otherwise, we would be inundated with information. So we have to make some assumptions in order to get through life and solve problems. But I always think it's important to know what those assumptions are. And so what I've started doing recently is asking students, when you do a physics problem, make a list of assumptions that you're making. So your air resistance is negligible, negligible friction, constant acceleration. Those are common assumptions for semester physics, that sort of thing, just to get them in the habit of it. And it's interesting to pay attention to what that step has done to student conversations. When I walk around class, when they're working on problems, listening to them to talk. And this is anecdotal evidence. I feel like in the last two years since I've implemented this step, I hear much more, I hear phrases like, well, what are we assuming for this problem? Did you assume that? I'm not sure I like that assumption. I hear kids say those phrases more and more and more. And then they did previously. So this idea of making them mindful about what they're writing down and what they're doing when they solve problems. I just happen to think that there's a very strong connection between thinking and writing and communicating. So if you can get kids to write about something, hopefully that will alter their thinking somehow. So encouraging assumptions when you solve a problem. And then finally kind of this idea of longer problems that are more open-ended. So the idea of open-ended investigations that are able to find. So we recently just finished an open-ended investigation where the goal was to safely land a human spacecraft on Mars using any landing strategy that you would like. It's kind of an engineering project. I mean, there's a lot of different ways you could do it. And so we were doing that project as a way to think about the connection between motions of DVATs, kind of kinematics, and dynamics. So what is the motion that you need to land safely on Mars and then how do you create that motion with rockets and parachutes and that sort of thing. So what it was pulled because there were a variety of different ways that students could do that. So you could have four or five different landing strategies. Then you can have an interesting conversation about, well, which one is the best and why. So this group over here may land on Mars, but maybe they need twice as much fuel as that group. And so then you can get an interesting conversation about the economics of space travel and that sort of thing. And talking about Mars is obviously important right now because of the work that NASA is doing with the curiosity. So it's kind of an interesting justification for why units are important too for the famous catastrophe from a couple of years ago with the crashed motion probe as well. So it's a good project. It's very interdisciplinary. Potentially brings in a lot of interesting conversations that aren't necessarily physics related. And it takes time. So it's a big project. And so students have to work in groups and learn how to break up aspects of this big project to get it done. So this is by no means an exhausted list, but this is a sample of some things that we do at ScienceMap to encourage students to be more purposeful with their problems. I mean, have we had any questions? Yeah. Encourage you to go ahead and use the chat area if you have a question that you'd like to consider. Okay. So to give you a sense, do we talk about this idea of we'll break some multiple representations? Well, what does this look like in the context of a student paper? Okay. So very asked. Relative to what? And I'm not... How fast? Oh, yeah. How fast with respect to the electron. Well, let me show you the student solution here. And it's nice. This isn't actually complete. It was a multi-page solution. But kind of as an example of in an open-ended problem where you've got some multiple representations. So here's a problem solution, sort of randomly picked a problem solution from a student that did this problem. And hopefully what you see is that there are different ways of thinking about the problem. So you've got sort of a picture diagram of what's going on down here. You've got what's called an energy bar chart. Right here you've got some math, mathematical representations of the problem. You've got a list of known information as well as a list of researched and assumed values. So again, getting students to be explicit about what they're doing as well. And sort of a traditional one-step mathematical approach would only have a solution that has kind of one line in it. But here you're giving students the opportunity to sort of communicate a little bit more of what their thought process is, which is, I think, helpful for me as a teacher. I can get a sense of what they know. But it's also helpful for them for no other reason than they get partial credit, which some of them certainly like that. The ones that need the answer real quick don't like this. And the ones that struggle a little bit more do like it as well. Anyway, you know, technology is an important part of education, no doubt. And so I wanted to talk a little bit about how technology can help make this easier. How can technology enhance our ability to generate problem-solving opportunities for students? So, you know, the first thing that springs to mind would be smartphones. So everybody's got a smartphone. Most of them have cameras. So students, in theory, could go out in the real world and videotape something that's interesting and bring it back into the classroom. So to give you an example, I was in Europe this summer and I was riding on the Eurostart, which is the high-speed train, which connects London and Paris. And I had my iPad with me. And I was just curious, how fast is the train going right now? So I just pulled out my iPad and I started shooting some video. And if anybody knows about the, I think it's the Vernier app or the Larva Pro app, the Video Physics app, I think on the iPad, I was able to use the image that I shot in class to generate a dataset that we actually used to figure out how fast the train is going. So that was kind of a cool example of using technology to kind of answer a real-world question. How is the, but it led to interesting conversations about, well, what is this scale? What can we use for scale in the background? And ultimately, we had to assume. We had to look at a car and assume, all right, there's a van. I think it's about this big. We're going to use that for scale. With videoing, you get interesting questions about perspective and that sort of thing. But again, the point is to generate conversation among students. So there's also something else that's kind of interesting. A couple of years ago, a student showed me a YouTube clip and he asked me, is it real? So I thought I'd share that with you because it's kind of interesting. So the basic premise here is that someone is sticking an iPhone inside of their guitar and pointing the iPhone up. Yeah, the student was asking whether or not this is real or whether or not someone has doctored the image. And I have an opinion on this. I will not give it to you. But I think you could do this with a lot of different YouTube clips. I think I've seen one where Kobe Bryant jumps over a swimming pool. I think there may have even been an article in the physics teacher about that. But these clips that are on YouTube, are they real? So it's kind of a fun activity to sort of apply physics to more kind of real-world context as well. We're lucky at Science and Math to have a really nice data analysis package called LoggerPro, which allows us to do some pretty complicated mathematics with a couple of clicks of a mouse. So if we have a data set, we can put our data into LoggerPro and we can do a variety of different types of fits, which gives us good insight into the behavior of a particular situation. So in the case of the train, I could kind of map the position of the train over time or something in the background and we could plot that on a graph of position versus time or velocity versus time and look at those different graphs and see from those graphs how we're going to figure out how fast the train is going, that sort of thing. So LoggerPro is a really nice way to... It takes... It makes data fitting very easy. It takes out a lot of the headaches about that. So it's really nice. We do a lot, again, do a lot of teamwork collaboration at GroupWorks. So we've recently been using Google Docs a lot, and even Facebook to a certain extent. And that's kind of an interesting situation. Back in the fall, we were doing an energy and sustainability project, and we had some students that were looking at how students, their peers... So Science and App is a residential school. Students live here. And so they were looking at how much energy their peers were using on a daily basis. So they literally set up a Facebook poll, a Facebook survey to survey their peers about their personal energy usage, which was interesting. And it also led to some really good statistical conversations about what is your sample? Is it a representative sample? Who's... It's a convenient sample, right? But how representative is it? How does that show up in your uncertainty analysis? It's probably better to have that survey than not, but at the end of the day, do you think the actual answer is bigger than this, smaller than this? What's the uncertainty, that sort of thing, as well? And actually, the last two or three years, I've been messing around a little bit with the Python, which is a programming language which you can use to do... some very powerful physics, and do some very interesting simulations with minimal coding knowledge. And so I think last year, a student in my AP calculus-based physics class asked me a question. And I had a hunch to what the answer was, but I wasn't quite sure. And so I went to... went sort of back home and wrote a program to look at this, the motion of a particle. It was a velocity selector situation, if you know what that is. What happens if the velocity is too high or too low, sort of specific explanation of the path of the particle. Let me actually have a picture of it here. And it was kind of cool because I was doing this independent of that. I had a student who was also doing some numerical simulations in Mathematica. So we came back two days later and had a really good conversation about the particle and we were able to use the Python to model. Simulation is a very powerful way to analyze complicated situations because computers are so powerful these days you can really do a lot. And for people who are interested in being professional scientists, knowing how to program is really important. So V-Python is actually a really nice way to do some complex coding or complex simulations with minimal coding knowledge. And NC State, I think, has a really good YouTube channel with some introductory V-Python stuff. So I would urge you to check that out if you're interested in that. So I also want to tell you a little bit about some research that I did last year when we had sort of been beginning to sort of be more explicit about students' assumptions and give them more opportunities to do things like pass the problem. I did some research last year on my students where I had them solve some open-end problems and I videotaped what they were doing and had them talk about their thought process and then analyze that. And I was looking at their responses and sort of contrasting them with another paper that I had read that looked at professional physicists. So, you know, postdocs and professors and looked at their ability to solve open-end problems. And what was really neat about the results of the research that I did was I found out that with five or six 90-minute lab sessions on open-end problem solving, my students were able to exhibit some very expert-like characteristics with very little time investment on my part. So that was really encouraging. They were able just with a little bit of practice, we were able to do things that even expert physicists should say they were experts in traditional problem solving. They weren't experts in the old defined problem solving. And that speaks to this idea that just because you're an expert in one thing doesn't necessarily mean you're an expert in another. So it was very encouraging to me to see these students get so much better at problem solving with such a minimal amount of time and put on my end. So I think that speaks to the importance of practice and purposeful, targeted practice as well, which was great. Now, the one piece that was a little bit weak in my students was this piece of metacognition, so self-monitoring what they were doing and asking themselves, so I got an answer, is that answer reasonable? Is it too big? Is it too small? That was a piece that was lacking, which I think there were some very good developmental psychology reasons why teenagers would have a problem with that, but I'm still interested in looking at are there ways that we can better encourage them to be more metacognitive to think about the process while they were solving problems. But it was very encouraging. It was sort of the first step. I'll probably do some additional follow-up research this year on a different group of students to see if I can extract some more information about what we do with science and math. So I'm cautiously optimistic about what we're doing here and think that it has some real possibility to help students become better at the problem-solving process. So kind of at the end of the day, I mean for you all the real issue is, what do I do? How do I take this back? What can I do to current practice to make it more consistent with this idea of problem-solving? So what I would urge you to think about here is to think about how could you take a traditional textbook problem and make it more aligned with this idea of purposeful problem-solving? So there's a fantastic head talk by a guy named Dan Meyer who is, I think he was a math teacher in California and now he's a graduate student, Stanford. But the link is here in PowerPoint. If you just google Dan Meyer and Ted Talk, you'll find it. But it's a great, great, great head talk about what differentiates exercises and problems, sort of textbook problems versus traditional problems, problem-solving that's a little bit more overfine. So I would urge you to check that out, especially for the math folks. But I think for other folks, even folks that aren't math, if you could just think for a minute about what does a textbook problem do for students that prevents them from thinking about some of these other issues and how could you tweak a textbook problem so it requires more thinking? How could you turn a textbook problem from an exercise or textbook exercise into a problem? So just think about that for a minute. And if anybody's got any suggestions or there are just simple ways, you don't have to start huge with this. You can start small. Just open up a textbook right now and look at it. What could you do to a textbook question to make it more of a problem than an exercise? Does anybody have any thoughts on how to do that? There's good wait time here. Take away information or add more? Absolutely. So throw in a couple of red herrings into the problem or take away information. Yeah, great. So again, one of the things that Dan Meyer talks about is how a traditional textbook problem, you need three pieces of information to solve the question and conveniently there are three pieces of information that are there. Maybe the real tricky ones have two, but absolutely by taking away some information or adding more, you make students have to think a little bit more. So other ideas about how to make a textbook exercise more of a problem? How to enhance the situation to require more assumptions? Yeah, absolutely. Right. So think about a situation that could potentially have, you know, how could you tweak the problem so it has multiple or the question so it has multiple answers based upon your assumptions? Right. So remove the cookbook process and ask students to create their, make the students create their own process. Yeah, absolutely. And that's a little bit more of a lab-based technique which is something I didn't touch on, but something that's certainly important. You know, sort of laboratory, I mean laboratory exercises should be about problem solving, right? You know, I have a question and I need to answer it, what do I have to do? So absolutely, yeah. You know, less cookbook type labs are a great way to get students to think a little bit more about that. Solve the problem two different ways. Right. And demonstrating that you could get to the answer this way or this way. Absolutely. Absolutely. So there's not just one way to do it. Yeah, these are all excellent ways to encourage students to be a little bit more purposeful and they're actually getting to think a little bit more about the problems that you're working on. So, and again, I mean, I understand that there are very real pressures of curriculum and content coverage and so I'm not advocating that everybody, you know, sort of goes out and scraps your curriculum and starts over again. I think it's important to, you know, you can integrate pieces of this strategy with minor tweaks to what you currently do. You don't have to completely overhaul what you're doing. If you leave here today with nothing else than knowing that there's a difference between an exercise and a problem and that problems tend to get students to think more, I think that's a key message and hopefully you can think about how to turn exercises and the problems as well. And if you have any questions about ideas or questions about how to do that in the future, I'll give you my email address here in a minute. Please feel free to forward those questions along. Okay. Sort of found that already. So I'm curious, so I've talked about some specific ways and other folks have given some good suggestions for how to encourage students to how to take textbook exercises and turn them into problems. But I'm curious if anybody else has other strategies or methods for getting students to problem solve, specific class or activities or specific techniques that you use with your students to encourage purposeful, goal-oriented, flexible problem solving. Anybody get anything that they could share? Ideas that they use? And there have been some good ones already, the ideas. Sort of more open-ended labs and multiple solution paths to problems. More assumptions, that sort of thing. Anybody have any other activities? Change your given value. Okay. So changing values in a given question. Mixing them up a little bit. I used to make my physics students follow a step-by-step process in solving problems. You had to write down given information problems, equations, solutions, and a check. Great. And we actually do, yeah, we do something similar at Science and Math. I mean, again, I mean, it's kind of a piece of that, but write a problem-solving process. And I like this idea of a check at the end, right? So I'm assuming that you're checking to see if the answer is reasonable. It doesn't make sense. And that's, yeah, absolutely. So that's a really important thing to do, really, or checking units, right? So that really encourages students to don't just stop when the calculator spits out the number, right? The calculator is only as smart as you make it. So if you make a typing mistake, then you might get an answer that isn't reasonable. So, and again, that really encourages students to be metacognitive, to think about their answer, to think about their thinking. Is this a reasonable number? And that's a really good last step as well. Yeah, great. I'm sure there are others as well. So kind of getting close to the end here, so we'll go ahead and wrap up. So some take-home messages from this, in addition to this idea of problem versus exercise. You know, hopefully it's obvious from the presentation, at least, that I think problem-solving is a really, really important skill. I mean, the rhetoric right now about sort of the 21st century economy and the skills that students are going to need and the jobs that they are going to have and even invented yet, that sort of thing. So we're in a world now where the sum of human knowledge you can access with a device the size of a credit card. So what students know and what they need to know, I think is a little different than what it was when I went through high school. So different skills set in problem-solving and open-ended problem-solving is certainly an important tool for them. Difference between problem and exercise as well. So don't reinvent the wheel. I think all good teachers are proud thieves, proud and honest thieves. And so, you know, there's a lot of great stuff out there already. So, you know, firmy questions are fantastic if you're a physics teacher. Just go look up firmy questions. Take things from other people. There's a lot of great information that's out there. If you want to steal anything from me, I'll be happy to send you some information as well. And don't be a martyr. I mean, do this. I think it's easier to do this sort of thing if you have help. So, you know, try to work with other people, try to collaborate. You know, if you're a science teacher and there's a math teacher, you can both try to sort of brainstorm with one another. If there are other science teachers at your middle school, if you're in a team with other folks, you know, trying to maybe a math-science combination of more sort of purposeful problem-solving with your students. That's really, really important. And finally, you know, don't go from zero to 60 in two nanoseconds. I mean, this is, you know, this is a gradual process. So start small. Unless you really want to start big, in which case, more power to you. But you don't necessarily have to change overnight. And actually, at Science and Math, it's taken us a number of years to get to where we currently are. And we're constantly tweaking. And we're constantly changing. I think I said this idea of writing down assumptions is about two years old now. So we're constantly looking at what we do and trying to evaluate and see if it's working. So, you know, the expectation of gradual change. I think change can be more sustainable. When, you know, sort of gradual and incremental. I think the chances of sort of buy-in from people around you and the chances of long-term success are probably better if you're starting small and integrating things over time. If you're really busy and pressed for time, it's more likely to stick down. So, yeah, just kind of four messages for you all to take home based on what we've talked about already. So I think Carol has a link to an online survey and evaluation. And we'd love to know if this information is useful to you all and if so, how it is and what you sort of got out of spending your time. We appreciate you spending your time here this afternoon. We know you all are busy. So thanks for joining us as well. There's my e-mail address. If you have any questions about this, I'm going to post the PowerPoint. And obviously the presentation will have that posted online as well. But if you have specific questions for me that you weren't able to ask or questions that come up, please feel free to contact me about anything and everything related to this topic. And I do, for people who want to see some primary source articles in the PowerPoint, I do have some references if you want to see a little bit more about what the research says about this. And I have more references, too, if you need them. So I have lots of references if you need them. So that is all that we have for today. Thank you for joining us. And yeah, thanks, everybody. We appreciate you participating. And hopefully we'll keep in touch. And if you have any questions, please do contact us. So I think we're just going to go ahead and exit. Maybe we'll just, we could pause here for just a second to see if there are any last comments. Yeah, I would actually be, you know, for middle school folks, I would actually be really curious to know kind of what are middle school students able to do with something like this? How, sort of how open-ended of a situation could a six or a seventh grader handle? You know, obviously my specialty is with older students. And so sometimes my perspective on what students can do can get a little bit more because of that. I'm going to make a great comment from one of the teachers talking about using a book of math mysteries with fourth to eighth graders with each mystery is two pages long and it requires students to weed out information, make assumptions, model, represent and solve the problem. That's great. That's right. And a comment from Victoria about our kids struggling, like your kids, yeah. Everybody struggles. Yeah, the science and math is interesting. The process to get into science and math is really competitive and so all of our students come here with a history of academic success. And so, you know, the first time they experienced academic difficulty is really a shock to them. So, you know, they've been successful using certain strategies prior to getting here. And so when you get them to try to ask them to do some things, why should I think? I've never had to think of that sort of thing. So, but, and again, I found out with honor students when I taught honors classes versus general classes of pro-atanic was similar thing and that honors kids were often much more resistant to this idea. Which is kind of ironic, but anyway. Okay, well, that about wraps it up. I'm going to... Here, it's my stroke, yeah. I think a lot of, this is hard stuff. It is not easy, to be sure. So, yeah, thank you, Victoria. And thank you all. I hope you all have a nice afternoon.