{"version":"1.0.0","segments":[{"speaker":"Pam Harris","startTime":1.95,"endTime":4.83,"body":"Hey, fellow"},{"speaker":"Pam Harris","startTime":1.95,"endTime":4.83,"body":"mathematicians. Welcome to the"},{"speaker":"Pam Harris","startTime":4.83,"endTime":8.64,"body":"podcast where Math is"},{"speaker":"Pam Harris","startTime":4.83,"endTime":8.64,"body":"Figure-Out-Able. I'm Pam."},{"speaker":"Kim Montague","startTime":8.85,"endTime":9.48,"body":"And I'm Kim."},{"speaker":"Pam Harris","startTime":9.84,"endTime":13.14,"body":"And we're here to"},{"speaker":"Pam Harris","startTime":9.84,"endTime":13.14,"body":"suggest that mathematizing is"},{"speaker":"Pam Harris","startTime":13.17,"endTime":16.23,"body":"not about mimicking, or rote"},{"speaker":"Pam Harris","startTime":13.17,"endTime":16.23,"body":"memorizing. But it's about"},{"speaker":"Pam Harris","startTime":16.26,"endTime":20.01,"body":"thinking, reasoning about"},{"speaker":"Pam Harris","startTime":16.26,"endTime":20.01,"body":"creating and using mental"},{"speaker":"Pam Harris","startTime":20.01,"endTime":24.03,"body":"mathematical relationships. That"},{"speaker":"Pam Harris","startTime":20.01,"endTime":24.03,"body":"mathematics class can be less"},{"speaker":"Pam Harris","startTime":24.03,"endTime":27.87,"body":"like it has been for so many of"},{"speaker":"Pam Harris","startTime":24.03,"endTime":27.87,"body":"us and more like mathematicians"},{"speaker":"Pam Harris","startTime":27.9,"endTime":32.01,"body":"working together. We answer the"},{"speaker":"Pam Harris","startTime":27.9,"endTime":32.01,"body":"question: if you're not teaching"},{"speaker":"Pam Harris","startTime":32.04,"endTime":33.66,"body":"algorithms, then what?"},{"speaker":"Kim Montague","startTime":34.65,"endTime":37.44,"body":"So today, Pam,"},{"speaker":"Kim Montague","startTime":34.65,"endTime":37.44,"body":"we're gonna dive into a hot"},{"speaker":"Kim Montague","startTime":37.44,"endTime":39.54,"body":"topic out in the world."},{"speaker":"Pam Harris","startTime":39.54,"endTime":40.23,"body":"Hot topic."},{"speaker":"Kim Montague","startTime":40.77,"endTime":43.62,"body":"And one that you"},{"speaker":"Kim Montague","startTime":40.77,"endTime":43.62,"body":"speak about quite a bit. And"},{"speaker":"Kim Montague","startTime":43.62,"endTime":48.9,"body":"that is Problem Strings, and"},{"speaker":"Kim Montague","startTime":43.62,"endTime":48.9,"body":"Problem or number Talks. So for"},{"speaker":"Kim Montague","startTime":48.9,"endTime":51.45,"body":"this episode, I'm just going to"},{"speaker":"Kim Montague","startTime":48.9,"endTime":51.45,"body":"lob some questions out to you"},{"speaker":"Kim Montague","startTime":51.45,"endTime":54.6,"body":"and get your perspective on some"},{"speaker":"Kim Montague","startTime":51.45,"endTime":54.6,"body":"key parts. Is that possible?"},{"speaker":"Pam Harris","startTime":54.6,"endTime":55.71,"body":"Absolutely. Yes,"},{"speaker":"Pam Harris","startTime":54.6,"endTime":55.71,"body":"let's do it."},{"speaker":"Pam Harris","startTime":55.92,"endTime":59.94,"body":"Alright. So first of all, you"},{"speaker":"Pam Harris","startTime":55.92,"endTime":59.94,"body":"call what we're going to talk"},{"speaker":"Pam Harris","startTime":59.94,"endTime":63.99,"body":"about today, Problem Talks,"},{"speaker":"Pam Harris","startTime":59.94,"endTime":63.99,"body":"where a lot of the world would"},{"speaker":"Pam Harris","startTime":63.99,"endTime":67.05,"body":"call them number talks. Can you"},{"speaker":"Pam Harris","startTime":63.99,"endTime":67.05,"body":"share a little bit about that?"},{"speaker":"Pam Harris","startTime":67.59,"endTime":71.52,"body":"Yeah, sure. So number talks are"},{"speaker":"Pam Harris","startTime":67.59,"endTime":71.52,"body":"great. I thoroughly respect the"},{"speaker":"Pam Harris","startTime":71.52,"endTime":73.68,"body":"authors of the number talk"},{"speaker":"Pam Harris","startTime":71.52,"endTime":73.68,"body":"books. I think they've done a"},{"speaker":"Pam Harris","startTime":73.68,"endTime":78.48,"body":"lot of good work. I think, all"},{"speaker":"Pam Harris","startTime":73.68,"endTime":78.48,"body":"of the blogs and the stuff on"},{"speaker":"Pam Harris","startTime":78.75,"endTime":81.93,"body":"MTBos, and there's a lot of"},{"speaker":"Pam Harris","startTime":78.75,"endTime":81.93,"body":"really good things out there,"},{"speaker":"Pam Harris","startTime":82.44,"endTime":85.2,"body":"where people are talking about"},{"speaker":"Pam Harris","startTime":82.44,"endTime":85.2,"body":"what they call number talks. And"},{"speaker":"Pam Harris","startTime":85.89,"endTime":88.17,"body":"like I said, I really appreciate"},{"speaker":"Pam Harris","startTime":85.89,"endTime":88.17,"body":"that work. So I just want to"},{"speaker":"Pam Harris","startTime":88.17,"endTime":92.85,"body":"start with well done, great job,"},{"speaker":"Pam Harris","startTime":88.17,"endTime":92.85,"body":"you have definitely added to our"},{"speaker":"Pam Harris","startTime":93.0,"endTime":96.18,"body":"repertoire of mathematics"},{"speaker":"Pam Harris","startTime":93.0,"endTime":96.18,"body":"teaching. However, I think it's"},{"speaker":"Pam Harris","startTime":96.18,"endTime":100.08,"body":"a little short sighted to call"},{"speaker":"Pam Harris","startTime":96.18,"endTime":100.08,"body":"them 'number talks' for a couple"},{"speaker":"Pam Harris","startTime":100.08,"endTime":102.84,"body":"of reasons. I would, for a"},{"speaker":"Pam Harris","startTime":100.08,"endTime":102.84,"body":"couple of reasons, I would"},{"speaker":"Pam Harris","startTime":102.84,"endTime":108.27,"body":"prefer to call them 'Problem"},{"speaker":"Pam Harris","startTime":102.84,"endTime":108.27,"body":"Talks'. I'm K-12. So I do work"},{"speaker":"Pam Harris","startTime":108.3,"endTime":110.94,"body":"Pre K-12. I do work with really,"},{"speaker":"Pam Harris","startTime":108.3,"endTime":110.94,"body":"teachers of really young"},{"speaker":"Pam Harris","startTime":110.94,"endTime":114.12,"body":"students. Sometimes I will say,"},{"speaker":"Pam Harris","startTime":110.94,"endTime":114.12,"body":"really young teachers, to me,"},{"speaker":"Pam Harris","startTime":114.15,"endTime":117.63,"body":"teachers of really young"},{"speaker":"Pam Harris","startTime":114.15,"endTime":117.63,"body":"students, to university people."},{"speaker":"Pam Harris","startTime":117.63,"endTime":123.12,"body":"We work together on teaching"},{"speaker":"Pam Harris","startTime":117.63,"endTime":123.12,"body":"pre-service teachers, and then"},{"speaker":"Pam Harris","startTime":123.12,"endTime":126.03,"body":"the gamut in between. So, you"},{"speaker":"Pam Harris","startTime":123.12,"endTime":126.03,"body":"know, high school was where I"},{"speaker":"Pam Harris","startTime":126.03,"endTime":129.75,"body":"started, and then I dove back in"},{"speaker":"Pam Harris","startTime":126.03,"endTime":129.75,"body":"and sort of consider myself an"},{"speaker":"Pam Harris","startTime":129.75,"endTime":135.54,"body":"expert now Pre K-12. So, because"},{"speaker":"Pam Harris","startTime":129.75,"endTime":135.54,"body":"of that, when I learned about"},{"speaker":"Pam Harris","startTime":135.54,"endTime":139.89,"body":"number talks to me, they're not"},{"speaker":"Pam Harris","startTime":135.54,"endTime":139.89,"body":"talks about 'number'. They're"},{"speaker":"Pam Harris","startTime":139.89,"endTime":144.48,"body":"talks about 'problems'. And"},{"speaker":"Pam Harris","startTime":139.89,"endTime":144.48,"body":"those problems could be number"},{"speaker":"Pam Harris","startTime":144.57,"endTime":147.42,"body":"oriented. They could be geometry"},{"speaker":"Pam Harris","startTime":144.57,"endTime":147.42,"body":"oriented. They could be"},{"speaker":"Pam Harris","startTime":147.69,"endTime":150.66,"body":"statistics oriented. Yeah, in"},{"speaker":"Pam Harris","startTime":147.69,"endTime":150.66,"body":"fact, Jo Boaler's just put out a"},{"speaker":"Pam Harris","startTime":150.66,"endTime":155.07,"body":"bunch of really nice statistic"},{"speaker":"Pam Harris","startTime":150.66,"endTime":155.07,"body":"talks called 'data talks'. But I"},{"speaker":"Pam Harris","startTime":155.07,"endTime":157.74,"body":"think we could have just called"},{"speaker":"Pam Harris","startTime":155.07,"endTime":157.74,"body":"them Problem Talks, and their"},{"speaker":"Pam Harris","startTime":157.74,"endTime":162.24,"body":"Problem Talks about statistical"},{"speaker":"Pam Harris","startTime":157.74,"endTime":162.24,"body":"stuff like data. So if we have"},{"speaker":"Pam Harris","startTime":162.24,"endTime":166.65,"body":"this more general, sort of,"},{"speaker":"Pam Harris","startTime":162.24,"endTime":166.65,"body":"these are Problem Talks, then we"},{"speaker":"Pam Harris","startTime":166.65,"endTime":169.98,"body":"can have specific Problem Talks"},{"speaker":"Pam Harris","startTime":166.65,"endTime":169.98,"body":"about or we can have Problem"},{"speaker":"Pam Harris","startTime":169.98,"endTime":174.36,"body":"Talks about specific topics in"},{"speaker":"Pam Harris","startTime":169.98,"endTime":174.36,"body":"math, and still use the same"},{"speaker":"Pam Harris","startTime":174.36,"endTime":178.02,"body":"sort of procedure, that they"},{"speaker":"Pam Harris","startTime":174.36,"endTime":178.02,"body":"have the same sort of"},{"speaker":"Pam Harris","startTime":178.02,"endTime":181.71,"body":"characteristics becomes the same"},{"speaker":"Pam Harris","startTime":178.02,"endTime":181.71,"body":"instructional routine, this is a"},{"speaker":"Pam Harris","startTime":181.71,"endTime":184.92,"body":"Problem Talk, oh, but we're"},{"speaker":"Pam Harris","startTime":181.71,"endTime":184.92,"body":"gonna now specify that we're in"},{"speaker":"Pam Harris","startTime":184.92,"endTime":188.22,"body":"these different sort of"},{"speaker":"Pam Harris","startTime":184.92,"endTime":188.22,"body":"categories. There's another"},{"speaker":"Pam Harris","startTime":188.22,"endTime":191.91,"body":"reason why I kind of push back"},{"speaker":"Pam Harris","startTime":188.22,"endTime":191.91,"body":"against number talks, or the"},{"speaker":"Pam Harris","startTime":191.91,"endTime":197.79,"body":"term number talks is because it"},{"speaker":"Pam Harris","startTime":191.91,"endTime":197.79,"body":"kind of, in the same way that I"},{"speaker":"Pam Harris","startTime":197.82,"endTime":200.4,"body":"pushed back a little bit against"},{"speaker":"Pam Harris","startTime":197.82,"endTime":200.4,"body":"people calling them 'math"},{"speaker":"Pam Harris","startTime":200.4,"endTime":204.24,"body":"talks', because then people say,"},{"speaker":"Pam Harris","startTime":200.4,"endTime":204.24,"body":"\"Oh, this is when we talk in"},{"speaker":"Pam Harris","startTime":204.24,"endTime":208.23,"body":"math.\" As if that's the only"},{"speaker":"Pam Harris","startTime":204.24,"endTime":208.23,"body":"time we talk in a math class. So"},{"speaker":"Pam Harris","startTime":208.23,"endTime":211.71,"body":"not true, right? Like, I want"},{"speaker":"Pam Harris","startTime":208.23,"endTime":211.71,"body":"kids talking all the time. It's"},{"speaker":"Pam Harris","startTime":211.71,"endTime":213.24,"body":"just that there's some times"},{"speaker":"Pam Harris","startTime":211.71,"endTime":213.24,"body":"where we're gonna have a"},{"speaker":"Pam Harris","startTime":213.24,"endTime":217.02,"body":"particular instructional"},{"speaker":"Pam Harris","startTime":213.24,"endTime":217.02,"body":"routine, and we have to call it"},{"speaker":"Pam Harris","startTime":217.02,"endTime":219.63,"body":"something so I'm okay calling it"},{"speaker":"Pam Harris","startTime":217.02,"endTime":219.63,"body":"a Problem Talk. Because we're"},{"speaker":"Pam Harris","startTime":219.63,"endTime":222.63,"body":"gonna talk about problems. So"},{"speaker":"Pam Harris","startTime":219.63,"endTime":222.63,"body":"therefore, it's a Problem Talk."},{"speaker":"Pam Harris","startTime":223.17,"endTime":225.51,"body":"And that's just it's a more"},{"speaker":"Pam Harris","startTime":223.17,"endTime":225.51,"body":"general name that I think fits a"},{"speaker":"Pam Harris","startTime":225.51,"endTime":227.7,"body":"little bit better. I don't have"},{"speaker":"Pam Harris","startTime":225.51,"endTime":227.7,"body":"any problem calling them number"},{"speaker":"Pam Harris","startTime":227.7,"endTime":232.8,"body":"talks, as long as we then"},{"speaker":"Pam Harris","startTime":227.7,"endTime":232.8,"body":"differentiate the instructional"},{"speaker":"Pam Harris","startTime":232.8,"endTime":236.13,"body":"routine from the other"},{"speaker":"Pam Harris","startTime":232.8,"endTime":236.13,"body":"instructional routine Problems"},{"speaker":"Pam Harris","startTime":236.13,"endTime":238.44,"body":"Strings, which we'll talk a"},{"speaker":"Pam Harris","startTime":236.13,"endTime":238.44,"body":"little bit more about later."},{"speaker":"Kim Montague","startTime":238.47,"endTime":240.42,"body":"Yeah, so you're"},{"speaker":"Kim Montague","startTime":238.47,"endTime":240.42,"body":"gonna hear us talk today and"},{"speaker":"Kim Montague","startTime":240.42,"endTime":244.17,"body":"call them Problem Talks. So"},{"speaker":"Kim Montague","startTime":240.42,"endTime":244.17,"body":"share with us a little bit about"},{"speaker":"Kim Montague","startTime":244.17,"endTime":246.39,"body":"your goals for a Problem Talk."},{"speaker":"Pam Harris","startTime":246.66,"endTime":248.94,"body":"Yeah, totally cool."},{"speaker":"Pam Harris","startTime":246.66,"endTime":248.94,"body":"So again, I like Problem Talks."},{"speaker":"Pam Harris","startTime":248.94,"endTime":252.57,"body":"They're excellent, an excellent"},{"speaker":"Pam Harris","startTime":248.94,"endTime":252.57,"body":"instructional routine. But I"},{"speaker":"Pam Harris","startTime":252.57,"endTime":255.24,"body":"think they have different goals"},{"speaker":"Pam Harris","startTime":252.57,"endTime":255.24,"body":"than other instructional"},{"speaker":"Pam Harris","startTime":255.24,"endTime":257.76,"body":"routines. So I'm glad you asked"},{"speaker":"Pam Harris","startTime":255.24,"endTime":257.76,"body":"me about goals right off the"},{"speaker":"Pam Harris","startTime":257.76,"endTime":262.23,"body":"bat. So I think there's a couple"},{"speaker":"Pam Harris","startTime":257.76,"endTime":262.23,"body":"short lived goals for Problem"},{"speaker":"Pam Harris","startTime":262.26,"endTime":265.65,"body":"Talks, and then a much longer"},{"speaker":"Pam Harris","startTime":262.26,"endTime":265.65,"body":"lived goal that lives and lives"},{"speaker":"Pam Harris","startTime":265.65,"endTime":269.01,"body":"and lives. So the short lived"},{"speaker":"Pam Harris","startTime":265.65,"endTime":269.01,"body":"goals. One of them is to sort of"},{"speaker":"Pam Harris","startTime":269.01,"endTime":273.06,"body":"poke around, like, I kind of"},{"speaker":"Pam Harris","startTime":269.01,"endTime":273.06,"body":"want to, it's formative"},{"speaker":"Pam Harris","startTime":273.06,"endTime":275.46,"body":"assessment. I want to sort of"},{"speaker":"Pam Harris","startTime":273.06,"endTime":275.46,"body":"feel where my students are, get"},{"speaker":"Pam Harris","startTime":275.46,"endTime":277.62,"body":"a flavor for how they're"},{"speaker":"Pam Harris","startTime":275.46,"endTime":277.62,"body":"thinking about something. So"},{"speaker":"Pam Harris","startTime":277.74,"endTime":281.46,"body":"even before I start a unit on"},{"speaker":"Pam Harris","startTime":277.74,"endTime":281.46,"body":"something, I might give them a"},{"speaker":"Pam Harris","startTime":281.49,"endTime":284.22,"body":"Problem Talk, where I throw out"},{"speaker":"Pam Harris","startTime":281.49,"endTime":284.22,"body":"a problem. It's a rich problem,"},{"speaker":"Pam Harris","startTime":284.22,"endTime":287.28,"body":"you could use lots of strategies"},{"speaker":"Pam Harris","startTime":284.22,"endTime":287.28,"body":"to solve it, and see what's"},{"speaker":"Pam Harris","startTime":287.28,"endTime":290.64,"body":"happening in my classroom before"},{"speaker":"Pam Harris","startTime":287.28,"endTime":290.64,"body":"I dive in with the unit, not"},{"speaker":"Pam Harris","startTime":290.64,"endTime":293.28,"body":"knowing what they're already"},{"speaker":"Pam Harris","startTime":290.64,"endTime":293.28,"body":"doing with the material. So if I"},{"speaker":"Pam Harris","startTime":293.34,"endTime":296.16,"body":"throw out a Problem Talk, then I"},{"speaker":"Pam Harris","startTime":293.34,"endTime":296.16,"body":"can get a really good sort of"},{"speaker":"Pam Harris","startTime":296.16,"endTime":298.89,"body":"formative idea of what's"},{"speaker":"Pam Harris","startTime":296.16,"endTime":298.89,"body":"happening out there. And then I"},{"speaker":"Pam Harris","startTime":298.89,"endTime":302.28,"body":"can respond, my instruction can"},{"speaker":"Pam Harris","startTime":298.89,"endTime":302.28,"body":"respond. But then I've done"},{"speaker":"Pam Harris","startTime":302.28,"endTime":304.29,"body":"that, right? And so now it's"},{"speaker":"Pam Harris","startTime":302.28,"endTime":304.29,"body":"time to move in and actually"},{"speaker":"Pam Harris","startTime":304.29,"endTime":306.99,"body":"develop relationships. There are"},{"speaker":"Pam Harris","startTime":304.29,"endTime":306.99,"body":"better things to use to then"},{"speaker":"Pam Harris","startTime":306.99,"endTime":310.47,"body":"develop relationships. So it's"},{"speaker":"Pam Harris","startTime":306.99,"endTime":310.47,"body":"good to kind of poke around, now"},{"speaker":"Pam Harris","startTime":310.47,"endTime":313.11,"body":"move on to do other things."},{"speaker":"Pam Harris","startTime":310.47,"endTime":313.11,"body":"There's another short lived one,"},{"speaker":"Pam Harris","startTime":313.23,"endTime":317.04,"body":"which is to prove to students"},{"speaker":"Pam Harris","startTime":313.23,"endTime":317.04,"body":"that there's more than one way"},{"speaker":"Pam Harris","startTime":317.04,"endTime":320.82,"body":"to solve the problem. Many of us"},{"speaker":"Pam Harris","startTime":317.04,"endTime":320.82,"body":"grew up in circumstances where"},{"speaker":"Pam Harris","startTime":320.82,"endTime":323.34,"body":"we were given the algorithm. It"},{"speaker":"Pam Harris","startTime":320.82,"endTime":323.34,"body":"was one and only one way to"},{"speaker":"Pam Harris","startTime":323.34,"endTime":325.74,"body":"solve problems. Maybe we did"},{"speaker":"Pam Harris","startTime":323.34,"endTime":325.74,"body":"stuff in our heads, but it was"},{"speaker":"Pam Harris","startTime":325.74,"endTime":329.31,"body":"never talked about or showed or"},{"speaker":"Pam Harris","startTime":325.74,"endTime":329.31,"body":"whatever. So Problem Talks can"},{"speaker":"Pam Harris","startTime":329.31,"endTime":333.84,"body":"be a great venue to prove to"},{"speaker":"Pam Harris","startTime":329.31,"endTime":333.84,"body":"students and teachers, parents,"},{"speaker":"Pam Harris","startTime":333.84,"endTime":336.39,"body":"everybody that there's more than"},{"speaker":"Pam Harris","startTime":333.84,"endTime":336.39,"body":"one way to solve a problem that"},{"speaker":"Pam Harris","startTime":336.39,"endTime":338.85,"body":"we could use relationships and"},{"speaker":"Pam Harris","startTime":336.39,"endTime":338.85,"body":"connections to solve problems."},{"speaker":"Pam Harris","startTime":339.12,"endTime":343.35,"body":"But y'all that needs to be short"},{"speaker":"Pam Harris","startTime":339.12,"endTime":343.35,"body":"lived, too. I fear that way too"},{"speaker":"Pam Harris","startTime":343.35,"endTime":347.34,"body":"many people continue to have"},{"speaker":"Pam Harris","startTime":343.35,"endTime":347.34,"body":"that purpose, that they're like,"},{"speaker":"Pam Harris","startTime":347.37,"endTime":348.96,"body":"\"No, I need to prove to these"},{"speaker":"Pam Harris","startTime":347.37,"endTime":348.96,"body":"kids, there's more the way to"},{"speaker":"Pam Harris","startTime":348.96,"endTime":351.78,"body":"solve it, look, see, see, this"},{"speaker":"Pam Harris","startTime":348.96,"endTime":351.78,"body":"person did that way. And that"},{"speaker":"Pam Harris","startTime":351.78,"endTime":354.21,"body":"kid did this way, that student"},{"speaker":"Pam Harris","startTime":351.78,"endTime":354.21,"body":"did it this way. And yay, look"},{"speaker":"Pam Harris","startTime":354.21,"endTime":357.66,"body":"how flexible we are.\" When in"},{"speaker":"Pam Harris","startTime":354.21,"endTime":357.66,"body":"reality, the class isn't"},{"speaker":"Pam Harris","startTime":357.66,"endTime":361.14,"body":"flexible at all. The first kid"},{"speaker":"Pam Harris","startTime":357.66,"endTime":361.14,"body":"doesn't know the second"},{"speaker":"Pam Harris","startTime":361.14,"endTime":363.12,"body":"student's strategy. And the"},{"speaker":"Pam Harris","startTime":361.14,"endTime":363.12,"body":"second student doesn't know the"},{"speaker":"Pam Harris","startTime":363.12,"endTime":366.24,"body":"third. And they didn't develop"},{"speaker":"Pam Harris","startTime":363.12,"endTime":366.24,"body":"it right there just by seeing"},{"speaker":"Pam Harris","startTime":366.24,"endTime":370.8,"body":"it. We have to do other more"},{"speaker":"Pam Harris","startTime":366.24,"endTime":370.8,"body":"focused things to help students"},{"speaker":"Pam Harris","startTime":370.8,"endTime":373.38,"body":"develop, most students develop"},{"speaker":"Pam Harris","startTime":370.8,"endTime":373.38,"body":"those strategies. Every once in"},{"speaker":"Pam Harris","startTime":373.38,"endTime":376.65,"body":"a while, Kim and I'll see"},{"speaker":"Pam Harris","startTime":373.38,"endTime":376.65,"body":"somebody use a strategy and bam,"},{"speaker":"Pam Harris","startTime":376.68,"endTime":379.92,"body":"we've got it, we own it. That's"},{"speaker":"Pam Harris","startTime":376.68,"endTime":379.92,"body":"probably true for everybody that"},{"speaker":"Pam Harris","startTime":379.92,"endTime":383.25,"body":"they can grab some things. It's"},{"speaker":"Pam Harris","startTime":379.92,"endTime":383.25,"body":"right on their zone, or the edge"},{"speaker":"Pam Harris","startTime":383.25,"endTime":385.17,"body":"of their zone of proximal"},{"speaker":"Pam Harris","startTime":383.25,"endTime":385.17,"body":"development. So they grab it,"},{"speaker":"Pam Harris","startTime":385.86,"endTime":389.67,"body":"they're ready to dive into it."},{"speaker":"Pam Harris","startTime":385.86,"endTime":389.67,"body":"Most students most of the time"},{"speaker":"Pam Harris","startTime":389.67,"endTime":393.57,"body":"need more concerted, focused"},{"speaker":"Pam Harris","startTime":389.67,"endTime":393.57,"body":"effort to help them develop the"},{"speaker":"Pam Harris","startTime":393.57,"endTime":397.05,"body":"relationships necessary to learn"},{"speaker":"Pam Harris","startTime":393.57,"endTime":397.05,"body":"a particular strategy. So it's"},{"speaker":"Pam Harris","startTime":397.05,"endTime":400.26,"body":"not enough for us to just say,"},{"speaker":"Pam Harris","startTime":397.05,"endTime":400.26,"body":"\"How'd you do it? How did you do"},{"speaker":"Pam Harris","startTime":400.26,"endTime":402.9,"body":"it? How'd you do it,\""},{"speaker":"Pam Harris","startTime":400.26,"endTime":402.9,"body":"continually over and over and"},{"speaker":"Pam Harris","startTime":402.9,"endTime":405.78,"body":"over again and expect that"},{"speaker":"Pam Harris","startTime":402.9,"endTime":405.78,"body":"students will pick up those"},{"speaker":"Pam Harris","startTime":405.78,"endTime":410.88,"body":"strategies. So it's, Problem"},{"speaker":"Pam Harris","startTime":405.78,"endTime":410.88,"body":"Talks can have two fine purposes"},{"speaker":"that are short lived","startTime":410.88,"endTime":413.88,"body":"one to"},{"speaker":"that are short lived","startTime":410.88,"endTime":413.88,"body":"poke around, and two that"},{"speaker":"that are short lived","startTime":413.88,"endTime":415.83,"body":"there's more than one way to"},{"speaker":"that are short lived","startTime":413.88,"endTime":415.83,"body":"solve the problem. But once"},{"speaker":"that are short lived","startTime":415.83,"endTime":418.92,"body":"you've done that, then we need"},{"speaker":"that are short lived","startTime":415.83,"endTime":418.92,"body":"to do other things. So what's"},{"speaker":"that are short lived","startTime":418.92,"endTime":422.88,"body":"the major strategy? The major"},{"speaker":"that are short lived","startTime":418.92,"endTime":422.88,"body":"strategy that we want to use"},{"speaker":"that are short lived","startTime":422.88,"endTime":427.59,"body":"Problem Talks for is to compare"},{"speaker":"that are short lived","startTime":422.88,"endTime":427.59,"body":"already constructed strategies"},{"speaker":"that are short lived","startTime":427.59,"endTime":432.27,"body":"for efficiency. Now, there's a"},{"speaker":"that are short lived","startTime":427.59,"endTime":432.27,"body":"lot to unpack there. We want to"},{"speaker":"that are short lived","startTime":432.27,"endTime":435.45,"body":"compare already constructed"},{"speaker":"that are short lived","startTime":432.27,"endTime":435.45,"body":"strategies. That means we've"},{"speaker":"that are short lived","startTime":435.45,"endTime":438.12,"body":"already had to construct it, not"},{"speaker":"that are short lived","startTime":435.45,"endTime":438.12,"body":"just a kid has one and a"},{"speaker":"that are short lived","startTime":438.12,"endTime":440.88,"body":"different kid has another. But"},{"speaker":"that are short lived","startTime":438.12,"endTime":440.88,"body":"we need a whole class to be"},{"speaker":"that are short lived","startTime":440.88,"endTime":442.98,"body":"messing around with a few"},{"speaker":"that are short lived","startTime":440.88,"endTime":442.98,"body":"strategies, or at least two"},{"speaker":"that are short lived","startTime":442.98,"endTime":446.46,"body":"strategies. Now, let's compare."},{"speaker":"that are short lived","startTime":442.98,"endTime":446.46,"body":"Now I give you a rich Problem"},{"speaker":"that are short lived","startTime":446.46,"endTime":450.99,"body":"Talk, a rich problem where we"},{"speaker":"that are short lived","startTime":446.46,"endTime":450.99,"body":"can now discuss, ooh, that"},{"speaker":"that are short lived","startTime":450.99,"endTime":455.94,"body":"strategy or this strategy and"},{"speaker":"that are short lived","startTime":450.99,"endTime":455.94,"body":"why. That's the major,"},{"speaker":"that are short lived","startTime":455.97,"endTime":461.04,"body":"overarching, ongoing, forever"},{"speaker":"that are short lived","startTime":455.97,"endTime":461.04,"body":"living purpose, for a Problem"},{"speaker":"that are short lived","startTime":461.04,"endTime":464.91,"body":"Talk to compare those already"},{"speaker":"that are short lived","startTime":461.04,"endTime":464.91,"body":"created already developed"},{"speaker":"that are short lived","startTime":464.91,"endTime":467.64,"body":"strategies towards efficiency."},{"speaker":"that are short lived","startTime":464.91,"endTime":467.64,"body":"Because now we want students to"},{"speaker":"that are short lived","startTime":467.64,"endTime":470.94,"body":"be able to choose strategies. So"},{"speaker":"that are short lived","startTime":467.64,"endTime":470.94,"body":"there's the main reason."},{"speaker":"Kim Montague","startTime":471.18,"endTime":473.22,"body":"So you do think"},{"speaker":"Kim Montague","startTime":471.18,"endTime":473.22,"body":"that they're valuable?"},{"speaker":"Pam Harris","startTime":473.64,"endTime":476.73,"body":"Absolutely. In fact,"},{"speaker":"Pam Harris","startTime":473.64,"endTime":476.73,"body":"let me prove it to you. They're"},{"speaker":"Pam Harris","startTime":476.73,"endTime":480.48,"body":"so valuable. I created"},{"speaker":"Pam Harris","startTime":476.73,"endTime":480.48,"body":"MathStratChat. Like"},{"speaker":"Pam Harris","startTime":480.51,"endTime":484.14,"body":"MathStratChat is a global"},{"speaker":"Pam Harris","startTime":480.51,"endTime":484.14,"body":"Problem Talk, where once a week"},{"speaker":"Pam Harris","startTime":484.14,"endTime":486.48,"body":"I throw out a problem and the"},{"speaker":"Pam Harris","startTime":484.14,"endTime":486.48,"body":"entire world throws in their"},{"speaker":"Pam Harris","startTime":486.48,"endTime":488.82,"body":"strategies. And you might be"},{"speaker":"Pam Harris","startTime":486.48,"endTime":488.82,"body":"like, \"Oh, Pam, I learned so"},{"speaker":"Pam Harris","startTime":488.82,"endTime":491.7,"body":"much from MathStratChat.\" Yeah,"},{"speaker":"Pam Harris","startTime":488.82,"endTime":491.7,"body":"absolutely. But I bet you would"},{"speaker":"Pam Harris","startTime":491.7,"endTime":495.81,"body":"have learned more quicker if"},{"speaker":"Pam Harris","startTime":491.7,"endTime":495.81,"body":"we'd been doing more focused"},{"speaker":"Pam Harris","startTime":495.81,"endTime":499.56,"body":"work towards actually developing"},{"speaker":"Pam Harris","startTime":495.81,"endTime":499.56,"body":"particular strategies. Yeah, for"},{"speaker":"Pam Harris","startTime":499.56,"endTime":502.38,"body":"most students need a bit more"},{"speaker":"Pam Harris","startTime":499.56,"endTime":502.38,"body":"focused work. But I love them,"},{"speaker":"Pam Harris","startTime":502.38,"endTime":504.69,"body":"right? We do MathStratChat once"},{"speaker":"Pam Harris","startTime":502.38,"endTime":504.69,"body":"a week, I put a lot of time and"},{"speaker":"Pam Harris","startTime":504.69,"endTime":508.32,"body":"effort and love the outcomes. I"},{"speaker":"Pam Harris","startTime":504.69,"endTime":508.32,"body":"love the response. We are"},{"speaker":"Pam Harris","startTime":508.32,"endTime":511.08,"body":"getting response from all around"},{"speaker":"Pam Harris","startTime":508.32,"endTime":511.08,"body":"the world. It's so fun to read"},{"speaker":"Pam Harris","startTime":511.08,"endTime":514.02,"body":"the different ways that people"},{"speaker":"Pam Harris","startTime":511.08,"endTime":514.02,"body":"are solving problems. So the"},{"speaker":"Pam Harris","startTime":514.02,"endTime":517.5,"body":"global Problem Talk is"},{"speaker":"Pam Harris","startTime":514.02,"endTime":517.5,"body":"MathStratChat. So of course, I"},{"speaker":"Pam Harris","startTime":517.5,"endTime":519.0,"body":"think they're wonderful. I love"},{"speaker":"Pam Harris","startTime":517.5,"endTime":519.0,"body":"them."},{"speaker":"Kim Montague","startTime":519.33,"endTime":521.94,"body":"So let's talk"},{"speaker":"Kim Montague","startTime":519.33,"endTime":521.94,"body":"about this other focused thing"},{"speaker":"Kim Montague","startTime":521.97,"endTime":524.64,"body":"that you are talking about. And"},{"speaker":"Kim Montague","startTime":521.97,"endTime":524.64,"body":"this is kind of what you're"},{"speaker":"Kim Montague","startTime":524.64,"endTime":529.47,"body":"known for, right? You emphasize"},{"speaker":"Kim Montague","startTime":524.64,"endTime":529.47,"body":"Problem Strings. Tell us a"},{"speaker":"Kim Montague","startTime":529.47,"endTime":530.49,"body":"little bit about those."},{"speaker":"Pam Harris","startTime":531.15,"endTime":534.39,"body":"So Problem Strings"},{"speaker":"Pam Harris","startTime":531.15,"endTime":534.39,"body":"are also an instructional"},{"speaker":"Pam Harris","startTime":534.39,"endTime":537.45,"body":"routine and the brilliance of"},{"speaker":"Pam Harris","startTime":534.39,"endTime":537.45,"body":"instructional routines is that"},{"speaker":"Pam Harris","startTime":537.45,"endTime":542.22,"body":"they can become routine. So that"},{"speaker":"Pam Harris","startTime":537.45,"endTime":542.22,"body":"as the what I'm supposed to do,"},{"speaker":"Pam Harris","startTime":542.22,"endTime":544.86,"body":"and how it looks, and what"},{"speaker":"Pam Harris","startTime":542.22,"endTime":544.86,"body":"happens here, as that becomes"},{"speaker":"Pam Harris","startTime":544.86,"endTime":548.52,"body":"routine, then students can not"},{"speaker":"Pam Harris","startTime":544.86,"endTime":548.52,"body":"put their mental and emotional"},{"speaker":"Pam Harris","startTime":548.52,"endTime":552.06,"body":"energy into knowing what to do."},{"speaker":"Pam Harris","startTime":548.52,"endTime":552.06,"body":"They can put their mental and"},{"speaker":"Pam Harris","startTime":552.06,"endTime":555.75,"body":"emotional energy into playing"},{"speaker":"Pam Harris","startTime":552.06,"endTime":555.75,"body":"with the numbers, and developing"},{"speaker":"Pam Harris","startTime":555.75,"endTime":559.2,"body":"the strategies, and developing"},{"speaker":"Pam Harris","startTime":555.75,"endTime":559.2,"body":"the relationships, and comparing"},{"speaker":"Pam Harris","startTime":559.2,"endTime":561.33,"body":"their strategies with others,"},{"speaker":"Pam Harris","startTime":559.2,"endTime":561.33,"body":"and all the kinds of things we"},{"speaker":"Pam Harris","startTime":561.33,"endTime":564.09,"body":"want to happen in an"},{"speaker":"Pam Harris","startTime":561.33,"endTime":564.09,"body":"instructional routine. So"},{"speaker":"Pam Harris","startTime":564.09,"endTime":567.42,"body":"Problem Strings are this really,"},{"speaker":"Pam Harris","startTime":564.09,"endTime":567.42,"body":"really important instructional"},{"speaker":"Pam Harris","startTime":567.42,"endTime":571.44,"body":"routine that then fill the"},{"speaker":"Pam Harris","startTime":567.42,"endTime":571.44,"body":"purpose that I just said Problem"},{"speaker":"Pam Harris","startTime":571.44,"endTime":574.62,"body":"Talks don't quite do. Problem"},{"speaker":"Pam Harris","startTime":571.44,"endTime":574.62,"body":"Talks don't help students"},{"speaker":"Pam Harris","startTime":574.62,"endTime":578.1,"body":"necessarily develop the"},{"speaker":"Pam Harris","startTime":574.62,"endTime":578.1,"body":"relationships that they need in"},{"speaker":"Pam Harris","startTime":578.1,"endTime":581.73,"body":"order for strategies to become"},{"speaker":"Pam Harris","startTime":578.1,"endTime":581.73,"body":"natural outcomes. Problem"},{"speaker":"Pam Harris","startTime":581.73,"endTime":587.07,"body":"Strings are the vehicle to"},{"speaker":"Pam Harris","startTime":581.73,"endTime":587.07,"body":"develop. They are the vehicle"},{"speaker":"Pam Harris","startTime":587.07,"endTime":591.27,"body":"for construction, for having"},{"speaker":"Pam Harris","startTime":587.07,"endTime":591.27,"body":"kids' brains literally change"},{"speaker":"Pam Harris","startTime":591.27,"endTime":595.74,"body":"into more and more sophisticated"},{"speaker":"Pam Harris","startTime":591.27,"endTime":595.74,"body":"thinkers. So what is a Problem"},{"speaker":"Pam Harris","startTime":595.74,"endTime":600.75,"body":"String? A Problem String is a"},{"speaker":"Pam Harris","startTime":595.74,"endTime":600.75,"body":"string or series of related"},{"speaker":"Pam Harris","startTime":600.75,"endTime":605.97,"body":"problems that are purposefully"},{"speaker":"Pam Harris","startTime":600.75,"endTime":605.97,"body":"designed and purposely sequenced"},{"speaker":"Pam Harris","startTime":606.15,"endTime":609.24,"body":"in order to construct mental"},{"speaker":"Pam Harris","startTime":606.15,"endTime":609.24,"body":"relationships in the learner's"},{"speaker":"Pam Harris","startTime":609.24,"endTime":612.45,"body":"head so that strategies, models,"},{"speaker":"Pam Harris","startTime":609.24,"endTime":612.45,"body":"and big ideas become natural"},{"speaker":"Pam Harris","startTime":612.45,"endTime":613.02,"body":"outcomes."},{"speaker":"Kim Montague","startTime":613.05,"endTime":615.51,"body":"So what is the"},{"speaker":"Kim Montague","startTime":613.05,"endTime":615.51,"body":"purpose of a Problem String?"},{"speaker":"Pam Harris","startTime":616.14,"endTime":619.17,"body":"The purpose of a"},{"speaker":"Pam Harris","startTime":616.14,"endTime":619.17,"body":"Problem String is to construct."},{"speaker":"Pam Harris","startTime":619.2,"endTime":622.95,"body":"It is to develop, it is to"},{"speaker":"Pam Harris","startTime":619.2,"endTime":622.95,"body":"literally help students' brains"},{"speaker":"Pam Harris","startTime":622.95,"endTime":626.19,"body":"get more and more sophisticated"},{"speaker":"Pam Harris","startTime":622.95,"endTime":626.19,"body":"as they think. Which means that"},{"speaker":"Pam Harris","startTime":626.19,"endTime":628.59,"body":"we use Problem Strings to help"},{"speaker":"Pam Harris","startTime":626.19,"endTime":628.59,"body":"students construct"},{"speaker":"Pam Harris","startTime":628.59,"endTime":631.74,"body":"relationships, which turn into"},{"speaker":"Pam Harris","startTime":628.59,"endTime":631.74,"body":"strategies. So that's the place"},{"speaker":"Pam Harris","startTime":631.92,"endTime":635.58,"body":"where we 'teach' strategies, we"},{"speaker":"Pam Harris","startTime":631.92,"endTime":635.58,"body":"don't 'direct teach' strategies."},{"speaker":"Pam Harris","startTime":635.58,"endTime":638.94,"body":"It's not about 'I do, we do, you"},{"speaker":"Pam Harris","startTime":635.58,"endTime":638.94,"body":"do.\" We use Problem Strings to"},{"speaker":"Pam Harris","startTime":638.94,"endTime":642.36,"body":"help students learn those"},{"speaker":"Pam Harris","startTime":638.94,"endTime":642.36,"body":"strategies and models and big"},{"speaker":"Pam Harris","startTime":642.36,"endTime":645.93,"body":"ideas as well. But it's the huge"},{"speaker":"Pam Harris","startTime":642.36,"endTime":645.93,"body":"place where we learn strategies."},{"speaker":"Pam Harris","startTime":645.93,"endTime":648.54,"body":"So let me tell you some things"},{"speaker":"Pam Harris","startTime":645.93,"endTime":648.54,"body":"that are particular about"},{"speaker":"Pam Harris","startTime":648.54,"endTime":652.11,"body":"Problem Strings. So like I said,"},{"speaker":"Pam Harris","startTime":648.54,"endTime":652.11,"body":"it's a series of related"},{"speaker":"Pam Harris","startTime":652.11,"endTime":654.96,"body":"problems. So if you just got one"},{"speaker":"Pam Harris","startTime":652.11,"endTime":654.96,"body":"problem, that's not a Problem"},{"speaker":"Pam Harris","startTime":654.96,"endTime":657.75,"body":"String. If you've got a bunch of"},{"speaker":"Pam Harris","startTime":654.96,"endTime":657.75,"body":"problems, but it's kind of like"},{"speaker":"Pam Harris","startTime":657.78,"endTime":661.11,"body":"a menu that you can choose from,"},{"speaker":"Pam Harris","startTime":657.78,"endTime":661.11,"body":"that's also not a Problem"},{"speaker":"Pam Harris","startTime":661.11,"endTime":664.38,"body":"String. Problem Strings are in"},{"speaker":"Pam Harris","startTime":661.11,"endTime":664.38,"body":"particular order, the order"},{"speaker":"Pam Harris","startTime":664.38,"endTime":670.23,"body":"matters, they are designed to"},{"speaker":"Pam Harris","startTime":664.38,"endTime":670.23,"body":"help develop. So it's not about"},{"speaker":"Pam Harris","startTime":670.23,"endTime":672.66,"body":"just picking and choosing"},{"speaker":"Pam Harris","startTime":670.23,"endTime":672.66,"body":"between problems. It's not sort"},{"speaker":"Pam Harris","startTime":672.66,"endTime":676.41,"body":"of a random, unrelated group of"},{"speaker":"Pam Harris","startTime":672.66,"endTime":676.41,"body":"problems, or even related that"},{"speaker":"Pam Harris","startTime":676.41,"endTime":680.19,"body":"you pick and choose from. But"},{"speaker":"Pam Harris","startTime":676.41,"endTime":680.19,"body":"it's the sequence matters. So if"},{"speaker":"Pam Harris","startTime":680.19,"endTime":682.92,"body":"the sequence matters, and we're"},{"speaker":"Pam Harris","startTime":680.19,"endTime":682.92,"body":"helping students develop those"},{"speaker":"Pam Harris","startTime":682.92,"endTime":686.19,"body":"relationships, then that's a"},{"speaker":"Pam Harris","startTime":682.92,"endTime":686.19,"body":"Problem String. They're also"},{"speaker":"Pam Harris","startTime":686.19,"endTime":691.05,"body":"focused. So a Problem Talk is"},{"speaker":"Pam Harris","startTime":686.19,"endTime":691.05,"body":"much more, it's less focused."},{"speaker":"Pam Harris","startTime":691.05,"endTime":694.71,"body":"It's like, however you do it is"},{"speaker":"Pam Harris","startTime":691.05,"endTime":694.71,"body":"a great. We're going to compare"},{"speaker":"Pam Harris","startTime":694.71,"endTime":698.46,"body":"those strategies. In a Problem"},{"speaker":"Pam Harris","startTime":694.71,"endTime":698.46,"body":"String, it's more focused. It's"},{"speaker":"Pam Harris","startTime":698.46,"endTime":701.58,"body":"not laser focused. We're still"},{"speaker":"Pam Harris","startTime":698.46,"endTime":701.58,"body":"letting students solve the"},{"speaker":"Pam Harris","startTime":701.58,"endTime":705.72,"body":"problem any way they can. So"},{"speaker":"Pam Harris","startTime":701.58,"endTime":705.72,"body":"when we give students a problem"},{"speaker":"Pam Harris","startTime":705.72,"endTime":709.41,"body":"in a string, we don't say, \"Use"},{"speaker":"Pam Harris","startTime":705.72,"endTime":709.41,"body":"this strategy.\" We say, \"Solve"},{"speaker":"Pam Harris","startTime":709.41,"endTime":712.65,"body":"it any way you want to.\" But"},{"speaker":"Pam Harris","startTime":709.41,"endTime":712.65,"body":"then we share the strategies"},{"speaker":"Pam Harris","startTime":712.68,"endTime":716.13,"body":"that will help towards that"},{"speaker":"Pam Harris","startTime":712.68,"endTime":716.13,"body":"focus. We know what the focus of"},{"speaker":"Pam Harris","startTime":716.13,"endTime":718.26,"body":"the string is, as teachers if"},{"speaker":"Pam Harris","startTime":716.13,"endTime":718.26,"body":"we're giving, if we're doing"},{"speaker":"Pam Harris","startTime":718.26,"endTime":722.67,"body":"that Problem String. And so we"},{"speaker":"Pam Harris","startTime":718.26,"endTime":722.67,"body":"craft the conversations around"},{"speaker":"Pam Harris","startTime":722.67,"endTime":725.76,"body":"where we're trying to go. Now,"},{"speaker":"Pam Harris","startTime":722.67,"endTime":725.76,"body":"the first time that you do a"},{"speaker":"Pam Harris","startTime":725.76,"endTime":730.08,"body":"Problem String, you will be less"},{"speaker":"Pam Harris","startTime":725.76,"endTime":730.08,"body":"focused. You'll entertain more"},{"speaker":"Pam Harris","startTime":730.08,"endTime":733.92,"body":"strategies. And then you sort"},{"speaker":"Pam Harris","startTime":730.08,"endTime":733.92,"body":"of, I kind of picture like"},{"speaker":"Pam Harris","startTime":733.92,"endTime":736.59,"body":"helping students focus on the"},{"speaker":"Pam Harris","startTime":733.92,"endTime":736.59,"body":"relationships that we want to"},{"speaker":"Pam Harris","startTime":736.59,"endTime":739.89,"body":"focus on. Kind of like I'm"},{"speaker":"Pam Harris","startTime":736.59,"endTime":739.89,"body":"picturing, like a spotlight kind"},{"speaker":"Pam Harris","startTime":739.89,"endTime":743.76,"body":"of focuses by crafting that"},{"speaker":"Pam Harris","startTime":739.89,"endTime":743.76,"body":"conversation to help them kind"},{"speaker":"Pam Harris","startTime":743.76,"endTime":746.97,"body":"of narrow it down so that the"},{"speaker":"Pam Harris","startTime":743.76,"endTime":746.97,"body":"conversation in the class is"},{"speaker":"Pam Harris","startTime":746.97,"endTime":749.52,"body":"more about whatever it is you're"},{"speaker":"Pam Harris","startTime":746.97,"endTime":749.52,"body":"trying to develop in that"},{"speaker":"Pam Harris","startTime":749.52,"endTime":753.66,"body":"particular Problem String. So"},{"speaker":"Pam Harris","startTime":749.52,"endTime":753.66,"body":"Problem String, systematically"},{"speaker":"Pam Harris","startTime":753.66,"endTime":757.26,"body":"nudged towards more efficient"},{"speaker":"Pam Harris","startTime":753.66,"endTime":757.26,"body":"and sophisticated strategies."},{"speaker":"Pam Harris","startTime":757.29,"endTime":759.12,"body":"It's not about leaving kids"},{"speaker":"Pam Harris","startTime":757.29,"endTime":759.12,"body":"wallowing in their own"},{"speaker":"Pam Harris","startTime":759.15,"endTime":762.09,"body":"caveman-like strategies. We want"},{"speaker":"Pam Harris","startTime":759.15,"endTime":762.09,"body":"kids to start there, they have"},{"speaker":"Pam Harris","startTime":762.09,"endTime":764.22,"body":"to start there, that's a"},{"speaker":"Pam Harris","startTime":762.09,"endTime":764.22,"body":"necessary starting place. But"},{"speaker":"Pam Harris","startTime":764.22,"endTime":766.89,"body":"then we help them get more"},{"speaker":"Pam Harris","startTime":764.22,"endTime":766.89,"body":"sophisticated and efficient by"},{"speaker":"Pam Harris","startTime":766.89,"endTime":767.94,"body":"using Problem Strings."},{"speaker":"Kim Montague","startTime":768.48,"endTime":771.72,"body":"What do you see as"},{"speaker":"Kim Montague","startTime":768.48,"endTime":771.72,"body":"the commonalities between those"},{"speaker":"Kim Montague","startTime":771.72,"endTime":772.71,"body":"two routines?"},{"speaker":"Pam Harris","startTime":773.1,"endTime":774.72,"body":"Absolutely. So"},{"speaker":"Pam Harris","startTime":773.1,"endTime":774.72,"body":"they're both instructional"},{"speaker":"Pam Harris","startTime":774.72,"endTime":775.71,"body":"routines. That's important."},{"speaker":"Kim Montague","startTime":775.71,"endTime":776.01,"body":"Yeah."},{"speaker":"Pam Harris","startTime":776.0,"endTime":778.61,"body":"So they will take a"},{"speaker":"Pam Harris","startTime":776.0,"endTime":778.61,"body":"little bit longer at the"},{"speaker":"Pam Harris","startTime":778.61,"endTime":782.75,"body":"beginning to get kids used to."},{"speaker":"Pam Harris","startTime":778.61,"endTime":782.75,"body":"Once, Kim and I know that, but"},{"speaker":"Pam Harris","startTime":782.75,"endTime":786.32,"body":"once kids, once it becomes"},{"speaker":"Pam Harris","startTime":782.75,"endTime":786.32,"body":"routine, then you should be able"},{"speaker":"Pam Harris","startTime":786.32,"endTime":789.47,"body":"to do them as a mini lesson. So"},{"speaker":"Pam Harris","startTime":786.32,"endTime":789.47,"body":"they're meant to be mini"},{"speaker":"Pam Harris","startTime":789.47,"endTime":791.3,"body":"lessons, not they shouldn't"},{"speaker":"Pam Harris","startTime":789.47,"endTime":791.3,"body":"necessarily take up the whole"},{"speaker":"Pam Harris","startTime":791.3,"endTime":794.48,"body":"class period. We think 10 to 20"},{"speaker":"Pam Harris","startTime":791.3,"endTime":794.48,"body":"minutes is ideal. Like I said,"},{"speaker":"Pam Harris","startTime":794.48,"endTime":798.14,"body":"it'll take you longer the first"},{"speaker":"Pam Harris","startTime":794.48,"endTime":798.14,"body":"time you do a Problem String, or"},{"speaker":"Pam Harris","startTime":798.14,"endTime":802.22,"body":"a Problem Talk. And the first"},{"speaker":"Pam Harris","startTime":798.14,"endTime":802.22,"body":"time you do one of its kind, of"},{"speaker":"Pam Harris","startTime":802.22,"endTime":804.74,"body":"its type with the material that"},{"speaker":"Pam Harris","startTime":802.22,"endTime":804.74,"body":"you're doing, it's going to take"},{"speaker":"Pam Harris","startTime":804.74,"endTime":806.96,"body":"a little bit longer. But let's"},{"speaker":"Pam Harris","startTime":804.74,"endTime":806.96,"body":"say I do a Problem String to"},{"speaker":"Pam Harris","startTime":806.96,"endTime":809.75,"body":"develop, hey, last week we"},{"speaker":"Pam Harris","startTime":806.96,"endTime":809.75,"body":"talked about the Doubling and"},{"speaker":"Pam Harris","startTime":809.75,"endTime":813.2,"body":"Halving strategy, that with a"},{"speaker":"Pam Harris","startTime":809.75,"endTime":813.2,"body":"given class, we might do a"},{"speaker":"Pam Harris","startTime":813.2,"endTime":816.53,"body":"Problem String that's focused"},{"speaker":"Pam Harris","startTime":813.2,"endTime":816.53,"body":"towards developing Doubling and"},{"speaker":"Pam Harris","startTime":816.53,"endTime":820.43,"body":"Halving multiplication strategy"},{"speaker":"Pam Harris","startTime":816.53,"endTime":820.43,"body":"and get a lot of kids sort of"},{"speaker":"Pam Harris","startTime":820.43,"endTime":822.32,"body":"thinking about it. But then we"},{"speaker":"Pam Harris","startTime":820.43,"endTime":822.32,"body":"got to come in again, up the"},{"speaker":"Pam Harris","startTime":822.32,"endTime":825.11,"body":"ante, do a string, like it get"},{"speaker":"Pam Harris","startTime":822.32,"endTime":825.11,"body":"more kids sort of thinking about"},{"speaker":"Pam Harris","startTime":825.11,"endTime":828.17,"body":"it, and kids kind of solidifying"},{"speaker":"Pam Harris","startTime":825.11,"endTime":828.17,"body":"the ideas. Do it again, get all"},{"speaker":"Pam Harris","startTime":828.17,"endTime":830.66,"body":"kids kind of like at least"},{"speaker":"Pam Harris","startTime":828.17,"endTime":830.66,"body":"playing with the ideas. And then"},{"speaker":"Pam Harris","startTime":830.66,"endTime":833.66,"body":"we kind of bring all the way"},{"speaker":"Pam Harris","startTime":830.66,"endTime":833.66,"body":"along, we sort of are bringing"},{"speaker":"Pam Harris","startTime":833.66,"endTime":836.93,"body":"words into it. But we don't"},{"speaker":"Pam Harris","startTime":833.66,"endTime":836.93,"body":"really generalize it until most"},{"speaker":"Pam Harris","startTime":836.93,"endTime":839.93,"body":"students are really kind of"},{"speaker":"Pam Harris","startTime":836.93,"endTime":839.93,"body":"playing with the relationships,"},{"speaker":"Pam Harris","startTime":839.93,"endTime":842.27,"body":"and they're getting it down."},{"speaker":"Pam Harris","startTime":839.93,"endTime":842.27,"body":"Then we put words to it to help"},{"speaker":"Pam Harris","startTime":842.27,"endTime":847.16,"body":"that continue to solidify as we"},{"speaker":"Pam Harris","startTime":842.27,"endTime":847.16,"body":"then generalize the relationship"},{"speaker":"Pam Harris","startTime":847.16,"endTime":851.12,"body":"that's happening. So as we go,"},{"speaker":"Pam Harris","startTime":847.16,"endTime":851.12,"body":"as we do the second, third or"},{"speaker":"Pam Harris","startTime":851.12,"endTime":853.82,"body":"fourth Problem String towards a"},{"speaker":"Pam Harris","startTime":851.12,"endTime":853.82,"body":"big idea, model, a strategy, a"},{"speaker":"Pam Harris","startTime":853.82,"endTime":856.85,"body":"particular one, then it becomes"},{"speaker":"Pam Harris","startTime":853.82,"endTime":856.85,"body":"more like a 10 to 20 minute kind"},{"speaker":"Pam Harris","startTime":856.85,"endTime":859.25,"body":"of thing that can happen in your"},{"speaker":"Pam Harris","startTime":856.85,"endTime":859.25,"body":"class. It's a mini lesson. What"},{"speaker":"Pam Harris","startTime":859.25,"endTime":862.76,"body":"else do they have in common?"},{"speaker":"Pam Harris","startTime":859.25,"endTime":862.76,"body":"They also in a Problem Talk or"},{"speaker":"Pam Harris","startTime":862.76,"endTime":866.9,"body":"Problem String, we believe that"},{"speaker":"Pam Harris","startTime":862.76,"endTime":866.9,"body":"the teacher chooses who shares"},{"speaker":"Pam Harris","startTime":867.17,"endTime":871.67,"body":"purposefully. Now it's not about"},{"speaker":"Pam Harris","startTime":867.17,"endTime":871.67,"body":"calling on a teacher's pet. It's"},{"speaker":"Pam Harris","startTime":871.67,"endTime":874.19,"body":"not about calling on the kid who"},{"speaker":"Pam Harris","startTime":871.67,"endTime":874.19,"body":"has it right all the time. It's"},{"speaker":"Pam Harris","startTime":874.19,"endTime":878.39,"body":"not about the kid who's fastest,"},{"speaker":"Pam Harris","startTime":874.19,"endTime":878.39,"body":"not that either. It is more"},{"speaker":"Pam Harris","startTime":878.39,"endTime":881.27,"body":"about what is the direction"},{"speaker":"Pam Harris","startTime":878.39,"endTime":881.27,"body":"we're trying to go right now. So"},{"speaker":"Pam Harris","startTime":881.27,"endTime":883.94,"body":"for example, in a Problem Talk,"},{"speaker":"Pam Harris","startTime":881.27,"endTime":883.94,"body":"I'm going to choose two chairs"},{"speaker":"Pam Harris","startTime":883.94,"endTime":886.52,"body":"purposely because I want to get"},{"speaker":"Pam Harris","startTime":883.94,"endTime":886.52,"body":"a variety of strategies. So I"},{"speaker":"Pam Harris","startTime":886.52,"endTime":889.94,"body":"don't necessarily want to choose"},{"speaker":"Pam Harris","startTime":886.52,"endTime":889.94,"body":"students who've all done the"},{"speaker":"Pam Harris","startTime":889.94,"endTime":894.11,"body":"same strategy and then put that"},{"speaker":"Pam Harris","startTime":889.94,"endTime":894.11,"body":"on the board 14 times. That's"},{"speaker":"Pam Harris","startTime":894.11,"endTime":896.36,"body":"not going to help move the"},{"speaker":"Pam Harris","startTime":894.11,"endTime":896.36,"body":"mathematics forward. And we only"},{"speaker":"Pam Harris","startTime":896.36,"endTime":898.52,"body":"have so much time, right? We"},{"speaker":"Pam Harris","startTime":896.36,"endTime":898.52,"body":"have precious time. So in order"},{"speaker":"Pam Harris","startTime":898.52,"endTime":900.95,"body":"to move the mathematics forward,"},{"speaker":"Pam Harris","startTime":898.52,"endTime":900.95,"body":"we want to get several. Now I"},{"speaker":"Pam Harris","startTime":900.95,"endTime":903.26,"body":"might have a student say, \"Yeah,"},{"speaker":"Pam Harris","startTime":900.95,"endTime":903.26,"body":"I just think different.\" And you"},{"speaker":"Pam Harris","startTime":903.26,"endTime":905.9,"body":"know we're trying to get several"},{"speaker":"Pam Harris","startTime":903.26,"endTime":905.9,"body":"different ones, and then not be"},{"speaker":"Pam Harris","startTime":905.9,"endTime":907.7,"body":"really clear about the"},{"speaker":"Pam Harris","startTime":905.9,"endTime":907.7,"body":"difference between models and"},{"speaker":"Pam Harris","startTime":907.7,"endTime":910.25,"body":"strategies. So they might give"},{"speaker":"Pam Harris","startTime":907.7,"endTime":910.25,"body":"us the same strategy on a"},{"speaker":"Pam Harris","startTime":910.25,"endTime":912.92,"body":"different model. And that's a"},{"speaker":"Pam Harris","startTime":910.25,"endTime":912.92,"body":"fine time for me to then clarify"},{"speaker":"Pam Harris","startTime":912.92,"endTime":915.17,"body":"that. \"Oh, so use the same"},{"speaker":"Pam Harris","startTime":912.92,"endTime":915.17,"body":"relationships that so and so"},{"speaker":"Pam Harris","startTime":915.17,"endTime":916.7,"body":"did. Well , we already have that"},{"speaker":"Pam Harris","startTime":915.17,"endTime":916.7,"body":"one on the board. So let's get"},{"speaker":"Pam Harris","startTime":916.7,"endTime":919.88,"body":"some more up here.\" Because I'm"},{"speaker":"Pam Harris","startTime":916.7,"endTime":919.88,"body":"going to choose the specific"},{"speaker":"Pam Harris","startTime":919.88,"endTime":924.5,"body":"model as well, so that I can"},{"speaker":"Pam Harris","startTime":919.88,"endTime":924.5,"body":"help compare. If the teacher's"},{"speaker":"Pam Harris","startTime":924.53,"endTime":927.8,"body":"thoughtful about the model they"},{"speaker":"Pam Harris","startTime":924.53,"endTime":927.8,"body":"use to model the relationships,"},{"speaker":"Pam Harris","startTime":927.8,"endTime":930.95,"body":"the strategies that kids are"},{"speaker":"Pam Harris","startTime":927.8,"endTime":930.95,"body":"using, that becomes an easier"},{"speaker":"Pam Harris","startTime":930.95,"endTime":934.55,"body":"task of comparing to the point"},{"speaker":"Pam Harris","startTime":930.95,"endTime":934.55,"body":"where even sometimes we're"},{"speaker":"Pam Harris","startTime":934.55,"endTime":938.06,"body":"purposeful, to choose to have"},{"speaker":"Pam Harris","startTime":934.55,"endTime":938.06,"body":"kids share different models with"},{"speaker":"Pam Harris","startTime":938.06,"endTime":941.48,"body":"the same strategy, because it's"},{"speaker":"Pam Harris","startTime":938.06,"endTime":941.48,"body":"about being purposeful. Now that"},{"speaker":"Pam Harris","startTime":941.48,"endTime":943.58,"body":"I have these different models"},{"speaker":"Pam Harris","startTime":941.48,"endTime":943.58,"body":"with the same strategy. Now kids"},{"speaker":"Pam Harris","startTime":943.58,"endTime":946.82,"body":"can actually really focus on the"},{"speaker":"Pam Harris","startTime":943.58,"endTime":946.82,"body":"strategy. So it's about being"},{"speaker":"Pam Harris","startTime":946.82,"endTime":949.79,"body":"purposeful. It's about what can"},{"speaker":"Pam Harris","startTime":946.82,"endTime":949.79,"body":"I do here to help move the"},{"speaker":"Pam Harris","startTime":949.79,"endTime":953.69,"body":"mathematics forward? I'm putting"},{"speaker":"Pam Harris","startTime":949.79,"endTime":953.69,"body":"big asterisk in the air caution,"},{"speaker":"Pam Harris","startTime":953.69,"endTime":958.25,"body":"caution, caution, with always an"},{"speaker":"Pam Harris","startTime":953.69,"endTime":958.25,"body":"eye towards equity. So let's say"},{"speaker":"Pam Harris","startTime":958.25,"endTime":961.1,"body":"today, we're going to focus the"},{"speaker":"Pam Harris","startTime":958.25,"endTime":961.1,"body":"conversation towards moving a"},{"speaker":"Pam Harris","startTime":961.1,"endTime":964.07,"body":"particular strategy forward. And"},{"speaker":"Pam Harris","startTime":961.1,"endTime":964.07,"body":"I'm walking around the room and"},{"speaker":"Pam Harris","startTime":964.07,"endTime":966.38,"body":"seeing what kids are doing or"},{"speaker":"Pam Harris","startTime":964.07,"endTime":966.38,"body":"I'm asking specific questions to"},{"speaker":"Pam Harris","startTime":966.38,"endTime":970.97,"body":"draw specific strategies. And I"},{"speaker":"Pam Harris","startTime":966.38,"endTime":970.97,"body":"see several students using the"},{"speaker":"Pam Harris","startTime":971.0,"endTime":974.27,"body":"thing that I want to move the"},{"speaker":"Pam Harris","startTime":971.0,"endTime":974.27,"body":"math. I know it will help move"},{"speaker":"Pam Harris","startTime":974.27,"endTime":977.21,"body":"the math forward, then I think"},{"speaker":"Pam Harris","startTime":974.27,"endTime":977.21,"body":"equity within that group of"},{"speaker":"Pam Harris","startTime":977.21,"endTime":980.15,"body":"kids. I'm thinking to myself,"},{"speaker":"Pam Harris","startTime":977.21,"endTime":980.15,"body":"\"Okay, who have I not call them"},{"speaker":"Pam Harris","startTime":980.15,"endTime":983.12,"body":"for a while? Who do I need to"},{"speaker":"Pam Harris","startTime":980.15,"endTime":983.12,"body":"position as a sense maker? Who"},{"speaker":"Pam Harris","startTime":983.27,"endTime":987.17,"body":"do I need to help position as"},{"speaker":"Pam Harris","startTime":983.27,"endTime":987.17,"body":"someone that is, that does have"},{"speaker":"Pam Harris","startTime":987.17,"endTime":990.26,"body":"good ideas in this class?\" So"},{"speaker":"Pam Harris","startTime":987.17,"endTime":990.26,"body":"I'm always thinking towards"},{"speaker":"Pam Harris","startTime":990.26,"endTime":993.62,"body":"equity. Now, I'm also at the"},{"speaker":"Pam Harris","startTime":990.26,"endTime":993.62,"body":"same time thinking bigger than"},{"speaker":"Pam Harris","startTime":993.62,"endTime":996.56,"body":"that, because I know just this"},{"speaker":"Pam Harris","startTime":993.62,"endTime":996.56,"body":"set of students have a strategy"},{"speaker":"Pam Harris","startTime":996.56,"endTime":998.69,"body":"that's going to move the math"},{"speaker":"Pam Harris","startTime":996.56,"endTime":998.69,"body":"forward. So I've got to also be"},{"speaker":"Pam Harris","startTime":998.69,"endTime":1001.63,"body":"aware of equity of who didn't"},{"speaker":"Pam Harris","startTime":998.69,"endTime":1001.63,"body":"have that strategy. And I need"},{"speaker":"Pam Harris","startTime":1001.63,"endTime":1004.18,"body":"to make sure I've pulled their"},{"speaker":"Pam Harris","startTime":1001.63,"endTime":1004.18,"body":"voice in at some other, later"},{"speaker":"Pam Harris","startTime":1004.18,"endTime":1006.49,"body":"time. Not maybe in that moment,"},{"speaker":"Pam Harris","startTime":1004.18,"endTime":1006.49,"body":"because it's not going to move"},{"speaker":"Pam Harris","startTime":1006.49,"endTime":1009.64,"body":"the math for that moment. But I"},{"speaker":"Pam Harris","startTime":1006.49,"endTime":1009.64,"body":"absolutely, am thinking about"},{"speaker":"Pam Harris","startTime":1009.64,"endTime":1013.93,"body":"equity all the time to make sure"},{"speaker":"Pam Harris","startTime":1009.64,"endTime":1013.93,"body":"that that's happening as well."},{"speaker":"Pam Harris","startTime":1014.5,"endTime":1018.19,"body":"So because of that the two"},{"speaker":"Pam Harris","startTime":1014.5,"endTime":1018.19,"body":"routines, Problem Strings and"},{"speaker":"Pam Harris","startTime":1018.19,"endTime":1021.49,"body":"Problem Talks also have in"},{"speaker":"Pam Harris","startTime":1018.19,"endTime":1021.49,"body":"common that the teacher is"},{"speaker":"Pam Harris","startTime":1021.49,"endTime":1025.36,"body":"modeling student thinking with a"},{"speaker":"Pam Harris","startTime":1021.49,"endTime":1025.36,"body":"model. At all times, we are"},{"speaker":"Pam Harris","startTime":1025.36,"endTime":1029.62,"body":"trying to make student thinking"},{"speaker":"Pam Harris","startTime":1025.36,"endTime":1029.62,"body":"visible, in order to construct"},{"speaker":"Pam Harris","startTime":1029.62,"endTime":1032.11,"body":"the relationships in a Problem"},{"speaker":"Pam Harris","startTime":1029.62,"endTime":1032.11,"body":"Strings, or compare the"},{"speaker":"Pam Harris","startTime":1032.11,"endTime":1035.71,"body":"strategies in a Problem Talk."},{"speaker":"Pam Harris","startTime":1032.11,"endTime":1035.71,"body":"It's easier, we can facilitate"},{"speaker":"Pam Harris","startTime":1035.71,"endTime":1037.78,"body":"that better when the"},{"speaker":"Pam Harris","startTime":1035.71,"endTime":1037.78,"body":"relationships are visible when"},{"speaker":"Pam Harris","startTime":1037.78,"endTime":1040.39,"body":"they're up in front of the class"},{"speaker":"Pam Harris","startTime":1037.78,"endTime":1040.39,"body":"so that we can point to them, we"},{"speaker":"Pam Harris","startTime":1040.39,"endTime":1044.47,"body":"can talk about them, we can pull"},{"speaker":"Pam Harris","startTime":1040.39,"endTime":1044.47,"body":"them apart, we can compare. So"},{"speaker":"Pam Harris","startTime":1044.47,"endTime":1048.49,"body":"we really, really like the idea"},{"speaker":"Pam Harris","startTime":1044.47,"endTime":1048.49,"body":"of having, it's necessary to"},{"speaker":"Pam Harris","startTime":1048.49,"endTime":1051.19,"body":"have visual models, whenever is"},{"speaker":"Pam Harris","startTime":1048.49,"endTime":1051.19,"body":"possible, like open number"},{"speaker":"Pam Harris","startTime":1051.19,"endTime":1055.15,"body":"lines, open arrays, ratio,"},{"speaker":"Pam Harris","startTime":1051.19,"endTime":1055.15,"body":"tables, graphs, all those kinds"},{"speaker":"Pam Harris","startTime":1055.15,"endTime":1057.91,"body":"of things will be really"},{"speaker":"Pam Harris","startTime":1055.15,"endTime":1057.91,"body":"helpful. So teachers choosing"},{"speaker":"Pam Harris","startTime":1057.91,"endTime":1061.51,"body":"models, and they're modeling"},{"speaker":"Pam Harris","startTime":1057.91,"endTime":1061.51,"body":"student making with a model, a"},{"speaker":"Pam Harris","startTime":1061.54,"endTime":1064.72,"body":"visual model when possible. And"},{"speaker":"Pam Harris","startTime":1061.54,"endTime":1064.72,"body":"then the last thing that I'll"},{"speaker":"Pam Harris","startTime":1064.72,"endTime":1067.42,"body":"mention that they have in common"},{"speaker":"Pam Harris","startTime":1064.72,"endTime":1067.42,"body":"is that all strategies are not"},{"speaker":"Pam Harris","startTime":1067.42,"endTime":1072.4,"body":"equal. So that unfortunately can"},{"speaker":"Pam Harris","startTime":1067.42,"endTime":1072.4,"body":"kind of become a side effect of"},{"speaker":"Pam Harris","startTime":1072.4,"endTime":1077.65,"body":"just doing number talks. No one"},{"speaker":"Pam Harris","startTime":1072.4,"endTime":1077.65,"body":"ever intends that. But you might"},{"speaker":"Pam Harris","startTime":1077.68,"endTime":1080.89,"body":"notice this, teachers, that if"},{"speaker":"Pam Harris","startTime":1077.68,"endTime":1080.89,"body":"you've ever tried number talks,"},{"speaker":"Pam Harris","startTime":1080.89,"endTime":1082.81,"body":"and you're like, \"I don't know,"},{"speaker":"Pam Harris","startTime":1080.89,"endTime":1082.81,"body":"I'm often getting the bang for"},{"speaker":"Pam Harris","startTime":1082.81,"endTime":1087.25,"body":"my buck.\" It might have been,"},{"speaker":"Pam Harris","startTime":1082.81,"endTime":1087.25,"body":"may not necessarily true, but it"},{"speaker":"Pam Harris","startTime":1087.25,"endTime":1090.61,"body":"might have been that because"},{"speaker":"Pam Harris","startTime":1087.25,"endTime":1090.61,"body":"you're just sort of letting all"},{"speaker":"Pam Harris","startTime":1090.61,"endTime":1093.58,"body":"strategies fly, that you didn't"},{"speaker":"Pam Harris","startTime":1090.61,"endTime":1093.58,"body":"really have a purpose towards"},{"speaker":"Pam Harris","startTime":1093.58,"endTime":1096.28,"body":"your Problem Talk or even your"},{"speaker":"Pam Harris","startTime":1093.58,"endTime":1096.28,"body":"Problem String that it kind of"},{"speaker":"Pam Harris","startTime":1096.31,"endTime":1099.37,"body":"gave the feeling tone, but like"},{"speaker":"Pam Harris","startTime":1096.31,"endTime":1099.37,"body":"all strategies are equal."},{"speaker":"Pam Harris","startTime":1099.37,"endTime":1102.64,"body":"Everything is sort of game, I"},{"speaker":"Pam Harris","startTime":1099.37,"endTime":1102.64,"body":"shouldn't say it that way"},{"speaker":"Pam Harris","startTime":1102.64,"endTime":1106.15,"body":"because everything is game, but"},{"speaker":"Pam Harris","startTime":1102.64,"endTime":1106.15,"body":"that we want the feeling, tone"},{"speaker":"Pam Harris","startTime":1106.15,"endTime":1109.6,"body":"in the class to be, \"Oh, cool."},{"speaker":"Pam Harris","startTime":1106.15,"endTime":1109.6,"body":"Nicely done. You did that. Now,"},{"speaker":"Pam Harris","startTime":1109.6,"endTime":1112.36,"body":"can we get even more efficient?"},{"speaker":"Pam Harris","startTime":1109.6,"endTime":1112.36,"body":"Can we get to be more clever?"},{"speaker":"Pam Harris","startTime":1112.36,"endTime":1115.21,"body":"Can we use those relationships"},{"speaker":"Pam Harris","startTime":1112.36,"endTime":1115.21,"body":"and even more sophisticated way?"},{"speaker":"Pam Harris","startTime":1115.72,"endTime":1117.7,"body":"It's not that you're not good"},{"speaker":"Pam Harris","startTime":1115.72,"endTime":1117.7,"body":"enough. It's that oh, we're"},{"speaker":"Pam Harris","startTime":1117.7,"endTime":1121.15,"body":"always striving for the cool,"},{"speaker":"Pam Harris","startTime":1117.7,"endTime":1121.15,"body":"clever strategy, that that's"},{"speaker":"Pam Harris","startTime":1121.15,"endTime":1123.67,"body":"kind of the atmosphere in this"},{"speaker":"Pam Harris","startTime":1121.15,"endTime":1123.67,"body":"class, ooh, I want my brain to"},{"speaker":"Pam Harris","startTime":1123.67,"endTime":1127.21,"body":"do that next time, real growth"},{"speaker":"Pam Harris","startTime":1123.67,"endTime":1127.21,"body":"mindset, kind of an idea.\" And"},{"speaker":"Pam Harris","startTime":1127.21,"endTime":1132.88,"body":"so one of the reasons that I do"},{"speaker":"Pam Harris","startTime":1127.21,"endTime":1132.88,"body":"this comparison is to sort of"},{"speaker":"Pam Harris","startTime":1132.88,"endTime":1136.27,"body":"help teachers realize these"},{"speaker":"Pam Harris","startTime":1132.88,"endTime":1136.27,"body":"different goals and that we need"},{"speaker":"Pam Harris","startTime":1136.27,"endTime":1140.23,"body":"to be cognizant of the reason"},{"speaker":"Pam Harris","startTime":1136.27,"endTime":1140.23,"body":"we're doing the routines, so"},{"speaker":"Pam Harris","startTime":1140.23,"endTime":1143.53,"body":"that we can get the bang for the"},{"speaker":"Pam Harris","startTime":1140.23,"endTime":1143.53,"body":"buck. Because I'm a little bit"},{"speaker":"Pam Harris","startTime":1143.71,"endTime":1148.03,"body":"concerned that if the only thing"},{"speaker":"Pam Harris","startTime":1143.71,"endTime":1148.03,"body":"teachers do is they hear Jo"},{"speaker":"Pam Harris","startTime":1148.03,"endTime":1151.33,"body":"Boaler, or somebody else talk"},{"speaker":"Pam Harris","startTime":1148.03,"endTime":1151.33,"body":"about number talks, and they're"},{"speaker":"Pam Harris","startTime":1151.33,"endTime":1153.58,"body":"like, \"Oh, I'm going to go do"},{"speaker":"Pam Harris","startTime":1151.33,"endTime":1153.58,"body":"it.\" And so they do it with a"},{"speaker":"Pam Harris","startTime":1153.58,"endTime":1156.55,"body":"purpose of there's more than one"},{"speaker":"Pam Harris","startTime":1153.58,"endTime":1156.55,"body":"way to solve a problem. They're"},{"speaker":"Pam Harris","startTime":1156.55,"endTime":1158.74,"body":"not going to get the bang for"},{"speaker":"Pam Harris","startTime":1156.55,"endTime":1158.74,"body":"their buck that they would if"},{"speaker":"Pam Harris","startTime":1158.74,"endTime":1162.31,"body":"they do both Problem Strings and"},{"speaker":"Pam Harris","startTime":1158.74,"endTime":1162.31,"body":"Problem Talks. Okay, I've gone"},{"speaker":"Pam Harris","startTime":1162.31,"endTime":1164.41,"body":"on for quite a while. Kim, what"},{"speaker":"Pam Harris","startTime":1162.31,"endTime":1164.41,"body":"are their questions? Yeah."},{"speaker":"Kim Montague","startTime":1164.42,"endTime":1166.91,"body":"Last one. So"},{"speaker":"Kim Montague","startTime":1164.42,"endTime":1166.91,"body":"you're talking about these two"},{"speaker":"Kim Montague","startTime":1166.91,"endTime":1170.15,"body":"routines and time is precious."},{"speaker":"Kim Montague","startTime":1166.91,"endTime":1170.15,"body":"You mentioned that. So what is"},{"speaker":"Kim Montague","startTime":1170.15,"endTime":1172.73,"body":"the interplay between the two?"},{"speaker":"Kim Montague","startTime":1170.15,"endTime":1172.73,"body":"If you had to do one or the"},{"speaker":"Kim Montague","startTime":1172.73,"endTime":1175.76,"body":"other more? Where would you"},{"speaker":"Kim Montague","startTime":1172.73,"endTime":1175.76,"body":"suggest?"},{"speaker":"Pam Harris","startTime":1176.0,"endTime":1177.62,"body":"So you're hearing me"},{"speaker":"Pam Harris","startTime":1176.0,"endTime":1177.62,"body":"clearly that I like both of"},{"speaker":"Pam Harris","startTime":1177.62,"endTime":1180.38,"body":"them, right? They're both"},{"speaker":"Pam Harris","startTime":1177.62,"endTime":1180.38,"body":"really, really good. However, I"},{"speaker":"Pam Harris","startTime":1180.38,"endTime":1184.61,"body":"think that Problem Strings give"},{"speaker":"Pam Harris","startTime":1180.38,"endTime":1184.61,"body":"us more bang for our buck as far"},{"speaker":"Pam Harris","startTime":1184.61,"endTime":1187.49,"body":"as construction, as far as"},{"speaker":"Pam Harris","startTime":1184.61,"endTime":1187.49,"body":"actually helping the"},{"speaker":"Pam Harris","startTime":1187.52,"endTime":1190.73,"body":"relationships happen. So I think"},{"speaker":"Pam Harris","startTime":1187.52,"endTime":1190.73,"body":"we need to do them more often."},{"speaker":"Pam Harris","startTime":1190.73,"endTime":1193.97,"body":"Like 80% of the time that we're"},{"speaker":"Pam Harris","startTime":1190.73,"endTime":1193.97,"body":"going to do these two routines,"},{"speaker":"Pam Harris","startTime":1194.12,"endTime":1196.52,"body":"I think we should be doing"},{"speaker":"Pam Harris","startTime":1194.12,"endTime":1196.52,"body":"Problem Strings. And then 20% of"},{"speaker":"Pam Harris","startTime":1196.52,"endTime":1199.79,"body":"the time, we can do Problem"},{"speaker":"Pam Harris","startTime":1196.52,"endTime":1199.79,"body":"Talks. So in 80% we're"},{"speaker":"Pam Harris","startTime":1199.88,"endTime":1204.59,"body":"structuring strategy, models and"},{"speaker":"Pam Harris","startTime":1199.88,"endTime":1204.59,"body":"big ideas. And then in the 20%"},{"speaker":"Pam Harris","startTime":1204.59,"endTime":1207.23,"body":"of the time we're comparing"},{"speaker":"Pam Harris","startTime":1204.59,"endTime":1207.23,"body":"those strategies towards"},{"speaker":"Pam Harris","startTime":1207.23,"endTime":1209.72,"body":"efficiency. Does that make"},{"speaker":"Pam Harris","startTime":1207.23,"endTime":1209.72,"body":"sense? Like we can't compare"},{"speaker":"Pam Harris","startTime":1209.84,"endTime":1212.24,"body":"already constructed strategies"},{"speaker":"Pam Harris","startTime":1209.84,"endTime":1212.24,"body":"if we haven't already"},{"speaker":"Pam Harris","startTime":1212.24,"endTime":1216.08,"body":"constructed them. So Problem"},{"speaker":"Pam Harris","startTime":1212.24,"endTime":1216.08,"body":"Strings construct. 80% of the"},{"speaker":"Pam Harris","startTime":1216.08,"endTime":1218.36,"body":"time we're doing these two,"},{"speaker":"Pam Harris","startTime":1216.08,"endTime":1218.36,"body":"you're doing Problem Strings."},{"speaker":"Pam Harris","startTime":1218.63,"endTime":1221.3,"body":"And then once you've got a"},{"speaker":"Pam Harris","startTime":1218.63,"endTime":1221.3,"body":"couple of constructed, then we"},{"speaker":"Pam Harris","startTime":1221.3,"endTime":1223.7,"body":"do a Problem Talk to sort of"},{"speaker":"Pam Harris","startTime":1221.3,"endTime":1223.7,"body":"compare those already"},{"speaker":"Pam Harris","startTime":1225.86,"endTime":1228.5,"body":"constructed strategies. Back to"},{"speaker":"Pam Harris","startTime":1225.86,"endTime":1228.5,"body":"Problem Strings, construct,"},{"speaker":"Pam Harris","startTime":1228.5,"endTime":1231.53,"body":"construct, construct. Then get"},{"speaker":"Pam Harris","startTime":1228.5,"endTime":1231.53,"body":"through another Problem Talk to"},{"speaker":"Pam Harris","startTime":1231.53,"endTime":1233.96,"body":"compare. Back to Problem String,"},{"speaker":"Pam Harris","startTime":1231.53,"endTime":1233.96,"body":"construct, construct construct."},{"speaker":"Pam Harris","startTime":1234.02,"endTime":1235.85,"body":"Then we throw in a Problem Talk"},{"speaker":"Pam Harris","startTime":1234.02,"endTime":1235.85,"body":"to compare."},{"speaker":"Kim Montague","startTime":1236.75,"endTime":1240.35,"body":"That was a lot to"},{"speaker":"Kim Montague","startTime":1236.75,"endTime":1240.35,"body":"digest. So if you've heard of"},{"speaker":"Kim Montague","startTime":1240.35,"endTime":1243.02,"body":"number talks, this may be a"},{"speaker":"Kim Montague","startTime":1240.35,"endTime":1243.02,"body":"little bit of a different"},{"speaker":"Kim Montague","startTime":1243.02,"endTime":1246.02,"body":"perspective. And if it resonates"},{"speaker":"Kim Montague","startTime":1243.02,"endTime":1246.02,"body":"with you, and you want to"},{"speaker":"Kim Montague","startTime":1246.02,"endTime":1249.59,"body":"remember some of the things that"},{"speaker":"Kim Montague","startTime":1246.02,"endTime":1249.59,"body":"Pam said, we have a download for"},{"speaker":"Kim Montague","startTime":1249.59,"endTime":1253.34,"body":"you. It's a one page doc that"},{"speaker":"Kim Montague","startTime":1249.59,"endTime":1253.34,"body":"outlines some of the things that"},{"speaker":"Kim Montague","startTime":1253.34,"endTime":1254.63,"body":"Pam talked about today."},{"speaker":"Pam Harris","startTime":1254.96,"endTime":1257.24,"body":"Yeah, so if you'd"},{"speaker":"Pam Harris","startTime":1254.96,"endTime":1257.24,"body":"like that download, you can go"},{"speaker":"Pam Harris","startTime":1257.24,"endTime":1261.26,"body":"to"},{"speaker":"Pam Harris","startTime":1257.24,"endTime":1261.26,"body":"mathisFigure-Out-Able.com/strings"},{"speaker":"Pam Harris","startTime":1261.32,"endTime":1266.06,"body":"V talks. Math is"},{"speaker":"Pam Harris","startTime":1261.32,"endTime":1266.06,"body":"readable.com/stringsVtalks,"},{"speaker":"Pam Harris","startTime":1266.09,"endTime":1268.91,"body":"download that handout, the handy"},{"speaker":"Pam Harris","startTime":1266.09,"endTime":1268.91,"body":"dandy handout, or you're welcome"},{"speaker":"Pam Harris","startTime":1268.91,"endTime":1270.05,"body":"to check out the show notes."},{"speaker":"Kim Montague","startTime":1271.34,"endTime":1272.96,"body":"Perfect. So"},{"speaker":"Kim Montague","startTime":1271.34,"endTime":1272.96,"body":"remember to join us on"},{"speaker":"Kim Montague","startTime":1272.99,"endTime":1275.81,"body":"MathStratChat on Facebook,"},{"speaker":"Kim Montague","startTime":1272.99,"endTime":1275.81,"body":"Twitter, or Instagram on"},{"speaker":"Kim Montague","startTime":1275.81,"endTime":1278.75,"body":"Wednesday evenings, where we"},{"speaker":"Kim Montague","startTime":1275.81,"endTime":1278.75,"body":"explore problems with the world."},{"speaker":"Pam Harris","startTime":1279.53,"endTime":1281.48,"body":"Please share the"},{"speaker":"Pam Harris","startTime":1279.53,"endTime":1281.48,"body":"podcast with your friends and"},{"speaker":"Pam Harris","startTime":1281.48,"endTime":1284.21,"body":"colleagues. Give us a rating and"},{"speaker":"Pam Harris","startTime":1281.48,"endTime":1284.21,"body":"review so that more people can"},{"speaker":"Pam Harris","startTime":1284.21,"endTime":1287.75,"body":"find the podcast so that more"},{"speaker":"Pam Harris","startTime":1284.21,"endTime":1287.75,"body":"people can learn that Math is"},{"speaker":"Pam Harris","startTime":1288.2,"endTime":1291.8,"body":"Figure-Out-Able. So if you're"},{"speaker":"Pam Harris","startTime":1288.2,"endTime":1291.8,"body":"interested to learn more math"},{"speaker":"Pam Harris","startTime":1291.83,"endTime":1294.59,"body":"and you want to help yourself"},{"speaker":"Pam Harris","startTime":1291.83,"endTime":1294.59,"body":"and your students develop as"},{"speaker":"Pam Harris","startTime":1294.59,"endTime":1297.53,"body":"mathematicians, then don't miss"},{"speaker":"Pam Harris","startTime":1294.59,"endTime":1297.53,"body":"the Math is Figure-Out-Able"},{"speaker":"Pam Harris","startTime":1297.53,"endTime":1300.47,"body":"podcast because Math is"},{"speaker":"Pam Harris","startTime":1297.53,"endTime":1300.47,"body":"Figure-Out-Able."}]}